Experimental Studies on Creation and Detection of Single Photons

Creation and Detection of Single Photons

Hatim Azzouz Thesis for the degree of Doctor of Philosophy in Physics c Hatim Azzouz, Stockholm 2016

ISBN 978-91-7649-342-7

Printed in Sweden by Universitetsservice US-AB, Stockholm, Stockholm 2016 Distributor: Department of Physics, Stockholm University Cover illustration: Red ﬂuorescence from Rhodamine 6G excited at 532 nm with the green confocal microscope. "The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom." Isaac Asimov

Abstract A growing number of technologies employ quantum properties in order to produce solutions that surpass the performance of conventional devices, or to execute operations that are fundamentally impossible with classical systems alone. In the field of optical quantum information science, photons are utilized to encode, communicate and manipulate information, making them vitally important. While photon production always constitutes the first step in any optical experiment, in the field of quantum information science, the recording of data through the process of photon detection is an equally crucial final step. This thesis deals with both the single photons generation (based on diamond color defects) and their detection, utilizing a novel type of superconducting detectors. In particular, part one of this thesis is devoted to the construction of custom-designed microscope setup, and the development of laboratory experiments, to enable the generation of single photons as well as the investigation of the optical and spin properties of diamond color centers. Confocal microscopy is used for this purpose, as it allows for the identification and addressing of individual color centers that emit only single photons. This microscope also feature an integrated self-built microwave and magnetic hardware setup, which allows for a wide range of spin environment spectroscopy studies. Single photon emission is demonstrated through both photon anti-bunching and Rabi oscillations at room temperature. The second part of the thesis offers an exploration of superconducting single photon detectors through experiment. Since electronics are an essential part of these detectors, the possibility of using a novel alternative scheme based on capacitive readout combined with fast gating to enable simplified readout is demonstrated. This scheme overcomes the limitations of conventional readout schemes, which require large bandwidth amplification and complex counting electronics. Besides photon detection, the capabilities of these detectors are also expanded to include high-energy particles in the MeV energy range, and the detectors are demonstrated to not only detect single α- and β-particles, but to do so with near unity efficiency. Finally, a multipurpose testing station for superconducting detectors is demonstrated with a central objective of optimizing the coupling efficiency of light to the active area of the detector, as well as to allow for a fast exchange of the optical fiber, thereby facilitating an efficient characterization of the detector. The optimization of this coupling efficiency was demonstrated through proof-of-principle experiments.

Contents

Sammanfattning på svenska ...... vii List of accompanying papers ...... viii

Part I: Preface 1 Introduction ...... 3 1.1 Background and motivation...... 3 1.2 Ideal single photon sources...... 4 1.3 Ideal single photon detectors...... 6 1.4 Thesis outline...... 7 1.5 My contributions...... 10 1.6 Acknowledgments...... 11

Part II: Single Photon sources 2 Intensity fluctuation statistics ...... 15 2.1 Classical description of light...... 16 2.1.1 Poissonian photon statistics...... 16 2.1.2 Classical second-order correlation function...... 17 2.2 Quantum description of light...... 18 2.2.1 Hanbury Brown-Twiss setup for photons...... 18 2.2.2 Quantized second-order correlation function...... 19 2.2.3 Photon bunching and antibunching...... 20 2.2.4 Is antibunched light the same as sub-Poissonian light?...... 22 3 Nitrogen-vacancy centers in diamond...... 23 3.1 Synthesis and generation of NV defects...... 24 3.2 Zero phonon line and phonon sideband...... 25 3.3 Physical structure...... 26 3.4 Electronic structure...... 27 3.5 Spin manipulation and readout...... 30 3.5.1 Optical spin polarization and spin-dependent florescence...... 30 3.5.2 Magnetic single spin manipulation...... 31 3.5.3 CW microwave experiments...... 32 3.5.4 Pulsed microwave experiments...... 32 4 Confocal Microscopy ...... 39 4.1 Principle of Operation...... 40 4.2 Optical components...... 42 4.2.1 Laser source as illumination...... 43 4.2.2 Lens objectives...... 43 4.2.3 Optical fibers...... 44 4.2.4 Other optical components...... 45 4.3 Optical considerations and design requirements...... 46 4.3.1 Light diffraction and resolution...... 46 4.3.2 Optical sectioning and pinhole size...... 49 4.3.3 The optical fiber as a pinhole...... 51 4.4 Detection and control electronics...... 52 4.4.1 Detection and readout software...... 52 4.4.2 Positioning systems and scanning software...... 53 4.4.3 Auto-correlator and coincidence unit...... 53 4.5 Implementation and experimental setup...... 54 4.5.1 The green confocal setup...... 54 4.5.2 The red confocal setup...... 59 4.6 Beyond confocal microscopy - STED microscopy...... 62 4.6.1 Principle of operation...... 63 4.6.2 Implementation...... 65 5 Spin manipulation and readout setup ...... 67 5.1 Microwave and magnetic hardware setup...... 67 5.2 Double-pass acousto-optic modulator setup...... 68 5.3 Integrated setup and timing control...... 71 6 Experimental results - NV center characterization ...... 73 6.1 Diamond sample preparation...... 73 6.2 Confocal scans of NV centers...... 74 6.3 Optical fluorescence spectrum...... 77 6.4 Demonstration of antibunching...... 77 6.5 Demonstration of Rabi oscillations...... 79

Part III: Superconducting Single Photon Detectors 7 Background and basic concepts...... 85 7.1 Superconductivity and working principle of SSPDs...... 85 7.1.1 Superconductivity...... 85 7.1.2 Energy gap...... 85 7.1.3 Phase transition and resistance...... 86 7.1.4 Microscopic absorption model...... 88 7.1.5 Hotspot formation...... 89 7.1.6 Phenomenological model...... 92 7.2 Quantification of the performance of an SSPD...... 93 7.2.1 Detection efficiency...... 94 7.2.2 Dead time...... 97 7.2.3 Dark counts...... 98 7.2.4 Timing jitter...... 99 8 SSPD design and measurement setup...... 101 8.1 Design and fabrication requirements...... 101 8.1.1 Particle absorption...... 102 8.1.2 Advantages of a nano-structured superconductor...... 103 8.1.3 NbTiN on silicon - an alternative to the NbN on sapphire-based SSPD. 104 8.1.4 Fabrication...... 104 8.2 Readout electronics and experimental setup...... 107 8.2.1 Measurement setup...... 107 8.2.2 Characterization...... 108 9 Capacitive readout and gating of the SSPD ...... 111 9.1 Introduction...... 111 9.2 Capacitive readout scheme...... 111 9.3 Gating behavior...... 115 9.4 Conclusion...... 119 10 High-energy particle detection ...... 121 10.1 Introduction...... 121 10.2 Sample preparation...... 122 10.3 Sample mounting and setup...... 123 10.4 Particle detection...... 125 10.5 Conclusion...... 129 11 A multi-purpose testing station ...... 131 11.1 Introduction...... 131 11.2 Dipstick construction...... 132 11.2.1 Design considerations and fabrication...... 132 134subsection.11.2.2 11.3 Scanning system...... 139 11.4 Estimation of the coupling efficiency...... 143 11.5 Conclusion...... 146

Part IV: Conclusion and Outlook 12 Conclusion and outlook ...... 151 12.1 Single photon source...... 151 12.2 Superconducting single photon detector...... 156

Part V: Appendix Appendix A Diamonds - utilisation and treatments ...... 165 A.1 Utilised diamond samples...... 165 A.2 Preparation and production of the nano-diamond powder (NDP) for the Nano- Sizer measurements...... 166 Appendix B High-temperature vacuum oven for the annealing of the diamonds ...... 167 vi

Appendix C Single photon spectrometer ...... 169 C.1 Grating parameters and design considerations...... 169 C.2 Spectrometer setup...... 174 Appendix D GL Theory ...... 179 Appendix E Single photon down conversion source ...... 181 E.1 Optical and setup components...... 181 E.2 Setup of the SPDC...... 184 Appendix F Setup and mounting for high-energy particle sources . . . . 187 Appendix G Additional information and photographs illustrating the coupling system ...... 191 G.1 Operation manual for the SSPD dipstick system...... 191 G.2 Calculated coupling value for a square-shaped active area...... 194 G.3 Additional photographs of the coupling system...... 195 Part VI: Bibliography Appendix Bibliography ...... 199 vii

Sammanfattning på svenska En växande mängd kvantteknologi använder kvantmekaniska egenskaper för att utforma och utveckla anordningar som antingen överträffar prestandan hos konventionella enheter eller utför operationer som är omöjliga med befintliga klassiska system. Specifikt när det gäller optisk kvantinformation utnyttjas fotoner för kodning, kommunikation och manipulation av information. Medan fotonproduktion utgör det första steget i ett experiment inom kvantinformation vetenskap, är registrering av information genom fotondetekteringsprocessen det sista, men lika avgörande, steg. Denna avhandling behandlar både generering av enstaka fotoner baserat på färgcentra i diamant, samt detektion som använder en ny typ av supraledande detektorer. I synnerhet är en del av denna avhandling ägnat åt konstruktionen av uppställningar och utveckling av laboratorieexperiment för att möjliggö- ra generering av enstaka fotoner samt möjliggör undersökning av färgcentra i diamant, både när det gäller deras optiska och spin egenskaper. Konfokal mikroskopiteknik används som ett medel för att identifiera och välja ett enda färgcentrum som endast emitterar en enda foton åt gången. Mikroskopet har även integrerad hårdvara för manipulation med hjälp av såvel mikrovågor som magnetfält, vilket gör det möjligt för ett brett spektrum av spin miljö spekt- roskopistudier. Fotonkällan realiserades genom demonstration av både foton antibunching och Rabi svängningar vid rumstemperatur. Den andra delen av avhandlingen syftar till att utforska och karakterisera supraledande fotondetektor genom ett par experiment. Eftersom elektroniken är lika viktigt som själva detektorn, undersökte vi möjligheten att använda en alternativ avläsningsprocedur baserad på ett nyt kapacitivt avläsningssystem i kombination med snabb gating som möjliggör en förenklad användning av detektorn, vilket gör det möjligt att övervinna begränsningarna från konventionella avläsningssystem som kräver en förstärkare med stor brandbredd och komplexa räknings elektronik. Förutom fotondetektering, utökade vi vårt koncept för upptäckt att även omfatta högenergipartiklar i MeV energiområdet, och visade inte bara detek- torns förmåga att effektivt upptäcka enstaka α- och β-partiklar utan också demonstrerat effektiviteten nära ett. Slutligen, har vi konstruerat och tillverkat en mångsidig teststation för detektorn med det huvudsakliga syftet att optimera kopplingseffektiviteten mel- lan den optiska fibern och den aktiva ytan hos detektorn, samt möjliggöra ett snabbt och lättillgängligt utbyte av den optiska fibern, varigenom en effektiv karakterisering av detektorn underlättas. Optimering av kopplingseffektiviteten visades genom proof-of-principle experiment. viii

List of accompanying papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Capacitive readout and gating of superconducting single photon detectors Hatim Azzouz, Reinier W. Heers, Sander N. Dorenbos, Raymond N. Schouten, Valery Zwiller, Review of Scientiﬁc Instruments 84 053108 (2013).

II Efﬁcient single particle detection with a superconducting nanowire Hatim Azzouz, Sander N. Dorenbos, Daniel De Vries, EstebanBermúdez Ureña, Valery Zwiller, AIP Advances 2, 032124 (2012).

III A highly versatile optical ﬁbre vacuum feed-through Ian A. Davidson, Hatim Azzouz, Klaus Hueck, Mohamed Bourennane, Submitted.

Reprints were made with permission from the publishers. Part I: Preface

1. Introduction

1.1 Background and motivation The notion of the photon as a bullet of quantized energy hν is considered the central image of the quantum revolution. This definition stems from the quantization of the electromagnetic field, which necessitates the presence of an elementary excitation of a single mode of discrete energy, hence a photon [1]. This modern photon concept was initially proposed by Einstein in 1905 [2] and brought to fruition by Dirac in 1927 [3]. However, the term ’photon’ was only coined in 1926 by Gilbert N. Lewis [4]. The adoption of the photon concept has led to radical advances in physics and allowed to illustrate the quantum ’paradoxical’ nature of light through pioneering experiments, e.g., the demonstration of photon antibunching [5], Bell’s inequality and entanglement [6–8]. Recently, photons have been considered fundamental objects for the realization of a growing amount of novel quantum technologies [9]. These technologies employ quantum properties in order to design and develop devices that either surpass the performance of conventional devices or execute operations fundamentally impossible with existing classical systems. Especially in the field of optical quantum information (QI) science, photons are utilized for encoding, communication and information manipulation. Since they travel at the speed of light and show only a weak interaction with the surroundings over long distances, which results in low noise and loss levels, and because they can be manipulated using linear optics, photons are considered the most promising candidates for a realization of qubits for novel communication and quantum cryptography schemes. A qubit is a quantum bit (analogous to the classical bit), consisting of a two-state quantum system where information is encoded into the states of photons (or other particles), with the photon polarization typically used as the degree of freedom that allows for photon encoding. While encoding in quantum communication applications makes use of single photons, the quantum key distribution (QKD), also referred to as quantum cryptography, strictly requires single photons. QKD is the most mature and commercially advanced application and offers the most secure form of communication which has yet been proposed [10, 11]. It utilizes single photons to allow two distant parties to establish a secret key, thereby forming a secure encryption channel. QKD does not prevent hacking attempts but detects 4 Introduction and alerts if the key security has been compromised because it is fundamentally impossible to clone the quantum state of a photon through eavesdrop- ping. Thus, if a pulse contains more than one photon, an eavesdropper will be able to store the extra photons and transmit the remaining single one, thereby compromising the security of the channel. While photon production constitutes the first step of any experiment in the field of QI science, the recording of data through the process of photon detection is the last but equally crucial step. Thus, research on single photon sources and single photon detectors has been stimulated and driven by these demands and prerequisites, in conjunction with the surging interest in the field of QI. Single photon source and -detectors are not only confined to an application in quantum technologies but are also considered for a variety of non-quantum applications ranging from metrology in remote sensing applications to medi- cal applications, e.g., imaging and clinical tomography, just to name a few. A detailed overview of a wide range of potential applications of single photon sources and -detectors is provided in [12, 13].

1.2 Ideal single photon sources A light source which ideally emits one and only one single photon at periodic intervals is referred to as a true single photon source (SPS) if it fulfills the following criteria: • The source is a solitary quantum emitter that allows to secure and realize an efficient one-photon number state. • The source emission is deterministic, i.e., it is triggered by a periodic excitation defined by the user at any arbitrary time, thereby guaranteeing a production of single photons on-demand. • The production of a single photon occurs with a certainty of 100 %. Con- sequently, the probability for multiphoton emission is 0%. • The source is highly polarized in both absorption and emission. • The ideal source exhibits a narrow photoluminiscnece line width and a well-defined spatial optical mode. • The emitted photons are indistinguishable. • The source exhibits a photostable emission behavior, with no bleaching or blinking. • The lifetime of the source is short (ps > τ > ns).

In reality, photon sources are often imperfect and deviate from the ideal case. But, depending on the intended application, certain key parameters can be identified and improved. In recent years, several approaches have been 1.2 Ideal single photon sources 5 adopted for single photon generation. An overview of all available SPSs is given in [12–14]. However, as a brief summary, we can distinguish single atoms and ions, single molecules, quantum dots (QDs), heralded photons and color centers, all of which share the deterministic property (to a certain extent) and can be said to be on-demand SPS systems. However, it should be mentioned that, although the distinction between deterministic and probabilistic photon creation processes is clear in theory, for some SPSs this difference may be obscure in practice. For example, the photon generation in the frequently used heralded source, which is based on the production of a pair of photons via spontaneous parametric downconversion (SPDC) in a nonlinear medium, is a strictly probabilistic process. However, it can still be utilized in a deterministic manner because one photon can be used to herald the creation of the other. While both atoms and trapped ions can be used for single photon generation and exhibit excellent optical properties, they are, however, difficult to isolate due to their complicated trapping schemes and the high vacuum requirements, making their integration into applicable physical systems a challenging task. The main disadvantages of single molecules are the relatively poor antibunching behavior and the lower photostability, with photobleaching limiting the duration of the operational illumination [15], although recent studies have demonstrated an improved controllability of the single photon emission field [16]. QDs are more favorable candidates and usually show excellent optical properties, even though drawbacks such as the cryogenic operating temperatures (4-30 K), as well as the low coherence times combined with the difficulty of producing indistinguishable photons limit their application potential. Color center defects in diamond are another excellent and promising candidate in the field of single photon generation [14]. With diamond as a platform, the photon generation scheme adheres to the technological preferences of a solid-state SPS system which can be operated at room temperature and therefore allows for an easy integration into existing networks. In addition, with the current development of crystal fabrication techniques that enable the design and growth of high-purity diamond crystals with suitably inserted impurities, color centers are becoming more and more attractive for an application in solid-state electronics. Diamond color defects can be operated at room temperature with coherence times of up to 2 ms and exhibit a unique photostable emission. The most widely studied color center is the nitrogen-vacancy (NV) center [14,17], which has been envisioned as a unique object viable not only as a robust SPS but also as a reliable spin qubit [18, 19]. Recently, it has also been more frequently applied in technologies beyond the field of QI processing, e.g., as flourescent biomarker and for nanoscale sensing applications [20]. Other color centers, such as silicon- (SiV) [21] and nickel- (NE8) 6 Introduction vacancy defects [22–24], are also attracting an increasing amount of interest in the field of QI science. In the first part of this thesis I will report on the investigation of color centers in diamond. Although silicon- and nickel-vacancies are currently also receiv- ing much attention, I will only consider and demonstrate antibunching for NV centers. This will be discussed in more detail in one of the following sections.

1.3 Ideal single photon detectors Next, we consider ideal single-photon detectors for which the following requirements apply: • The probability of detecting an incident photon within a detection gate is 100 % over a broad spectral range, i.e., the detection efficiency (DE) is close to unity. • The number of dark counts, which describes the probability of detecting false events in the absence of an incident photon, should be zero. • The dead time, defined as the time interval during which the detector is unable to detect an incident photon, is zero. • The jitter time, which is the the time interval between the absorption of a photon and the generation of the corresponding electrical signal, is zero. • The possibility to determine the number of incoming photons, usually referred to as photon-number resolution. Similar to the photon sources, the performance of current detection technologies deviates from the ideal case, and only a subset of the properties listed above may be realized in a particular detector. Typically, single-photon avalanche photodiodes (SPAD)1 and photomultiplier tubes (PMT) are most commonly used for single photon detection. How- ever, the materials utilized in these detectors are often materials with a relatively large bandgap, such as silicon2, making the detection inefficient at a wavelength of 1550 nm, which is the preferred wavelength for fiber optics- based telecommunication. A superconducting single photon detector (SSPD)3 is a promising and highly attractive detector candidate, which offers a better performance over a wide range of parameters when compared with existing detectors. With its very low dark count and small jitter timing, the SSPD is the popular choice for QKD applications, and it is expected to have an increasing influence on

1Also known as APD. 2With a bandgap of 1.1 eV, silicon exhibits a rather large bandgap compared to the bandgap of a typical superconductor, which is in the meV-range. 3Also known as superconducting nanowire single photon detector (SNSPD). In this thesis it is referred to as SSPD. 1.4 Thesis outline 7 the field of QI for optimized DE values. By integrating an SSPD into a low-Q optical cavity with reflecting mirrors, and depending on the combination of the selected substrate thickness and filling factor, the DE can be increased to 60-80 % [25], compared with the 36 % reported as the highest achieved DE at a wavelength of 1550 nm for conventional meander SSPDs [26]. Conventionally, SSPD have used NbN nanowires. But, in 2013, it has been shown that the DE can be improved to > 90% when using amorphous tungsten silicide (W-Si) nanowires instead [27]. A disadvantage of the SSPD, however, is that it needs to be operated at cryogenic temperatures. The second part of this thesis focuses on SSPDs and reports on an early conventional SSPD prototype with a comparatively low detection efficiency. A comparison of the performance of selected typical detectors is given in Table 1.1.

Detector type Operation Detection Dark Timing Max count Refs. temperature [K] efﬁciency [%] count [Hz] jitter [ps] rate [MHz] PMT (IR) 200 2 200 × 103 300 10 [28] SPAD (InGaAs) 240 10 16 × 103 55 100 [29] SPAD (Si) 250 75 @ 650 nm 25 400 100 [30] SSPD (conventional NbN) 3-4.2 1-36 < 10 60 100 [26] SSPD1 (NbN in cavity) 1.8 57 < 100 30 1000 [31] SSPD2 (NbN in cavity) 2.1 80 1000 - > 10 [25] SSPD (W-Si) 2 90 10 150 0.025 [27]

Table 1.1: Comparison of selected typical single photon detectors based on [12, 32]. The detection efﬁciency is given for photons with a wavelength of 1550 nm for all detectors except for the Si SPAD, which is used to detect photons with a wavelength of 650 nm. The SPPD1 features an integrated hydrogen silsesquioxane (HSQ) mirror structure cavity and an anti-reﬂection coating, whereas the NbN for SSPD2 was sandwiched between SiO and SiO2 as upper and lower cavity layers, respectively. The detector described in this thesis is the one listed as the conventional SSPD.

1.4 Thesis outline This thesis is partly based on publications in scientiﬁc journals and partly on unpublished work. My contributions are described in more detail in the following section. The thesis is divided into two main parts: PartII Single Photon Sources and Part III Superconducting Single Photon detectors. The ﬁrst part focuses on SPSs, with all research performed at the Quantum Infor- mation and Quantum Optics (KIKO) lab at Stockholm University (SU). Most research associated with the second part was conducted as part of a collaborative research project with Prof. Valery Zwiller from the Quantum Transport (QT) group at the Delft University of Technology (TU Delft). 8 Introduction

More precisely, PartII is concerned with the construction of a custom- designed setup for the generation of single photons, as well as the manipulation of spin properties focused around NV centers. As an introduction, the first chapter discusses intensity fluctuation statistics, focusing on the second-order correlation function as a necessary tool for characterizing a single photon source. Subsequently, a description of the used sample, especially the physical and electronic properties of NV centers, is presented in Chapter3. The chapter concludes with a description of the spin manipulation and spectroscopy techniques for reading out and studying the spin properties of NV centers. Chapter 4 introduces the confocal microscopy technique as a means to identify and il- luminate NV centers, commonly referred to as an SPS setup. The chapter first compares conventional and confocal microscopy, followed by a description of the basic microscopy terminology and confocal design considerations. Next, a description and performance characterization of two custom confocal setups is given, each using a different excitation wavelength: the first is using a green laser to excite the NV centers, and the second a red laser source to excite the intended nickel and silicon vacancy centers. An alternative approach based on the concept of confocal microscopy, known as stimulated emission depletion (STED) microscopy, is described and implemented at the end of the chapter. In Chapter5, the spin manipulation and readout setup is described. This includes a custom-designed microwave and magnetic resonance hardware setup, utilized for the manipulation of NV spin properties and the demonstration of Rabi oscillation. PartII concludes with a presentation and discussion of the results of the investigation of the NV centers (Chapter6), where both antibunching and Rabi oscillation are demonstrated. Chapters4,5 and6 are central parts of PartII. All results of the photon detection experiments presented in this part were achieved using SPADs. The second part of this thesis (Part III), describes my research performed as part of the QT group at TU Delft. The basic concepts of superconductic- ity are introduced in Chapter7, where the underlying principle behind the detection process and the quantifying performance characteristics of SSPDs are described. The SSPD design and fabrication requirements are described in Chapter8, followed by the utilized experimental readout setup. The electronics are as essential for the detection as the detector itself, and different readout schemes have been investigated to ensure an optimal readout. The work presented in Chapter9( Paper I) covers our first collaboration project that investigated the possibility of using an alternative readout scheme. In contrast to conventional readout schemes, which require the use of large bandwidth amplification and complex pulse counting electronics, the capacitive readout of the alternative integrating scheme greatly simplifies the readout of these detectors and allows for an easy multiplexing. The only drawback of this approach, i.e., a loss of time information, can be compensated for through fast gating of 1.4 Thesis outline 9 the detector. At the end of the chapter, we also show that this is possible at the single-photon level by detecting heralded photons. Besides photon detection, it is also interesting to see if SSPDs can be used as high energy particle detectors with the aim of improving detection devices in the fields of high energy and nuclear particle detection physics in the same way they are currently affecting optics and communication research. Chapter 10( Paper II) presents the results of our second collaborative work, where we investigated an extension of the detection concept to include high energy particles in the MeV range, and examined the SSPD detection ability and efficiency, particularly for α-, β-, and γ-particles. Because of the hazardous nature of the experiment, and for safety reasons, university authorities at Kavli Institute of Nanoscience would only allow the experiment to be carried out at the Reactor Institute Delft (RIH)4, under strict and constant supervision of an on-site expert by whom the handling and setting of the emitting samples was arranged. Therefore, the entire SSPD setup was dismantled, and then moved to and re-built at the reactor. The delicate and time-consuming sample preparation and sample positioning processes were performed under the supervision of senior radiochemist Daniel De Vries. The results of my work at QT initiated the design and development of a novel and reliable multipurpose SSPD testing setup for our KIKO lab at Stock- holm, with the main objective of ensuring a good coupling between fiber and detector by using a 3-axis nanopositioning system. Furthermore, for a detection at different wavelengths, the setup is designed to allow for an easy and swift replacement of the optical fiber. This is ensured by using a specially designed optical fiber vacuum feedthrough based on a modified standard optical fiber bulkhead connector with a low weak rate and a low optical loss, making it suitable for high-vacuum applications (Paper III). The design and construction of the SSPD test station was informed by the previous work on confocal microscopy to merge both the SPS and SSPD into one setup. The design and construction of the multipurpose setup, as well as the characterization measurements, are described in Chapter 11. Although slightly modified, Chapters 9 and 10 are essentially taken from Paper I and II, respectively, whereas only the part describing the vacuum feedthrough in Chapter 11 is taken from Paper III. The thesis is ended with a conclusion and outlook (Chapter 12).

4Also referred to as the department of Radiation and Isotopes for Health (RIH), which operates the only nuclear reactor in the Netherlands, the Hoger Onderwijs Reactor (HOR). 10 Introduction

1.5 My contributions Contribution to the laboratory setup All the experimental work described in this thesis was either undertaken directly by me, or by project students under my direct supervision. At the start of my PhD project, my lab was entirely empty, thus I was involved in all stages of the build-up of a modern nano-photonics lab, and was responsible for the design, purchase, and construction of all experimental setups. Among the systems I designed and constructed were: Two confocal microscopes, the microwave setup, the SSPD testing station, a vacuum oven system suitable for annealing the NV center samples, a highly sensitive single photon spectrometer, and a compact single photon down conversion source (more details can be found in AppendixB,C andE). The most signiﬁcant part of this work was the design and construction of the two confocal microscopes, including the microwave setup, which is described in detail later in this thesis.

Contribution to papers Paper I Capacitive readout and gating of superconducting single photon detectors Both Reinier W. Heers and I equally contributed to the design of the experiments. This holds true for the laboratory work as well. However, I analyzed the data and wrote the paper. Sander N. Dorenbos designed and fabricated the superconducting detector. Raymond N. Schouten helped with the design and construction of the readout electronics. Prof. Valery Zwiller supervised the experiments. All co-authors participated in the discussion of the results and commented on the manuscript at all stages. Paper II Efﬁcient single particle detection with a superconducting nanowire In this work, I made major contributions ranging from coordinating and arranging the logistics with the nuclear reactor authorities at Delft, designing and performing all the described experiments, to analyzing the data and writing the paper. Sander N. Dorenbos and Esteban B. Ureña designed and fabricated the superconducting detector. Dr. Daniel De Vries was assigned as chemist to supervise the preparation of the radioactive samples. He also provided input for writing the paragraph Sample Preparation and Methods. Prof. Valery Zwiller supervised the experiments. All co-authors participated in the discussion of the results and commented on the manuscript at all stages. Paper III A highly versatile optical ﬁbre vacuum feed-through The experiment was designed by Dr. Ian Davidson and me based on preliminary work undertaken by Klaus Hueck under my supervision. The experimental setups were jointly constructed by Ian Davidson and me, with the measurements principally being performed by Ian Davidson. Ian Davidson and I jointly analyzed the data and contributed equally to the writing of the 1.6 Acknowledgments 11 paper. Prof. Mohamed Bourennane supervised the experiment. All co-authors participated in the discussion of the results and commented on the manuscript at all stages.

1.6 Acknowledgments During the making of this thesis I have been fortunate to get to know and collaborate with many people to whom I owe my deepest gratitude for making this thesis possible. First of all I would like to thank my supervisor, Mohamed Bourennane, for giving me the opportunity to work in the intriguing field of Quantum Informa- tion and Quantum Optics, and offering me a brand new laboratory to admin- ister and run as I pleased. I would also like to express my deepest gratitude to Valery Zwiller for giving me the opportunity to work on superconducting detectors in his group, and for providing many ideas and much guidance during my detector work. Special thanks go to Hans Blom who enthusiastically discussed and answered all my questions concerning confocal microscopy and single photon sources. I owe my gratitude to Ian Davidson for the vast amount of discussion and feedback on superconducting single photon detector theory and application, and for his thorough proofreading of this thesis. Sander N. Dorenbos and Reinier W. Heers, it was nice working with you and thanks for the successful collaboration. Reinier’s enthusiasm and Sander’s serenity was a source of great comfort during the long and at times arduous measurements. I would like to acknowledge the other team members of the KIKO group, who created an inspiring and joyful atmosphere. Especially Jan Bogdanski, Magnus Rådmark, Elias Amselem, Johan Ahrens, Nima Rafiei, Kate Blanchfield, Ally Hameedi, Muhammad Sadiq, Ashraf Abdelrazig Mo- hamedelhassan, Christian Kothe, Hannes Hübbel, and Isabelle Herbauts. I had the pleasure to supervise a number of students. First there was Per Nilsson, thanks for your programming contributions and for constructing the control software. Lars Johann Wacker, thanks for assisting me with building the prototype microwave setup - it proved very useful! A great thank should also be given to Klaus Hueck for his great efforts constructing the multi- purpose station for the detector. Although I didn’t have the pleasure to meet Christoph Dittel in person, his spin work based on our prototype microwave setup were impressive, and provided the Rabi oscillation results for this thesis. There are numerous people in both Sweden and the Netherlands, who have helped and supported me enormously during my work. Unfortunately, they are too many to name, but I am deeply thankful to all of them, and owe them all my greatest appreciation. 12 Introduction

Finally, I would like to express my deepest gratitude to my family for their endless moral support, patience, and understanding. Part II: Single Photon sources

2. Intensity ﬂuctuation statistics

Since the objective of this work is to both produce and observe non-classical phenomena of light, the focus of this chapter is mainly to highlight the theoretical differences between classical and quantum light sources, as well as to develop an experimental method for analyzing the nature of light sources, particularly to identify a single photon [33–36]. However, before considering the basic concepts and terminologies of quantum optics, it is instructive to start with a brief historical overview of the research that led to the development of quantum optics. The radical change in the concept of light can be traced back to the work of Max Planck, who hypothesized that radiation from a black-body is emitted in discrete energy packets which he called quanta [37, 38]. Based on this, Einstein went on to propose the concept of the quantization of light as an explanation for the newly discovered photoelectric effect [2]. Shortly afterwards, in 1909, Einstein inspired yet another revolutionary conception of the nature of light, i.e., the wave-particle duality [39]. Partic- ularly, by applying Planck’s radiation formula, Einstein proposed a solution to the problem of the energy fluctuations observed when measuring the black body radiation, and noted that the radiation energy gave an extra term proportional to the average number of quanta. This was clearly incompatible with the classical wave theory of light but anticipated a new theory of photon statistics. More specifically, a deeper understanding of the full statistical properties of the various types of light became the main approach in the development of quantum mechanics as an attempt to elucidate the seemingly contradicting duality. However, it was the work of Hanbury Brown and Twiss, published in 1956 [40], who studied correlation effects in the intensity received by two separate detectors, and the invention of the laser in 1960 [41], that widened the horizon of the field, and inspired sophisticated photon statistics experiments and observations of non-classical optical phenomena. For a long time, only thermal sources had been available. But, with the new light source, a statistical distinction between thermal and laser light was experimentally demonstrated. In contrast to Planck’s formula, laser light with its coherent radiation was shown to exhibit a statistical distribution corresponding to that of a Poisso- nian distribution for the number of photons. From a classical perspective, the same statistical treatment of photons also predicted a theoretical non-classical type of light with a more narrow photon distribution, i.e., sub-Poissonian light. 16 Intensity fluctuation statistics

Although Einstein correctly hypothesized the particle nature of light in 1905, the existence of the photon was not proven until 1977 by Kimble et al., who observed the effect of photon antibunching using light emitted by sodium atoms [5]. The sub-Poissonian behaviour was then verified in 1983 by Short et al. [42]. The antibunching and sub-Poissonian phenomena are closely related and are both considered a clear proof of the quantum nature of light, as discussed later. In the following, the classifications of the light beam according to photon statistics is briefly discussed. Subsequently, the analysis technique of photon statistics based on intensity fluctuation correlations and its restrictions on classical light is described. Finally, the Hanbury Brown-Twiss interferometer is presented as an experimental device enabling the analysis of light sources and re-examined considering the quantum nature of light.

2.1 Classical description of light 2.1.1 Poissonian photon statistics When considering the quantum nature of light, a common approach is to examine photon statistics where the light beam is regarded as a stream of photons rather than a classical wave. From the classical point of view, perfectly coherent light beams with constant intensity are the most stable form of light, thereby setting the limit for the nature of classical light. Since the photon distribution in a coherent state is Poissonian, this allows a threefold classifi- cation of light according to the variance of their photon number distributions known as: Poissonian, super-Poissonian and sub-Poissonian. For a Poissonian photon distribution, the variance (∆n)2 of the photon number distribution is related to the mean value n¯ through (∆n)2 = n¯, which is the narrowest distribution classical light can exhibit, whereas it is broader for a super-Poissonian distribution: (∆n)2 > n¯. While a constant and coherent light intensity is Pois- sonian, it is easy to imagine that a time-varying fluctuation in intensity would lead to a larger fluctuation in photon number, hence a super-Poissonian photon number distribution. Examples of super-Poissonian statistics are thermal and chaotic light. Experimental observations of Poissonian and super-Poissonian statistics are consistent with the classical theory of light. However, this is not true for sub-Poissonian light. Compared to Poissonian photon statistics, sub-Poissonian light features an even narrower photon number distribution (∆n)2 < n¯), suggesting a state ’more stable or quieter’ than coherent light. Sub-Poissonian light has no classical counterpart and is therefore considered a clear signature of the quantum nature of light. However, observation of sub- Poissonian light is a rather non-trivial quantum task because its sensitivity to optical losses requires fast single-photon detectors with rather high quantum efficiencies. 2.1 Classical description of light 17

2.1.2 Classical second-order correlation function An alternative approach is to analyze the statistics of photons by quantifying the intensity fluctuations using a technique known as second-order correlation function. This was conceptually introduced by the British radio astronomers Robert Hanbury Brown and Richard Twiss in their pioneering work in 1956 [40], where they adapted an intensity interferometer and applied its intensity correlation effects to the measurement of the angular diameter of stars. The restrictions for the second-order correlation function predicted by the classical and quantum descriptions are radically dissimilar. It is this discrepancy that is used to differentiate between classical and non-classical fields. Before examining in more detail the quantum description of the HBT experiment and the non-classical implications on the second-order correlation function, let us briefly introduce the intensity correlation measurements and the conditions they imply for classical light. Particularly, we consider the detection of the intensity of two light beams that have not been optically mixed. However, we impose a time delay on one of the intensities prior to detection. The output of both detectors is connected to a correlator that counts and stores the measured intensity as a function of time and multiplies the intensities of both photodetectors for different detection time differences. Assuming the same (point) source for the two beam intensities, i.e., one spatial mode, the output of the correlator will be proportional to the normalized temporal second-order correlation function for a classical single-mode, defined by hI(t)I(t + τ)i g(2)(τ) = , (2.1) hI(t)ihI(t + τ)i where I(t) = E(t)∗E(t) is the detected intensity at time t. The brackets h...i indicate the ensemble average calculated by integrating over a long time interval. In other words, g(2)(τ) describes how the joint intensity probability of measuring an intensity I at time t + τ depends on the value of the intensity at time t. Whereas the term first-order coherence function indicates that g(1)(τ) describes amplitude correlations based on the properties of the first power of the electric field, the second-order symbol in g(2)(τ) refers to correlations characterized by the intensity properties instead, which is to the second power of the electric field. For classical fields, the properties of g(2)(τ) are given by

g(2)(0) ≥ 1, (2.2) g(2)(0) ≥ g(2)(τ). (2.3)

The proofs for these classical inequalities can be found in literature [43– 45]. However it is worth addressing their heuristic derivation and how they can be intuitively understood. Since the variance of the intensity is given by ∆I2 = hI2i − hIi2, the second-order correlation can be expressed as g(2)(0) = 18 Intensity ﬂuctuation statistics

(∆I2/hIi2) + 1 at τ = 0. Remembering that the variance obeys ∆I2 ≥ 0, we find that the value of the normalized second order coherence function is larger than or equal to 1 at zero time delays, as stated by Eq. (2.2). By applying the Cauchy-Schwartz inequality, one can relate the degree of coherence of the second-order correlation function g(2) at later times to the zero time delays. Since hI(t)i2 = hI(t + τ)i2 for stationary processes, we then get hI(t)I(t + τ)i2 ≥ hI(t)2i2, leading to Eq. (2.3). For a perfectly coherent stable source (i.e., ∆I = 0), it is easy to show that (2) g (τ) = 1 for all time delay values τ because the intensity I0 is constant. Since this is valid for all time delays including the special case of zero-time delay, we also get g(2)(0) = 1. Next, we consider any source with a fluctuating intensity1 with a time-scale determined by the coherence time of the source, i.e., light which is coherent only in time intervals shorter than τc. In this case, it can be shown that the correlation function factorizes and g(2)(τ) → 1 for τ τc [46], since the intensity fluctuations will be uncorrelated at times t and t + τ. However, if τ τc, correlations between fluctuations will occur at the two times. Particularly for τ = 0, the inequality in Eq. (2.2) applies and g(2)(0) > 1. To summarize, for any time-varying intensity, the correlation function decreases for increasing values of τ, reaching the value of unity for τ → ∞, whereas, for a non-varying intensity, it is a constant value, g(2)(τ) = 1 for all values of τ. While Eq. (2.2) gives the upper limit for a zero time-delay of the second-order coherence function for classical fields, Eq. (2.3) consequently yields the restriction that the degree of second-order coherence can never exceed its value at zero time delay. In the following, we will see that the inequality equations (2.2) and (2.3) are violated by quantum light and are used to experimentally demonstrate the quantum nature of light.

2.2 Quantum description of light 2.2.1 Hanbury Brown-Twiss setup for photons The setup of Hanbury Brown and Twiss (HBT) interferometer is similar to classical interferometry systems such as the Michelson stellar interferometer. However, while the later correlates phase ﬂuctuations of two waves, the HBT setup measures the spatial correlation between ﬂuctuations in intensity. Since the spatial coherence is determined by the spread of the angles within which the light arrives at the interferometer, measuring a small angle requires a large distance between detectors. However, as the distance between the detectors

1Examples of classical fluctuating fields are thermal or chaotic light. It is possible to show that for all chaotic light g(2)(τ) = 1+kg(1)(τ)k, where g(1)(τ) is the first order temporal correlation function. 2.2 Quantum description of light 19 increases, it becomes more difficult to sustain the collection mirrors in stable positions adequately to achieve interference patterns on the two correlated detectors. Thus, HBT proposed an intensity interferometer based on separate detectors, i.e., it does not even require a physical connection between the detectors − the correlations may be extracted later. More specifically, the original HBT setup allowed a lateral adjustment of one of the detectors in order to be able to investigate intensity correlations between various spatial modes at zero-time delay. However, in our case, it is more interesting to slightly modify the original HBT setup so that it allows to measure the temporal correlation instead of the spatial coherence. A schematic illustration of the HBT setup is shown in Figure 2.1. The HBT setup consists of a 50:50 beam splitter (BS) that equally distributes the incident beam intensity (stream of photons) between the transmission and reflection outputs of the BS, onto the detectors D1 and D2. The detectors are connected to an electronic unit that stores the measured counts from both detectors while simultaneously recording the time that elapses between the counts from the two detectors. By varying the time difference, i.e., the time delay between the detection events, g(2)(τ) can be measured.

Figure 2.1: Conceptual schematic illustration of the interferometer setup proposed by Hanbury Brown and Twiss. The electronic unit consisted of an auto-correlator whereas the delay line was set by adding coaxial cables connected between detector D2 and the auto-correlator.

2.2.2 Quantized second-order correlation function In the classical picture, where the incoming beam is considered as light intensity, the 50:50 BS will divide the incident intensity such that half of the intensity is going to each arm. However, this is no longer valid when considering a quantized ﬁeld. When assuming a stream of photons instead, with 20 Intensity ﬂuctuation statistics long time intervals between successive photons, an impinging photon on the BS will have a 50% probability to be directed onto only one of the detectors, but not both. Hence the correlator will record no event at τ = 0, i.e., there will be no correlation between the two detectors. Only when a subsequent photon is directed towards the counter-detector, an event is recorded. We realize that, while we very well might have events for larger time delay values, we will never have any at τ = 0. Now, because the correlation function, i.e., Eq. (2.1), was expressed in terms of intensity, it needs to be rewritten so that the value of g(2)(τ) is expressed in terms of coincidences between photon count rates. g(2)(τ) is then given by

hn (t)n (t + τ)i g(2)(τ) = 1 2 , (2.4) hn1(t)ihn2(t + τ)i where ni(t) is the number of photon counts on detector i at time t. When focusing on single-mode ﬁelds, the quantum interpretation of the expression in Eq. (2.4) at τ = 0 can be simpliﬁed to

haˆ†(t)aˆ†(t + τ)aˆ (t + τ)aˆ (t)i hnˆ(nˆ − 1)i 2 g(2)(0) = 1 2 2 1 = , (2.5) † † hnî haˆ1(t)aˆ1(t)ihaˆ2(t + τ)aˆ2(t + τ)i where nˆ = aˆ†aˆ is the number operator and hnî denotes the expected photon number detection values. Remembering the definition ∆nˆ ≡ nˆ − hnî, Eq. (2.5) can be rewritten as a function of the variance of the photon number h(∆nˆ)2i:

h(∆nˆ)2i − hnˆi g(2)(0) = 1 + . (2.6) hnˆi2

Thus, if the single mode ﬁeld is in a coherent state, i.e., h(∆nˆ)2i = n¯ for a Pois- sonian photon number distribution, we get g(2)(0) = 1. This was also predicted by the classical theory of light. A non-classical beam containing n photons is known as Fock- or number states. Since the number state |ni is an eigenstate of the number operator, Eq. (2.5) can be rewritten as n(n − 1) g(2)(0) = , n ≥ 1 (2.7) n2

2.2.3 Photon bunching and antibunching Let us more closely examine the results of the quantum description and the implications of Eq. (2.7), and compare them with the classical theory. The classical limit for a perfectly coherent light is g(2)(τ) = 1. Now, if the timing between the photons is more narrow, i.e., the photons are bunched together, the probability of detecting photons arriving together in pairs is higher around 2.2 Quantum description of light 21

τ = 0 than at later times, leading to g(2)(0) > 1. Subsequently, we expect g(2)(τ) to be larger for small values of τ than for higher values, such that g(2)(0) > g(2)(τ). This phenomenon was already predicted by the classical theory, for instance, by Eqs. (2.2) and (2.3) for thermal light, and is referred to as photon bunching. The converse case, where g(2)(0) < g(2)(τ), is referred to as antibunching. Here, the light ﬁeld consists of photons more equally spaced, and the probability of detecting two photons simultaneously is lower than the probability of detecting them at different times. Furthermore, we have seen that the no-event observation at τ = 0 discussed for the case of a beam consisting of individual photons leads to the non-classical result of g(2)(τ) = 0. Hence, we can conclude that g(2)(0) < 1. Clearly, this is a violation of the classical restrictions of both Eq. (2.2) and Eq. (2.3). In fact, antibunching is considered a conclusive signature of the quantum nature of light. While we expect that g(2)(0) = 0 for an ideal single-photon source emitting one photon, Eq. (2.7) implies that the expected g(2)(0) value is 0.5 for photon number states with n = 2. Because of the experimental challenges and difﬁ- (2) 1 culties in arranging a single-photon source setup, the condition g (0) < 2 is used as the upper limit to identify photon antibunching. Table 2.1 summarizes the conclusions of this chapter, and the resulting typical curves for g(2)(τ) are shown in Figure 2.2.

Figure 2.2: The normalized second-order function for various single-mode fields. The fluctuating field corresponds to a bunched photon stream (blue curve) whereas the perfectly coherent field corresponds to a random photon stream. The dashed line indicates the level for Poissonian light). Only the quantum one-photon state shows antibunching. 22 Intensity fluctuation statistics

Model Light source g(2) property Photon stream (∆n)2 property I(t) (for all τ) (for all T) Classical All g(2)(0) ≥ 1 g(2)(0) ≥ g(2)(τ) Coherent g(2)(τ) = 1 Random Poissonian = n¯ Constant Chaotic/thermal g(2)(0) > 1 Bunched super-Poissonian > n¯ Time-dependent g(2)(0) > g(2)(τ) Quantum 1-photon state g(2)(0) < 1 Antibunched sub-Poissonian < n¯ Constant g(2)(0) < g(2)(τ)

Table 2.1: Classiﬁcation of light according to the second-order correlation function and photon statistics.

2.2.4 Is antibunched light the same as sub-Poissonian light? As mentioned earlier, although antibunching and a sub-Poissonian photon distribution are closely related, it is important to note that they are different manifestations of the same optical quantum phenomenon. It is true that, from Eq. (2.6), sub-Poissonian statistics indicates that g(2)(0) < 1 which, as we already established, also means antibunching for some range of τ, unless g(2)(τ) is time-independent. However, this cannot be a general conclusion, since g(2)(0) < g(2)(τ) does not necessarily entail that g(2)(0) < 1. In fact, the first experimental demonstration of antibunching [5] is an example of a source for which g(2)(0) < g(2)(τ), but which also exhibited a super-Poissonian distribution over some time interval. More specifically, since the measured correlation function, although increasing, had its initial value at unity, it did not fulfill the inequality g(2)(0) < g(2)(τ) for all values of (τ). The inequality was true only for a finite delay (τ). Hence, although the light was strictly super- Poissonian, it was considered antibunched for a certain time period. Also, it has been experimentally demonstrated that non-classical light, while bunched, still can be sub-Poissonian for a certain time interval T [47]. Thus, although the two effects (antibunching and sub-Poissonian) are not causally related, it is natural that they frequently coincide for certain fields, since they are both expressions of the same quantum nature of light2.

2A more thorough discussion of this topic can be found in [34, 48]. 23

3. Nitrogen-vacancy centers in diamond

Color centers in diamond are fluorescent point defects in the crystal lattice. They consist of one or more foreign atoms or vacant lattice sites replacing the lattice atom, and are uniquely determined by their optical properties (emission and absorption spectra), hence the term color center [49]. Numerous color centers have been identified in diamond and studied extensively in order to understand their structure and to control their physical properties [14]. One of these color centers that has received considerable attention and has undergone a renewed exploration is the nitrogen-vacancy (NV) center, due to its favorable photo-luminescence properties. Trapped (as an artificial atom) in the diamond lattice, the NV center proved as a reliable photo-stable single photon source, which can be operated at room temperature with no signs of bleaching. Spurred by the first demonstration of anti-bunching in 2000 [50, 51], the NV center was soon envisioned as a suitable candidate for quantum optical network applications. However, it is the exquisite magnetic and spin properties that are the most interesting aspect of the NV center and what sets it apart from other color centers. Since establishing the coupling between luminescence and the electronic spin state of the center [18, 19, 52], and the demonstration that the luminescence intensity can be modulated and manipulated at room temperature by applying a magnetic field [53,54], the NV center was identified as an attractive qubit for many quantum information processing applications [17]. Only a few color centers possess this unique magneto-optic property1. However, if the spin properties are not relevant for the desired application, many other color centers, such as nickel- and silicon-vacancies can serve as fluorescent emitters [14]. As mentioned elsewhere in this work, nickel- and silicon-vacancy centers were also among the first defects proposed for investigation. However, since their photo-luminescence properties are quite similar to that of the NV center in most respects, we will only focus on the NV center. Thus, in this chapter, we will only consider the generation of NV defects along with their various host crystals, as well as the basic electronic energy level structure of the NV

1Recently, the silicon-vacancy center has also received increasing attention because it displays similar electron spin and photo-luminescence properties, although it shows a sharper optical spectrum than the NV center, suggesting it as yet another promising potential qubit [21]. 24 Nitrogen-vacancy centers in diamond center. The chapter ends with a description of spin manipulation and readout techniques required for the realization of a single qubit.

3.1 Synthesis and generation of NV defects Most of the diamond samples used for research applications are synthesized [14, 17, 20] and come in different forms and shapes such as bulk crystals, thin films and nanocrystals. According to the employed cultivation method, i.e., chemical vapor deposition (CVD) or a high-pressure high-temperature (HPHT) crystal formation technique, synthetic diamonds are generally referred to as CVD or HPHT diamonds [49], respectively. CVD is a relatively new diamond fabrication technique that allows for the diamond to be grown from a hydrocarbon gas mixture, and produces thin films of polycrystalline diamond with dimensions in the range from several microns to a few millimeter. The HPHT method has been used since 1950 and is the most widely employed method due to its low cost. The method is an attempt to mimic the natural ge- ological process conditions. The majority of the commercially used synthetic diamonds are HPHT crystals, typical with dimension of a few millimeter, and are considered useful as hard-wearing edges on cutting and drilling tools. Syn- thetic nanocrystalline diamonds can be obtained by grinding large crystals to sub-100-nm-sized particles. The two predominant defects in both natural and synthetic diamonds are nitrogen impurities and vacancy2 aggregations, and based upon concentrations of the nitrogen impurities, diamonds are categorized in two major groups, namely type I and type II [55–58]. While type II refers to diamonds without any detectable nitrogen impurities, diamonds are classified as type I when they contain detectable amounts of nitrogen3. For type I diamonds, two major sub- divisions are further identified. Diamonds that contain nitrogen in aggregated forms (comprised of a pair or more nitrogen atoms) are known as type Ia, whereas those with isolated substitutional nitrogen atoms are referred to as type Ib. While very rare in natural diamonds, virtually all synthetic diamonds fall into the type Ib category. Although many types and forms of diamonds4 have been tested during the course of this work, we are only focusing on type Ib synthetic diamonds in this thesis. Due to the stress caused by the single nitrogen atom inside the lattice structure, the nitrogen defect is efficient in trapping a moving vacancy injected

2When denoting a crystal defect, lattice vacancy refers to a missing atom leaving a hole on its regular atomic site. In this case, by a vacancy we mean a missing carbon atom. 3The sensitivity limit of conventional IR absorption spectroscopes used to detect the impurities is around 1 ppm (parts per million). However, typical nitrogen concentrations are >10 ppm and may be as high as 3000 ppm [55]. 4All tested samples are listed and compared in Table A.1. 3.2 Zero phonon line and phonon sideband 25 during growth, thereby reducing the lattice tension and producing the NV centers [49,59]. The concentration of NV centers can be increased by high-energy radiation5 followed by annealing at high temperatures6 [61]. The high radiation damage produces cracks in the diamond and thereby vacancies in the diamond lattice, whereas annealing at > 700◦C makes the vacancies mobile7 leading to the migration of vacancies and their ultimate trapping by nitrogen atoms, resulting in the formation of NV centers. A suitable NV concentration can be reached by controlling the irradiation dose. However, for the samples used in this study, no alternation of the NV center concentration was needed as it was readily fabricated. This will be described in more detail in section 6.1.

3.2 Zero phonon line and phonon sideband Before considering the physical and electronic structures of the NV center, it is instructive to brieﬂy introduce two key concepts: the zero phonon line and the phonon sideband. In a solid where atoms are locked in a lattice, the internal energy determining its temperature primarily manifests itself as vibrational energy. In quantum mechanics, a collective vibrational energy mode in a lattice is expressed as a phonon. Thus, while an excited isolated atom releases the energy difference between the ground and the excited state as a photon, in a solid, the same energy is converted into internal heat energy represented by the creation of a phonon. However, in a solid, it is also possible for the energy to be released as a combination of both phonons and photons, with the phonon release being the dominating process. The de-excitation between two energy levels generates a broad light spectrum in a solid because different fractions of released energy are transferred to the phonon for each electron de-excitation event. The broad spectrum consists of both a zero phonon line (ZPL) and a phonon sideband (PSB). While the ZPL is a narrow peak with Lorentzian line shape representing the photons that received all the available energy without the involvement of phonons, the PSB represents photons that had to share their energy with a phonon. The PSB is characterized by the observation of Stokes-shifted lines, with absorption and emission at higher and lower energies, respectively. 26 Nitrogen-vacancy centers in diamond

Figure 3.1: a) Schematic illustration of the face-centered cubic lattice structure of diamond with an NV center. The nitrogen atom is depicted in green, the carbon atoms in black, the vacancy as an empty hole and the extra electron in red [62]. The lattice constant of the diamond is 3.57 Å, with a nearest-neighbour distance of 1.55 Å between the carbon atoms. b) The C3v symmetry group of the NV center is represented by a set of operations that, including the identity rotation, consists of 2πn/3 rotations around the symmetry axis of the NV center represented by the z-axis, and reﬂections in the three planes containing the symmetry axis and any of the three nearest-neighbor carbon atoms Ci.

3.3 Physical structure Figure 3.1 illustrates an NV center as a point defect in diamond formed through the incorporation of a vacant carbon lattice site adjacent to a substitutional nitrogen impurity in the face-centered cubic (fcc) diamond lattice oriented along the [111] crystalline direction, thereby breaking the translational symmetry of the diamond crystal and reducing it to rotations and reﬂections, known as C3v symmetry operations. Speciﬁcally, by breaking down the crystal symmetry, the bonds in the crystal are consequently broken down as well. This results in dangling bonds by which single electron orbits can be represented. The nature of the physical structure and the electronic states, together with the corresponding energy properties of the NV center, are governed by the associated C3v symmetry, as the single electron orbitals 8 and their associated energy levels are derived by applying the C3v symmetry .

5This includes electrons, protons, neutrons, and gamma rays, or ion implantation [60]. 6A self-built high-temperature oven for annealing purposes is described in AppendixB. 7Vacancies are immobile at room temperature. 8 A more thorough and detailed description of C3v symmetry and group theory can be found in [17, 63]. 3.4 Electronic structure 27

The NV center is known to exist in two charge states, i.e., the electrically neutral state referred to as NV0 and the negatively charged state de- noted as NV−, identified by their optical ZPL features at 575 nm (2.156 eV) for the neutral state and 637 nm (1.945 eV) for the negatively charged state [14, 17]. The NV0 complex involves five unpaired electrons; three dangling carbon bonds surrounding the vacancy and a pair of valence electrons associated with the nitrogen. In case of the negative state NV−, an extra electron is captured from the lattice, resulting in a total of six electrons. Thus the highest electron density mostly occurs on the side with the three carbon atoms and the hole. Although both charge states have been identified as single photon sources [50, 51, 64], the neutral state has not yet demonstrated any magneto-optically activity [65], and therefore the focus has been mainly on NV−. Therefore, in this thesis, we are exclusively considering the negatively charged state, and will simply refer to it as NV. Photostability is also among the beneficial properties of an NV center9, with no evidence of photobleaching observed under regular optical excitation (at 532 nm) at room temperature compared to other single-photon emitters [66]. However, under intense illumination, photoconversion of NV− to NV0 and photoblinking with time constants between 0.3 µs and 3.6 µs have been observed [67]. But this process is not well understood at the present time [17].

3.4 Electronic structure Optical properties The basic optical transition can be described by a standard three-level energy model with an electronic ground state 3A, an excited state 3E and a metastable state 1A [50]. This is illustrated in Figure 3.2. Since the NV center is characterized by its unique C3v symmetry together with the additional electron pair, the energy level labels are dictated by the C3v group theory, and thus both the ground and excited states form spin triplet states (S = 1). They can be further split into three quantum spin sub-levels (ms = −1,0,+1), whereas the metastable state forms singlet states [68]. The main electronic transition between the ground state and the excited state is resonant at a ZPL wavelength of 637 nm, and can be excited to decay to the ground state at any wavelength below 640 nm. We used off-resonant light with an excitation wavelength of 532 nm (2.33 eV). While only a few percent (4%) of the emission intensity is concentrated around the ZPL, most of the emitted light appears in the associated extended PSB between 630 and 800 nm [20,63]. In comparison, the associated ZPLs for nickel- and silicon-vacancies are 800 and 738 nm, respectively [14].

9Photostability has also been reported for NV0 [17, 20]. 28 Nitrogen-vacancy centers in diamond

8 7

8γ7

8 7

Figure 3.2: Electronic structure of NV center, where 3A is the ground state, 3E the excited state and 1A denotes the metastable dark state. From left to right: the optical transitions between the three spin levels ms = −1,0,+1 at the absence of both microwave and magnetic manipulation, the spin-spin coupling at zero-field magnetic resonance occurring at 2.87 GHz, and the Zeeman splitting under the presence of an external magnetic field oriented along the axis of the defect. The colored arrows indicate the radiative transitions (green denotes the excitation pump and red is the emission fluorescence), whereas the dashed black indicates the non-radiative decay. Vibronic phonon sideband (PSB) transitions are indicated by the yellow continuum, and both conduction and valence bands are indicated by the red continuum. 3.4 Electronic structure 29

Due to thermal broadening, the sharp peak of the ZPL is very weak compared to the PSB and may not even be observable at room temperature. How- ever, a cooling of the NV center to low temperatures (<10 K) has been reported to suppress the broad spectrum and reveal fine and sharp ZPL structures [69]. In this work, however, all presented experiments involving the NV center were performed at room temperature. The excited state can also decay through a non-radiative transition10 to the metastable state, also known as shelving or dark state, since the photons trapped in this state lead to a shelving in population and create dark periods between excited and ground states. Particularly, under strong illumination, the shelving in the metastable state accounts for the observed photon bunching behavior (g2(0) > 1). The lifetime of the metastable state is around 300 ns [70], which is significantly longer than the radiative lifetime of the excited state. Studies suggest that the lifetime of the excited state depends on the refraction index of the employed host material, i.e., a bulk or a nanodiamond crystal. The relatively high refractive index (nd=2.4) of the bulk diamond crystal causes refraction at the interface [71]. This leads to a small collection solid angle making it difficult to extract light from an NV center. To increase the extraction efficiency, smaller crystals such as nanocrystals can be used. Because of the sub-wavelength dimension of the nanocrystal, the refraction becomes negligible. However, this comes at the price of a considerably longer lifetime of approximately 25 ns [71] compared to the 13 ns [68,72] observed for the bulk diamond.

NV spin Hamiltonian The triplet states are created because the surplus electron can form a spin S = 1 pair with one of the three dangling carbon bonds, yielding three quantum spin states ms = −1,0,+1 for both the ground state and the ﬁrst excited state. Both the ground and excited triplet states are further split into three spin sublevels. Because the unpaired electrons have a higher energy when their spins are parallel (ms = ±1) than when their spins are anti-parallel (ms = 0), the degeneracy between ms = 0 and ms = ±1 can be lifted by the spin-spin interaction. It is instructive to consider the spin Hamiltonian of the NV center in order to understand the effect of the different perturbations. The relevant

10Non-radiative transitions are associated with the release of a phonon in the lattice. 30 Nitrogen-vacancy centers in diamond parts of the ground state NV Hamiltonian can be written as follows:11

2 Hgs = D(Sz) +2γBzSz + γBxSx, (3.1) | {z } | {z } z f s magnetic where D is the energy difference between ms = 0 and ms = ±1, known as the zero-field splitting (zfs), which corresponds to a frequency of about 2.87 3 GHz for the ground state A at room temperature. Sz denotes the spin operator. The corresponding zero-field fine structure splitting of the excited state 3E is about 1.42 GHz. In conjunction with the ZPL at 637 nm, the 2.87 GHz zero- field magnetic ground state splitting resonance is a clear signature of an NV center. When applying an external static magnetic field Bz parallel to symmetry axis of the NV center, however, the degeneracy of the ms = ±1-states is split by the Zeeman effect, revealing two resonances with a frequency difference given by the second term of Eq. (3.1), where γ is the electron gyromagnetic ratio given by (2π·2.8 MHz/Gauss). The coefficient γBx stems from the applied microwave, and will be discussed in more detail when considering Rabi oscillations.

3.5 Spin manipulation and readout 3.5.1 Optical spin polarization and spin-dependent florescence The optical spin preparation and spin readout of the NV center is enabled by a combination of spin variety of both the excited and ground states, and the in- tersystem crossing decay paths between the radiative and the non-radiative states. Specifically, the magneto-optic behavior represented by the varying spin-dependent fluorescence is determined by the non-radiative dark state with different allowed decay paths for ms = 0 and ms = ±1. Figure 3.2 shows the non-radiative transitions, where the transition from the excited triplet state 3E 1 to the singlet dark sate A is only allowed from ms = ±1 states, whereas de- 1 3 cays from the singlet A to the excited ground state A occur primary to ms = 0 state. Thus, the singlet dark state serves as a bridge between the ms = ±1

11Since the excited state 3A does not depend on any orbit splitting at room temperature and only weakly depends on the crystal strain and the temperature, the spin-orbit and strain Hamiltonians are neglected and only spin-spin is considered. Furthermore, interactions such as the nuclear hyperfine interaction with the nitrogen and neighboring carbon nuclear spins are neglected as well. The interaction with the nitrogen nucleus accounts for a contribution given by SA¯NIN + N 2 N 2 ¯N P[(Iz ) −(I ) /3], where A is the hyperfine coupling tensor between the electron spin and the nitrogen nucleus spin, IN is the nitrogen nuclear spin and P the electric quadrupole coupling. This nitrogen interaction term is relevant for close spin resonance examinations of the hyperfine structure associated to the transition ms = 0 →ms = −1. However, since this is not necessary for the demonstration of Rabi oscillations, it is neglected in this work. 3.5 Spin manipulation and readout 31

and ms = 0 states. For the remaining optical radiative transitions, since the photon mediating the transitions between the electronic states cannot change the overall spin, these (optical) transitions are highly spin-preserving [17,20]. Thus, during each cycle, the total spin is preserved and transitions can only occur between levels of the same spin. Consequently, this mechanism leads to a complete polarization of the NV center into the ms = 0 ground state by optical excitation. This process is known as optical spin polarization and the polarization strength of a particular spin projection is determined by the optical illumination. Thus, the ms = 0 ground state is both the brightest and most favored projection into which the NV center is optically polarized. S. Felton et al. reported a probability of up to 92% for the optical polarization of the ms = 0 ground state [65]. However, the subject remains a controversy as different values have been reported in literature and the underlying mechanism is not fully understood. Considering the significantly longer lifetime of the in- 1 3 termediate dark state A compared to the excited triplet state E, the ms = ±1 ground state is less populated than the ms = 0 ground state, as it undergoes fewer fluorescence cycles. Thus, a difference in fluorescence occurs between the ms = ±1 and ms = 0 ground states, with the ms = 0 ground state being the state with the strongest fluorescence. The initial optical contrast between the two states is between 25-40% [20,63] and is a transient effect, lasting less than a microsecond, because a constant optical excitation eventually re-pumps the electron to the ms = 0 ground state.

3.5.2 Magnetic single spin manipulation These optical dynamics of the NV center are collectively utilized as a technique to optically read out the spin state of the center while simultaneously spin-polarizing it into ms = 0 spin projection. Specifically, the optical readout technique is implemented by comparing the average florescence intensity measured for the spin state in interest with calibration florescence measurement corresponding to the prepared spin state, i.e. ms = 0 or ms = ±1. Addi- tionaly, by applying a control field such as a microwave resonant to its transition, the spin states can be manipulated. Despite the challenges addressing a single spin by microwaves, isolating a single NV center in a confined optical excitation volume through the technique of confocal microscopy and applying a microwave through a wire loop placed in close proximity to the NV center, a single spin can be prepared, manipulated and read out. The utilized preparation and readout setup is discussed in more details in chapter5. Read out observations of single electron spins of the NV center are commonly separated into continuous-wave (CW) and pulsed microwave experiments. In both cases, an off-resonant optical excitation wavelength (532 nm) is used in order to excite the electrons in the PSB, as the vibronic relaxation 32 Nitrogen-vacancy centers in diamond times are much shorter (∼ ps) than the long lived excited states (∼ ns). Typ- ically, most experiments are prepared in the ms = 0 ground state as it shows a stronger fluorescence than the ms = ±1 states and therefore represents the preparation fidelity.

3.5.3 CW microwave experiments In a CW experiment, both an optical excitation and a microwave are continuously applied at a constant power, and the microwave is then scanned over a certain frequency range while measuring the fluorescence. While optical excitation polarizes the NV center into the ms = 0 state, a decrease of the fluorescence intensity is observed once the microwave frequency is in resonance with the transition ms = 0 → ms = ±1. The electron spin resonance occurs at 2.87 GHz in the absence of a magnetic field, whereas the two transitions, i.e., ms = +1 and ms = −1, are shifted by 2γBz in the presence of a finite magnetic field.

3.5.4 Pulsed microwave experiments Rabi oscillation While CW microwave experiments allow to measure the energy levels of the NV spin system and serve as a calibration measurement by means of resonant frequency fine-tuning, pulsed microwave experiments allow for an observation of the spin dynamics in the time domain. For the realization of qubits, this process is necessary in order to drive the spin transitions and enable spin state manipulation. In this regard, it is convenient to consider the ground state 3A under an external magnetic field, as the two occurring split states ms = +1 and ms = −1, following the Zeeman splitting, are susceptible to magnetic transition and can be selectively driven in the presence of a sufficiently strong magnetic field. For a convenient strength of the magnetic field, we end up with three different states: (|ms = 0i ≡ |0i,|ms = −1i ≡ | − 1i and 1 |ms = +1i ≡ | + 1i, of which three different pseudo spin- 2 transitions can be constructed:{|0i,| − 1i}, {|0i,| + 1i} or {|0i,| ± 1i}. Each of these transitions constitutes an effective two- state quantum system that allows to create a qubit, as illustrated in Figure 3.3. 1 For the sake of convenience, let us consider the pseudo spin- 2 system {|0i,| − 1i}. By applying a pulsed microwave frequency, a pulsed oscillating magnetic field Bx(t) = Bx cosωt is generated with an angular frequency ω perpendicular to the symmetry z-axis, in addition to the applied external magnetic field Bz. Thus, the spin is subject to a net magnetic field given by

B = Bzz + Bx cos(ωt)x, (3.2) 3.5 Spin manipulation and readout 33

Figure 3.3: Illustration of Zeeman splitting for the NV center. For the energy levels of 2 the NV center in its ground state, the dominating part of Eq. (3.1) (D(Sz) + 2γBzSz) is plotted as a function of an external magnetic field. While the spin states | − 1i and | + 1i are perturbed by the magnetic field, the |0i state remains unaffected. The zero- field fine structure splitting D between the |0i and | ± 1i states occurs at around 2.87 GHz, whereas the crossing between the |0i and |−1i states occurs at around Bz = 1025 G.

where Bz and Bx are constants. Given the magnetic dipole moment η = γS with a gyromagnetic ratio γ and a spin S, the interaction Hamiltonian for this system in a magnetic ﬁeld can be written as

H = −ω0Sz − ΩR cos(ωt)Sx, (3.3) where ω0 = γBz and ΩR = γBx. If the qubit is initialized in |0i at time t = 0, the probability of ﬁnding the qubit in |1i is [33]

Ω2 1 1 q P (t) = R − cos ( 2 + 2)t , (3.4) 0→1 2 2 ΩR δ ΩR + δ 2 2 where δ = ω − ω0 describes the detuning. The maximum amplitude is achieved when the angular frequency ω is tuned in such a way that the resonance condition δ = 0 is satisfied. Thus, when in resonance with the transition of interest, the angular frequency ω drives the magnetic transition so that the population oscillates between the two states with a characteristic frequency ΩR, known as Rabi frequency. The qubit is then said to oscillate between the |0i and |1i states. Thus, the probability of finding the qubit in |1i for a resonant microwave pulse is 1 P (t) = [1 − cos(Ω t)]. (3.5) 0→1 2 R By sending a resonant microwave pulse with a length of duration t = π , ΩR the spin is flipped so that the qubit is sent from |0i to |1i, whereas a pulse of length t = 2π has no effect because it returns the qubit to the initial state ΩR 34 Nitrogen-vacancy centers in diamond

|0i. These pulses are known as π- and 2π-pulses. It becomes apparent that variable Θ-pulses with lengths of durations t = Θ will create different super- ΩR positions of the spin states, sending the ground state |0i into the superposition cosΘ|0i + isinΘ|1i.A π -pulse, for instance, sends the ground state |0i into √ 2 the superposition 1/ 2(|0i + i|1i). The Rabi√ frequency ΩR linearly depends on the microwave power IMW , i.e., ΩR ∝ IMW [18]. Thus, for a given microwave power, knowing the Rabi frequency is of paramount importance as it allows for a careful design of Θ-pulses with an adequate length for spin manipulation applications, thereby enabling the control of a single qubit state.

Spin environment spectroscopy Specifically, the coherence properties of the NV center can be determined by studying the complex spin environment of the NV. This is enabled by the use of Θ-pulses through electron spin resonance (ESR)12 spectroscopy techniques. Although the aim of this work is to demonstrate Rabi oscillations rather than investigating the coherence properties of the NV center through sophisticated spectroscopy techniques, it is worth to briefly introduce some selected techniques. Particularly, any particle in the spin environment with a non-zero spin induces a magnetic dipole moment which contributes to a spin bath with a slightly fluctuating effective magnetic field that interacts with the NV. This interaction results in the NV spin to become decoherent. While the coherence of the NV center depends on both the 13C nuclei in the diamond lattice and the nitrogen impurities comprising the spin environment, the nitrogen impurities are considered to be the main cause for the decay of the NV spin coherence [73]. It has been demonstrated that for highly pure diamond samples with negligible concentrations of nitrogen impurities, where the spin environment is mainly affected by the spins of the 13C nuclei, the coherence time could be improved to a few hundred microseconds [63]. Ultra-long room temperature coherence times in the order of 2 ms were reported for ultra-pure isotopically engineered diamond with the 13C nuclear spin content depleted to 0.3% [74]. By applying the following spectroscopy techniques, we can study the spin environment and thereby reveal the origin of the NV decoherence: • π-pulse sequence: The long term damping process due to the spin-lattice relaxation is determined by the population decay of the spin state. This relaxation is also known as longitudinal relaxation because it affects the motion along the direction of the applied field during the phononic interactions with the crystal lattice. It is characterized by the time constant T1 and measured through a π-sequence, as illustrated in Figure 3.4. At first, the spin state is prepared into the |0i state by spin-polarization via a green laser pulse, after which the fluorescence level at |0i is read. Hereafter, the

12Also known as electron paramagnetic resonance (EPR). 3.5 Spin manipulation and readout 35

spin is prepared into the |1i state by a π-pulse, where π represents a microwave pulse with a duration sufficient to flip the spin state from |0i to|1i. The spin state is allowed to evolve freely for a duration t before it is read out. The time period over which the fluorescence decays represents the relaxation time T1. For nanodiamonds, the T1 has been reported to be in the range of microseconds [75].

Π Π

Figure 3.4: Illustration of a π-pulse sequence with the help of a Bloch sphere. The Bloch sphere is used to describe the spin manipulation as a transformation of a vector in the sphere. The initial vector represents the preparation into the |0i state after which it is excited to the |1i state via a π-pulse. The state evolves freely for a time duration t before it is read out. The green vector indicates the current spin state whereas the blue vector illustrates the effect of the applied microwave pulse.

• Ramsey fringes: The damping mechanism determined by the spin-spin relaxation (also known as transverse relaxation) is due to the inﬂuence of the spin environment on the NV spin, and gives rise to a dephasing time characterized by T2. By using the Ramsey pulse technique consisting of the microwave pulse sequence π/2 − τ − π/2, as shown in Figure 3.5, we can measure the dephasing time T2 in which random phase shifts have occurred between the spin states |0i and |1i. After initializing the spin state into the |0i state, the ﬁrst microwave pulse excites the spin state into a superposition state via the π/2-pulse, after which it evolves freely for a time duration t and gains a phase. The second microwave π/2-pulse projects the spin state with its gained phase into a measurable population difference. Typically, T2 is in the order of a few hundreds of nanoseconds [63]. • Hahn echo spectroscopy: Also known as spin echo spectroscopy, this technique eliminates external inhomogeneities caused by the statistic ex- 36 Nitrogen-vacancy centers in diamond

Π Π

Figure 3.5: Illustration of the Ramsey pulse sequence with the help of a Bloch sphere.√ The initial π/2-pulse excites the grounds state |0i into the superposition state 1/ 2(|0i+i|1i) around the y-axis, after which the spin state evolves freely for a time duration t while being rotated around the z-axis with an angle depending on the applied magnetic ﬁeld. This phasing process is represented by the light blue arrows. The second π/2-pulse projects the x-component of the state onto the z-axis after which the spin state is read out.

ternal magnetic shifts due to spins precessing at different rates in the spin bath. Thus, the Hahn echo method enables the measurement of the intrin- ∗ sic coherence time T2 of the NV center as it allows to observe dynamical changes of the spin bath environment independent of the applied external magnetic field Bz. Particularly, the Hahn echo technique consists of a π/2 −t − π −t0 − π/2-sequence, as illustrated in Figure 3.6, where, similarly to the Ramsey sequence, the spin state is excited into a superposition state by the first π/2-pulse followed by a free precession time τ in which a dephasing occurs. However, the dephasing is removed by applying an inverse π-pulse that inverts the magnetization vectors and thus eliminates the phase-shift. The last π/2-pulse projects the spin state back onto the z-axis for readout. In contrast to the the Ramsey pulse technique, the Hahn echo sequence remains insensitive to the external magnetic field. Furthermore, the Ramsey sequence is unable to detect dynamical changes between two subsequent measurements, as the spin environment is probably different for each repeated measurement. However, because the Hahn echo technique eliminates the effect of external inhomogeneities, it is insensitive to changes in 3.5 Spin manipulation and readout 37

the spin environment between measurements and therefore allows to detect dynamical changes for sufﬁciently recorded measurements.

Π Π Π

Figure 3.6: Illustration of the Hahn echo pulse sequence with the help of a Bloch sphere.√ The initial π/2-pulse sends the grounds state |0i into the superposition state 1/ 2(|0i + i|1i) around the y-axis, after which the spin state evolves freely for a time duration t while being rotated around the z-axis with an angle depending on the applied magnetic ﬁeld. An inverse π-pulse inverts the z-component of the spin around the y-axis during which the spin gains a relative phase shift with an inverse sign. The spin then undergoes a refocusing phase of duration t0 after which the x-component is projected back on the z-axis for readout.

4. Confocal Microscopy

Confocal microscopy (CM) allows to outperform conventional wide-field microscopy by offering several advantages, e.g., an improvement in contrast and resolution, as well as a controllable depth of field [76–80]. More specifically, by using a point illumination technique and introducing a spatial pinhole eliminating a defocusing of the image caused by out-of-focus light, the created images appear sharper and show a better contrast compared to images acquired with conventional wide-field microscopes. This, however, comes with the in- convenience of a relatively time-consuming scan of the sample since only one illumination spot can be observed at a time. By assembling a series of the obtained optical scan sections, a reconstruction of a three-dimensional image of a volume of the specimen is possible. Whereas it has gained popularity in semiconductor physics and materials science and is applied for the examination of defects and studies on single optical transitions, the coupling to nearby spins and other effects otherwise impossible to observe, CM has become an invaluable tool in the scientific and industrial communities, with typical applications in the fields of biology and materials science [78–81]. In this thesis, it is this confocal illumination technique that is utilized to reveal the presence of single emitters and isolate them. More specifically, while the colored defects serve as the actual photon emitters, CM allowed to examine and selectively excite NV centers in order to generate single photon states. It is this combination of the confocal microscope apparatus and the defects that is commonly referred to as a single photon source setup [50, 51]. Although CM systems are commercially available, a self-built confocal setup allows for a greater flexibility with the possibility of incorporating other devices for studying the properties of the emitters. In this chapter, I will present our self-built confocal microscope. The working principle of a confocal microscope is briefly introduced followed by a description of the main optical components that constitute a confocal microscope, and the design considerations required for a confocal setup to allow for the detection of antibunching. Subsequently, two different setup approaches, a so-called green and red confocal setup, are presented with the emphasis on the green setup. The chapter concludes with a discussion and implementation of an alternative microscope setup based on the CM concept, referred to as stimulated emission depletion (STED) microscopy. 40 Confocal Microscopy

4.1 Principle of Operation The basic concept of CM was introduced in 1957 by Marvin Minsky [82] with the objective to overcome the shortcomings of traditional microscopes. Before considering the confocal setup, it is therefore instructive to first illustrate the differences between a traditional and a confocal microscope. Particularly, it is useful to compare the typical geometry of illumination used for each technique, as illustrated in Figure 4.1. In conventional wide-field fluorescence microscopy, the objective focuses a wide illumination cone onto the sample, thereby flooding a large depth of the specimen over a wide area in intense uniform and simultaneous illumination, as shown in Figure 4.1a. The resulting image of the object is simultaneously projected onto a camera or photodetector. Since all parts of the specimen are illuminated at the same time, all excited spots on the sample will laterally interfere with each other and contribute to the projected image. In combination with the stray fluorescence background light from areas outside the focal plane, this leads to a significantly reduced contrast and image resolution. Consequently, weaker light signals at the focal plane might not even be detectable as they are being concealed and overshadowed by the emitted background light. To circumvent this obstacle and improve contrast, CM utilizes a fundamentally different approach by introducing a point illumination such that only a point spot of the specimen is illuminated at a time, thereby eliminating any lateral interference on the resulting image formation process. This is illustrated in Figure 4.1b. Especially for our purpose, where the defects are arbitrarily distributed only sub-microns apart from each another and each defect only emits weak light signals, this approach is critical for identifying as well as isolating individual emitters and detecting them without simultaneously collecting light emitted from adjacent defects. However, despite the significant reduction of the lateral size of the illumination spot and the improved image contrast, out-of-focus light still contributes to the collected light and compromises the image sharpness. By adding a confocal aperture, also referred to as a pinhole, in an optically conjugate plane before the image detector, as shown in Figure 4.1b, any light from outside the focal plane not passing through the pinhole is suppressed. The pinhole configuration constitutes the most decisive part of the confocal microscope, hence the name. Figure 4.2 shows in more detail the role and the filtering principle of the pinhole. The object is placed at the focal point of the objective. The light emitted from the object is collected and collimated by the objective after which it is focused by a lens onto the confocal pinhole. Any light emitted from a point not in focus, i.e., below or above the focal plane, will be focused either after or before the pinhole and therefore becomes blocked by the pinhole plate. Thus, besides an improved image contrast, an additional advantage of CM is the elimination of stray light. However, 4.1 Principle of Operation 41

Figure 4.1: Comparison of an a) conventional and b) confocal microscope in terms of principle of operation (top) and geometry of illumination (bottom). Three (additional) parts essential for a confocal microscope setup are: a laser source, a confocal aperture (pinhole) and a 3D scanning system.

the increased depth resolution comes at the cost of a lower signal intensity because much of the emitted light is absorbed at the confocal aperture plate. Clearly, the pinhole diameter determines the thickness of the optimal obtainable focal plane, also known as optical sectioning, as depicted in Figure 4.1b. In section 4.3.2 we will discuss the confocal effect and the optical sectioning in more detail and consider the appropriate pinhole size for our setup. 42 Confocal Microscopy

Another essential part of the CM setup is a 3D scanning system. As only one pixel of the object is illuminated at a time, obtaining a two-dimensional image of the entire sample requires a scanning of the diffraction-limited laser beam spot across the sample, or to move the sample relative to the beam, pixel-by-pixel to form a line, then line-by-line to form a two-dimensional ma- trix. A three-dimensional image, if desired, is obtained by repeating the same scanning process for different depths. Although modern confocal microscopes are highly modified compared with the original version, the principle of operation is still similar. To briefly summarize the principle of operation of the CM illustrated in Figure 4.1b, the collimated light from a pump laser is reflected by a dichroic mirror onto the objective, which then focuses the light to a sub-micron spot onto the sample. The back-emitted light from the sample is collected and collimated by the same objective and transmitted through the dichroic mirror onto a lens that focuses the light onto the pinhole and to the photo-detector. In order to obtain 3D information, the sample is mounted on a triple-axis motorized piezo stage.

Figure 4.2: Operation principle of the pinhole. The solid red line represents light emitted from a point in focus, whereas the dashed lines represent light that is emitted out of focus (blue: above; black: below the focal plane).

4.2 Optical components Since a number of optical elements form the framework of numerous key concepts and deﬁnitions of the terminology associated with CM, it is convenient to ﬁrst start with the introduction of certain main optical elements before we move on to the terminology and consider the design requirements for our CM setup. 4.2 Optical components 43

4.2.1 Laser source as illumination In microscopy, any light source that can provide photons to the sample is considered an illumination source. Usually, incoherent white light sources are used in conventional microscopy. However, lasers are the preferred illumination sources in confocal microscopes due to their high radiance and high degree of monochromaticity and coherence. In conventional microscopy, a high coherency is usually not desirable since the wide-ﬁeld illumination leads to unwanted interference, which reduces the image quality. But, due to the single-point-of-illumination approach in CM, interference is effectively eliminated. In addition to the listed qualities, a laser beam can be easily shaped by special integrated optics to deliver a high-quality Gaussian beam proﬁle. Furthermore, in our case, we needed to provide the appropriate pump wavelength in the green spectrum that is able to excite the NV centers. In order to meet this requirement, we used an Nd:YAG (neodymium-doped yttrium aluminum garnet) diode-pumped solid state laser (Cobolt TorTM Series), converted by second harmonic generation, emitting green light at a wavelength of 532 nm with a < 0.3 nm narrow line and a maximum average output power of 0.4 W.

For the planned and projected excitation of silicon- and nickel-vacancy centers, a diode laser emitting red light with a wavelength of 689 nm was used in a second setup. Thus, based on the utilized pump light source, in the following, I will distinguish the two CM setups by referring to them as the green and the red confocal setup, respectively.

4.2.2 Lens objectives An objective is a set of lenses stacked together to form an ideal lens system with minimum aberration effects. Besides magnification purposes, the objective lens determines the quality of parameters such as the light transmission, image contrast and certainly also the resolution, and as such is considered a crucial element of any microscope system. An important descriptor of the objective lens is the numerical aperture (NA), which is a measure of the light- gathering capability of the objective. Figure 4.3 demonstrates the concept of the NA, where the objective is considered to be a single lens with a diameter D and a focal length f . The cone of light gathered from a spot, or focused to one, has a maximum angle α because of the finite aperture size of the objective. Thus, the numerical aperture can be defined as [83]

NA = ng sinα, (4.1) 44 Confocal Microscopy

where ng is the refractive index of the cover glass. Considering Snell’s law, in case of air, it becomes 0 NA = sinα . (4.2)

Figure 4.3: Comparison of the numerical apertures of two objectives: air and oil objectives.

It is evident that the maximum NA value for an air objective1 is unity. Rays at an angle larger than α will not be transmitted through the glass-air interface and as such will not reach the objective. However, by filling the space between the cover glass and the objective with a fluid matching the index of the cover glass, the NA can be increased. With an index of around 1.5, oil provides an excellent match to the cover glass which has a refractive index of 1.52. The maximum practically achievable NA value is 1.6. The NA is a parameter of paramount importance since it not only determines the brightness but also limits the resolution of the microscope system, as discussed later. For our setup, we used four objectives with different NA values and mag- nifications. They are listed and compared in Table 4.1. However, while only the oil objective was used for the antibunching detection measurements, the objectives with NA values of 0.9 and 0.7 were used for testing and alignment purposes. With its long working distance of 4 mm, which allows for an easy mounting and calibration, the 0.7 NA objective was used in the initial phase of alignment. Depending on the quality of the performed calibration and the amount of light gathered, the 0.9 NA objective was used to optimize the light collection of the setup. Due to the use of oil which induced a certain ’messi- ness’ to our setup, the 1.4 objective was used during the final stage to collect more light. The 10x magnification objective with 0.25 NA was merely used as a detection lens to focus the light onto the pinhole.

4.2.3 Optical fibers Optical fibers are flexible cylindrical dielectric strings that offer a practical and adequate means to transmit light from one end to the other. They con-

1I.e., when air is ﬁlling the space between the cover glass and the objective. 4.2 Optical components 45

Objective types #1 #2 #3 #4 Numerical aperture 1.4 0.9 0.75 0.25 Immersion oil none none none Magniﬁcation 100x 100x 100x 10x Working distance [mm] 0.17 0.31 4 10.6 Field of view [mm] 25 25 25 22 Parfocal length [mm] 45.06 45 45 45.06 Cover glass thickness [mm] 0.17 - - - Manufacturer Zeiss Zeiss Zeiss Olympus

Table 4.1: Comparison of the objective types used in our confocal microscopy setup. sist of a transparent core typically made of glass or plastic surrounded by a cladding layer. Because the refractive index of the core is greater than the refractive index of the cladding, the optical fiber is able to support the propagation of light along its axis within the core through the principle of total reflection, thereby acting as an efficient light waveguide. Optical fibers come in two types: single-mode fibers (SMFs) and multi-mode fibers (MMFs). As the name indicates, in an MMF, light waves are dispersed into various propagation paths such that many transverse modes are supported, while only a single transverse mode is supported in an SMF. This is due to the physical difference in inner core diameter between the two types, with the MMF being significantly wider than the SMF. Typical diameters of MMFs are in the order of 50 µm, whereas they are in the order of a few microns for SMFs. An SMF only allows one mode with a Gaussian profile to propagate through the core, which is ideal for coupling and guiding the propagating Gaussian laser beam, and ensure beam Gaussianity throughout the optical path of the setup. Com- pared to an MMF, coupling light into an SMF is a much more challenging task. Therefore, in our experiments, MMFs were used at the end stage of the HBT setup to couple as many photons as possible to the detectors and when spatial filtering was no longer necessary.

4.2.4 Other optical components It is also necessary to mention a few often neglected but yet important components of both the CM and HBT setup, namely the dichroic mirror and the beamsplitter. While the dichroic mirror, also referred to as an interference filter, selectively separates light by transmitting a limited color spectrum while reflecting a different color, the beam splitter splits the incident light beam into two light beams. The dichroic mirror used in our setup was a long-pass fil- 46 Confocal Microscopy ter with a cut-off wavelength of 550 nm. Placed at an incident angle of 45◦ to the incoming light, it is highly reflective below the cut-off wavelength but highly transmissive for larger wavelengths, leading to a reflection of the 532 nm green light and a transmission of the 637 nm red light. A similar dichroic mirror was used in the red setup designed with a cut-off wavelength of 715 nm, thereby reflecting the 689 nm light beam and transmitting the 780 nm beam. The beam splitter constitutes a crucial part of the HBT setup and it is commonly formed as a cube made of two triangular glass prisms glued together at their base. The thickness of the resin is designed so that it will reflect half of the incident light and transmit the other half due to frustrated total internal reflection.

4.3 Optical considerations and design requirements 4.3.1 Light diffraction and resolution As mentioned above, an essential feature of CM is that the illumination is reduced to a point source. Besides the quality of the laser beam, the spot- formation ability is highly determined by the optical lens system. Since the objective is the dominating element in any microscope system, we will focus our attention on its properties when considering the resolution in general. Typically, the resolution of any optical imaging system is restricted by misalignment and aberrations produced by imperfect lenses. However, not even in an aberration-free imaging system with homogeneous illumination using the highest quality objective lens would it be possible to produce a true single point. Due to diffraction, the light from a point object will somewhat spread after passing through the finite circular aperture of the objective and produce a ’bullseye’ pattern extending to a larger area instead of a point, with a central bright circular disk known as the Airy disk which, together with a series of surrounding dimmer concentric rings, is referred to as Airy pattern, as illustrated in Figure 4.4. Consequently, the diffraction places a limit on the maximum (lateral) resolution of any optical system. Since the diffraction rings are too weak to affect the obtained image, it is the angular spreading of the first minimum from the aperture that causes the blurriness of the image. The Airy pattern is quan- titatively described as an intensity distribution by the point spread function (PSF). The PSF is a 3D function that maps the dimensional intensity distribution along the optical axis z and is mathematically expressed as a first-order 4.3 Optical considerations and design requirements 47

Figure 4.4: Illustration of the Airy pattern created by a point source.

Bessel function2. The narrowest cross-section of the 3D PSF is what is referred to as an Airy disk, with about 84% of the total energy being confined to the central disk. The radius of the Airy disk is defined as the resolution element (resel) usually termed one Airy unit (AU), and is useful for determining an appropriate pinhole size. When discussing the resolution, another definition is used by the microscopy community to quantify the intensity distribution area within the Airy disk, i.e., the full width at half maximum (FWHM), where the intensity drops to half of the maximum value. The FWHM is generally preferred because it does not require any prior knowledge of the functional form of the collected data and as such can easily be measured on any signal by determining the point where the intensity drops to 50 %. In the following, any equations with reference to the PSF will refer to the FWHM of the intensity. In terms of the FWHM, the radius of the Airy disc is then given by [83]:

λ R = 0.51 . (4.3) Airy NA

2Given the optical units ρ = (2πrNA)/λ and ξ = (2πzNA2)/(nλ), where r is the radial distance in the image plane and z the perpendicular distance, a common approximation of the PSF is 2 2 2J1 (ρ)/ρ for ξ = 0 [76]. 48 Confocal Microscopy

The radius of the diffraction-limited focus spot is only determined by the wavelength λ and the NA of the objective. Thus, the single-point resolution can be improved by either increasing the NA of the objective or by using a shorter wavelength.

Resolution of a conventional wide-ﬁeld microscope

When examining two equally bright points separated by a distance ∆xlateral, they are considered to be resolved if the separation distance is equal or larger to the radius of the Airy disk, i.e., if [80, 84]

λ ∆x ≥ 0.51 em , (4.4) lateral NA where λem is the emission wavelength. This is known as the Rayleigh criterion and is an approximate relation based on the assumption that two source points are distinguishable if a reasonable dip between the two peaks is visible. The dip was deﬁned by Rayleigh to be 26% of the maximum intensity [85]. Eq.(4.4) is used to determine the maximum lateral resolution of conventional wide-ﬁeld microscopes. Since the best objectives have typical NA values of around 1.6, as a rule of thumb to determine the best obtainable lateral resolution of a microscope, the resolution is approximately equal to the wavelength of the light source. Thus, the best obtainable resolution of a conventional microscope is around 200 nm. The axial resolution, which shows an ellipsoid geometry, is given by [80,84]

λ ∆z ≥ 1.77 em . (4.5) axial NA2 Resolution of a confocal microscope In CM, the total three-dimensional PSF is composed of both the point illumination intensity point distribution PSFill and the detection intensity point distribution PSFdet , and can be expressed as a product of the two distributions [80]:

PSFtot (x,y,z) = PSFill(x,y,z) × PSFdet (x,y,z). (4.6) This means that the confocal microscope generates two point images: one by point illumination onto the object by the objective lens, the second by detection of the same projected point of the object into the image space through a ﬁnite pinhole. With the same Rayleigh criterion in mind, i.e., a 26% dip in intensity between two adjacent points, it can be shown that the lateral resolution is reduced to [76]

λ ∆x ≥ 0.37 ex , for PH < 0.25AU. (4.7) lateral,CM NA 4.3 Optical considerations and design requirements 49

It is worth noting that, while the lateral resolution in wide-field microscopy is determined by the emission wavelength, for CM, it is solely determined by the excitation wavelength. Eq. (4.7) was solved for the case where the pinhole (PH) diameter was assumed to be "infinitely" small or close to zero (in reality, PH < 0.25 AU), where PSFdet is approximately similar in size to PSFill. But, in practice, the pinhole diameter cannot be "infinitely" small. On the other hand, if we consider a very large pinhole diameter (PH > 1 AU), PSFdet PSFill, and Eq. (4.7) can be written as

λ ∆x ≥ 0.51 ex , for 1AU < PH < ∞. (4.8) lateral,CM NA Since the pinhole is much bigger than the Airy unit, it is not surprising that the lateral resolution in Eq. (4.8) seems to be similar to the resolution obtained for a conventional microscope through Eq. (4.4). However, there is still a slight gain in resolution by a factor (λem/λex) via the Stokes shift. Consequently, for a pinhole size between 0.25 and 1 AU, the value 0.37 in Eq. (4.7) must be substituted with a corresponding value between 0.37 - 0.51. For the axial resolution, a perpendicular cut through the PSF only yields a modest improvement of the measured resolution, which can be expressed as [76]

0.64λ¯ ∆zaxial,CM ≥ √ , for PH < 0.25AU, (4.9) (n − n2 − NA2) ¯ where n is the refractive index of the√ immersion medium and λ is the mean 3 ¯ wavelength roughly given by λ = λemλex. Also, here, Eq. (4.9) is valid for the case where the pinhole size is ’inﬁnitely’ small. Depending on the selected pinhole size in the range from 0.25 to 1 AU, the value 0.64 in Eq. (4.9) must be substituted with a corresponding value between 0.64-0.88.

4.3.2 Optical sectioning and pinhole size Although CM does not offer a considerable increase in axial resolution compared to conventional wide-ﬁeld microscopy, it is the confocal approach with the ability of optical sectioning that is considered as the true effective resolution and consequently the strength of a confocal microscope. The optical sectioning is determined by the pinhole dimension and its effectiveness is deﬁned as the rate at which the detected intensity drops off in the axial direction [80]. According to Eq. (4.6), the total probability of detecting an intensity event at both the point illumination in the specimen plane and at the detection pinhole for light originating from an Airy disk is PSFtot (x,y,z) = √ 3 ¯ = √λemλex A more accurate expression is λ 2 2 2 . λem+λex 50 Confocal Microscopy

0.84 × 0.84 = 0.656. Note that, because the individual probability is smaller than unity, the total probability is consequently always PSFtot (x,y,z) < 1. The remaining 16% light intensity originating from the concentric rings have a probability of PSFtot (x,y,z) = 0.026, which is around an order of magnitude lower compared to light from the Airy disk. The probability is, for instance, even worse for a spot with an initial intensity of 1%, with a final total probability of 1 · 10−4. These estimations illustrate the strength of the confocal optical sectioning by clearly demonstrating how the detection of any signal originating from an out-of-focus image will drop dramatically the farther away (laterally) the point is from the focal point. In light of these considerations, it is tempting to think that using a pinhole with the smallest possible size is the most sensible approach to improve the resolution and the confocality. However, by reducing the pinhole size, the amount of signal arriving at the detector is also reduced. Since the background noise is either less affected by the confocal effect or constant, this will in general result in a decreased signal-to-noise ratio. Increasing the excitation intensity is an option to boost the weak reduced fluorescent signal, but only to a certain extent, since a too high intensity might have a damaging effect on the fluorescent sample. Furthermore, it has been shown that decreasing the pinhole size below a diameter corresponding to the first minimum of the Airy disk, no significant improvement of the optical sectioning is achieved [76, 81, 86]. Therefore, a pinhole of 1 AU is considered to be the optimal compromise between signal strength and confocality. Therefore, in the following, we will aim for a pinhole size that is approximately the size of the Airy disk. The pinhole size can be determined by multiplying the magnification power of the microscope with the radius of the Airy disk. Since the microscope magnification is mainly determined by the objective Mob j, the radius of the pinhole is given by

Rpinhole = Rairy × Mob j. (4.10) As shown above, the selected pinhole size will also affect the expected confocal resolution. Since we are aiming for a pinhole size around 1 AU, we estimate the lateral resolution to be equal to the radius of the Airy disk so that the equal sign of the inequality Eq. (4.8) applies

λ ∆x = 0.51 ex , for PH = 1AU. (4.11) lateral,CM NA For determining the axial resoltuion, Eq. (4.9) is adapted accordingly and can now be expressed as

0.88λex ∆zaxial,CM = √ , for PH = 1AU. (4.12) (n − n2 − NA2)

To conclude the resolution and pinhole size discussion, let us examine the 4.3 Optical considerations and design requirements 51 expected optical performance of our setup by inserting some typical values. Assuming a pump laser with a wavelength of λ = 532 nm focused by an oil objective with an NA value of 1.4, we find that the radius of the Airy disk is 190 nm, which, according to Eq. 4.11, is the estimated value for the lateral resolution as well. Thus, the Airy disk radius of around 200 nm defines the maximum lateral resolution of our confocal setup. Similarly, we calculated the axial resolution to be ∼ 450 nm compared to the ∼ 570 nm obtained for the conventional microscope, which is an improvement by approximately 30%. Using the same oil objective with a magnification strength of Mob j = 100, we calculated the appropriate pinhole size to be around 20-30 µm. The calculated resolutions and a comparison between CM and WF for different light sources are given in Table 4.2. Although CM offers a slightly better resolution, it was not our main concern to improve the resolution for observing the defects but rather to selectively excite and optimally collect their photon counts. Since our defects are nanosized and their density can be easily controlled, making them somewhat easy to isolate, it is the optical sectioning ability and filtering of the defocused light that we were interested in4.

Oil objective (NA=1.4)

Pump Laser ∆xlateral ∆zaxial

λex CM WF CM WF 532 194 233 454 578 689 251 280 571 704

Table 4.2: Calculated resolutions (in nm) for two different light sources (ND:YAG and diode laser) with wavelengths of 532 and 689 nm, respectively. The lateral and axial resolution values of our confocal microscope were estimated for PH ∼ 1 AU and compared with the resolution performance of a conventional wide-ﬁeld microscope with the same oil objective. Since PH ∼ 1 AU in our case, we assumed that Rairy ∼ ∆xlateral ∼ Rpinhole × Mob j.

4.3.3 The optical fiber as a pinhole Typically, a metallic plate with a drilled hole, or slit, is used as a confocal pinhole. However, a proper alignment of the micron-sized pinhole is both a challenging and time-consuming task. An alternative and popular approach [87, 88] is to replace the conventional pinhole with an optical fiber and use a coupling lens to focus the light onto the fiber. More specifically, the SMF

4It is encouraging to notice that there is an important difference between the resolution and the ability to locate the position. For a tiny and isolated fluorescent object, the position can often be determined with a precision better than the resolution. 52 Confocal Microscopy and the coupling lens are arranged in a mounting system so that the focal distance of the lens can be easily fine-tuned with a micrometer screw allowing for an optimal coupling to the fiber. Besides offering both adjustment flexibility and stability in alignment, the SMF supports only a single propagation mode for a given wavelength due to its relatively small transmitting core size. Hence, the core serves as both an efficient pinhole blocking out-of-focus light and as an effective spatial filter suppressing other modes than the fundamental mode. The radius of the transmitting core of the SMF used for our setup was around 2.3µm. Above, we calculated that, in order to satisfy the requirement of a pinhole size of 1 AU for our setup, the appropriate pinhole radius has to be around ∼ 20 µm. Thus, we used an objective with 10x magnification as a coupling lens in order to focus the diffraction-limited spot to a radius of ∼ 2 µm and adequately match it to the fiber core. Although conventional pinholes with sizes varying from 15 to 50 µm were initially used in our confocal microscope setup, the experiments presented in the following sections were all performed with the SMF used as a pinhole, since this proved to be the most suitable approach.

4.4 Detection and control electronics 4.4.1 Detection and readout software For our confocal microscope, we used single-photon avalanche diodes (SPAD5) with silicon photon detectors. Basically, the SPAD exploits the photoelectric effect where the incident light, during its interaction with the atoms in the photo-cathode, releases electrons, which consequently triggers the release of even more electrons in the multiplication region, thereby generating an avalanche effect. Due to the avalanche effect, the incident photon can be detected by an electronic circuit. The SPAD is operated in the Geiger-mode which allows a biasing of the SPAD above the breakdown voltage in order to achieve this high gain and to detect single photons. Subsequent to the avalanche effect, an active quenching circuit is used to reduce the excess bias voltage below the breakdown voltage and eventually restore the voltage level. This cycle is known as the pulse dead time in which the detector is unable to detect any incoming photons. The dead time of an SPAD is around 50 ns. During the metastable state, due to thermal excitation, spontaneous avalanches can occur in the detector. These are random and referred to as dark counts. Dark counts are deﬁned more thoroughly in section 7.2.3. For now, we think of them as false detection events occurring at a later time of the SPAD’s operational stage. The used SPAD detectors

5SPCM model with the fiber connection option from PerkinElmer. 4.4 Detection and control electronics 53 had dark count rates around 100 cps. Furthermore, the detectors showed a detection efficiency of around 65% at a wavelength of 640 nm and a slightly lower efficiency at a wavelength of 780 nm.

4.4.2 Positioning systems and scanning software The main requirement for a scanning system in a confocal microscope is a fast and high precision positioning with steps in the sub-micron range. Typi- cally, in most confocal microscopes, a high scan rate is achieved by moving the laser beam spot rather than the object. However, the simplest and most advantageous way to scan the object is to move the object and leave the rest of the optics permanently fixed. We applied both approaches in our confocal setups. More specifically, the object was moved when using the green CM setup while it was the beam spot that was moved when using the red CM setup. Hence, two different positioning systems were used. For the green setup, a 3D Jena TRITOR series piezo-nanopositioning system with dimensions of 40 mm × 40 mm × 34 mm was used and mounted on another micrometer-stage for rough adjustments. The 3D-piezomotors had a motion range of 80 µm in closed loop control with a resolution of 2 nm (only limited by the noise of the power amplifier) and a typical repeatability of 20 nm per axis. For the red setup, the arrangement of the positioning system was slightly different. The x- and y- piezo positioners were replaced by a steering mirror mounted before the objective. The mirror was mounted on a 2D tilting piezo positioner with a motion range of 1.6 milliradians (mrad) in both the x- and y-axis, resulting in a limited sample scan area of 5 µm × 5µm. The resolution of this setup is 0.04 µrad and the typical repeatability is 1.1 µrad. To also scan in the z-direction, the object remained mounted on the z-axis piezo positioner. The optical arrangement of this setup will be discussed in more detail in section 4.5.2. A scanning program was written in order to control the scanning systems while recording the detected counts. Moreover, the scanning program can scan in one, two or three dimensions while visualizing the obtained data in real time.

4.4.3 Auto-correlator and coincidence unit As discussed in section 2.2.1, a device that is able to measure the time difference between two incoming signals and store their counts, a so-called auto-correlator, is essential for intensity correlation measurements and consequently for the detection of antibunching. For our single photon source setup, we used the PicoQuant PicoHarp 300 time-correlated single photon counting (TCSPC) correlator module with a resolution of 4 ps and two 54 Confocal Microscopy identical but independent input channels. The first channel was triggered by one SPAD signal. The second channel was connected through a delay line to another SPAD detector. This way, when a signal is received from the detector on the first channel, an internal timer is triggered, which is stopped as soon as a pulse from the second channel is received. The use of a delay line allows to monitor events detected prior to the trigger event. When scanning over a certain time period, the recorded time differences are stored in a certain time slot and the resulting statistical data can be displayed as a correlation function proportional to the normalized temporal second-order correlation function for a classical single-mode, as defined by Eq. (2.1). When the CM setup was not connected to the HBT setup and the correlator, a self-built electronic counter unit, also referred to as a coincidence unit, was used for mere basic photon counting purposes during confocal calibration and scanning. The self-built6 coincidence unit was built on a Xilinx XC4VSX35 on a ML402 Evaluation board. The used unit had 8 input ports in the form of BNC connectors for coaxial cables and was connected to the computer.

4.5 Implementation and experimental setup 4.5.1 The green confocal setup Confocal microscope Oversimplified diagrams of CM systems often ignore the numerous additional optical components that are needed and used to properly guide and shape the beam along the entire optical path. Figure 4.5 is a more accurate representa- tion of the implemented self-built green confocal microscope setup utilized to produce single photons. By following the optical path, the purpose and contribution of each component is given. To start with, the beam quality of the illumination light is ensured by coupling the green laser beam from the Nd:YAG laser to an SMF using a coupling lens7 (CL1), thereby delivering a laser beam with a Gaussian profile, which is then collimated by the second coupling lens (CL2) into a diffraction-limited beam. Besides, the fiber coupling also serves as a knob by which the light power can be adjusted, and allows to swap between different laser sources without affecting the alignment. A green bandpass filter centered at around 532 nm with a bandwidth of 18 nm was placed after CL2 to ensure that only the 532 nm beam is transmitted while blocking any other frequencies, such as the second harmonic 1064 nm

6The coincidence unit was built and developed for the planned study of Rabi oscillations and for other studies and experiments within our group. 7The coupling lens is also referred to as a collimator lens and comes in a package pre-designed and aligned to fit with the SMF connector and to collimate light from the fiber. For both CL1 and CL2, we used a Thorlabs F220APC-532 lens with an NA of 0.25 as fiber collimator. 4.5 Implementation and experimental setup 55

Figure 4.5: The green confocal microscope setup (top) and the telescope conﬁguration (bottom) expanding the incoming beam with a factor of f2/ f1.

frequency. Hereafter, the laser beam is expanded by a pair of lenses (L1 and L2) with different focal lengths forming a telescope, also known as a beam expander. The principle of the beam expander is illustrated in Figure 4.5. By expanding the beam radius, the whole lens pupil at the rear of the objective is filled, thereby effectively increasing its NA value and allowing the beam to reach its diffraction-limited performance. The green light is reflected by a dichroic mirror (DM1) and guided into the objective, which then focuses the light into a diffraction-limited spot on the sample. The red light emitted from the sample is then collected by the same objective, transmitted through DM1 and then passes through two additional dichroic mirrors (DM2 and DM3). These serve as filters that effectively clean the emitted red light from any green light that was not blocked by DM1. The red fluorescence light is coupled to a single mode fiber (SMF2) by an objective (0.25 NA and M10x) that serves as a coupling lens (CL3). On the same mount, but just before CL3, a long-pass edge-filter with a cut-off wavelength of 632 nm was placed to ensure that nei- 56 Confocal Microscopy ther scattered light nor reflected red light is coupled into the optical fiber. The red light from the SMF was fed to the detector (SPAD), and for each detected photon a pulse is produced by the SPAD and fed into the coincidence unit. The counts from the coincidence unit are reported to a computer for analysis. Af- ter each successful detection operation, a scanning software stores the counts and moves the 3D stage on which the sample is mounted. In the setup, SMF2 serves as the actual pinhole, whereas PH1 and PH2 are pinholes merely used for the initial alignment. Furthermore, for a proper alignment, L2 is placed on a single-axis translation stage to carefully match its focal point to that of L1. Apart from CL3, all other couplers are mounted on a two-axis translation stage and two-axis rotation stages to enable beam alignment. CL3 is mounted on a three-axis translation stage to optimize the coupling to the SMF. Other (regular) reflecting mirrors to guide the beam (not shown in the schematic) are all mounted on two-axis rotation stages. While it is the beam expander configuration that allows the system to operate in the confocal mode, the microscope can be switched to operate in conventional mode by inserting both a flippable lens (L3) and a mirror (M1) into the beam path. L3 narrows the incoming beam so that a smaller fraction of the objective’s lens pupil is filled, resulting in a wide-field illumination of the sample, wheras M1 reflects and guides the collected collimated image onto a lens (L4) that projects a focused image onto a CCD camera instead of the pinhole. Both L3 and L4 are mounted on single-axis translation stages as well, so that both the objective and the camera can be located at suitable focal lengths.

Hanbury Brown-Twiss setup For the antibunching detection experiments, SMF2 in Figure 4.5 was connected to the HBT setup instead of the detector, as illustrated in Figure 4.6. The incoming beam is thereby split in two by the beamsplitter and both beam arms are directed into the coupling lenses CL4 and CL5 and coupled to MMFs connected to the SPADs.

Calibration and testing After assembling and aligning the setup, the photon detection through the entire green confocal microscope setup was optimized. Then, highly fluorescent samples8 emitting photons at a wavelength of around 655 nm (when pumped with the green light) were used to simulate the emission from NV-emitters. Because of the high fluorescence, the emission from the sample offered high count rates, making it ideal for the fine alignment and for further optimizing the coupling of the photons into the confocal detection stage. Subsequent to the calibration stage, the performance of the confocal microscope was tested using samples with simple periodic micron line structures for

8Either Qdots from Invitrogen or Rhodamine 6G were used. 4.5 Implementation and experimental setup 57

Figure 4.6: The Hanbury Brown-Twiss setup based on the conceptual schematic illustration in Figure 2.1.

imaging. With the repetitive structures covering the entire surface, the patterns can be easily identified, making them an optimal sample for testing. The microscope was initially operated in the conventional wide-field mode, with L3 and M1 inserted, and the wide-field image was monitored with the CCD camera. The focus of the image was determined by manually moving the piezo positioner along the z-direction, after which the optimal focus position was recorded. The system was then switched to confocal mode (by removing L3 and M1 from the beam path). By fine scanning around the recorded z-position, a sharper focus was obtained and kept throughout the test. A 2D scan of the sample was hereafter performed in confocal mode. Figure 4.7a shows an image of a confocal scan of a sample with 2 µm thick line structures and a spacing of around 20 µm. The ’Z’ value given above the image indicates the focus position of the performed scan. The color scaling on the right refers to the recorded photon counts per second. Since the detected photons are from reflection, the laser power is adjusted accordingly for each sample to achieve a useful count rate. Thus, the counts are rather arbitrary and should not be compared for different test scans. Compared to an image of the same sample recorded on a scanning electron microscope (SEM), shown in 4.7b, the confocal scan yielded a high-quality image comparable to the SEM micrograph, revealing not only similar line structures but even sub-micron dark-edged structures and the wavy landscape of the sample. In order to test the ability of the confocal microscope to resolve yet finer and more closely spaced line structures, we used a grating with a periodicity of 700 nm as a scanning sample. The obtained image is shown in Figure 4.8a. For comparison, an image was also taken with a conventional microscope, which is shown in Figure 4.8b. Al- 58 Confocal Microscopy though able to resolve the sub-micron structures in good quality as predicted by theory, the image is not so sharp due to the used objective with a relatively low numerical aperture (0.75 NA) and as such, the resolution was compromised. However, this is not of concern since this is compensated for during the antibunching measurements by using the oil objective.

Figure 4.7: a) A confocal scan image of a sample with 2 µm thick etched line structures and a periodicity of around 20 µm. The 80 µm × 80 µm scanned area was scanned with a dry objective (0.75 NA), in steps of 0.5 µm, resulting in a total scan duration of around 7 hours. b) and c) For comparison, SEM micrographs of the same sample at two different magniﬁcation factors. 4.5 Implementation and experimental setup 59

Figure 4.8: a) A 20 µm × 20 µm confocal scan image of a grating with a periodicity of 700 nm recorded in steps of 50 nm resulting in a total scan duration of around 45 hours. b) An image of the same grating taken with a conventional wide-ﬁeld microscope for comparison.

4.5.2 The red confocal setup After construction and testing of the green confocal setup, we initiated an attempt to build a confocal microscope utilizing a red source (689 nm) to excite the nickel- or silicon-vacancy centers with an emission spectrum in the range from 780 to 800 nm. This setup is very similar9 in design and operation

9This implies replacing the necessary optics, e.g., the optical fibers, and the dichroic and coupling mirrors, with anti-reflection coatings suitable for the red light. 60 Confocal Microscopy to the green setup, except for the employed x- and y-translation stages. Figure 4.9 shows a schematic illustration of the self-built red setup. As described earlier, for reasons of speed, the x- and y-translation stages were replaced by a tilting x-y mirror mounted before the objective, thereby enabling a movement of the beam spot instead of the object. However, this is not a straightforward process and requires a special optical design consideration. In order to be able to change the position of the focused spot on the object (i.e., to move the beam), we need to change the direction of the incoming beam, i.e., the beam has to enter the rear of the objective at an incident angle. However, merely using the tilting mirror to direct the inclined beam onto the objective is not sufficient. Doing so will introduce a displacement so that the beam will hit a different spot on the rear of the objective for each tilting step, resulting in an arbitrary beam movement. In order to account for the induced displacement and to ensure that the incoming beam is hitting the exact same spot of the objective’s rear pupil, we used a configuration with two sets of correction lenses with similar focal lengths f = f3 = f4 = 250 mm, as shown in Figure 4.10. By placing L5 at a distance f from the two-dimensional tilting mirror and L6 at the same distance from the objective, we ensure that, while the beam enters at a different incidence angle, it will still hit the same spot - at the center - of the objective. Although the correction will work regardless of the distance between L5 and L6, the distance must be equal to the sum of the focal lengths of the two lenses, i.e., 2 f , to guarantee a collimated beam after the correction lenses. Next, in order to calculate the distance the beam moves during each tilting step, let us examine the trigonometry of the incident beam and its final spot location on the sample in Figure 4.11. Here, we treat the objective as a simple lens and consider two incoming beams forming an angle θ, hitting two spots a distance dtilt apart. According to this simple geometry, the relation between the distance dtilt and the angle of the incoming beam is given by

dtilt = fob j tanθ ≈ fob jθ, (4.13) where fob j is the focal length of the objective. We know from basic optics that when rotating a mirror by an angle β, the incident beam is deﬂected by an angle 2β. Thus, when rotating the mirror by an angle θtilt , Eq. (4.14) can be rewritten to express the distance the spot moves in terms of the angular motion of the tilting mirror as

1 d = f θ . (4.14) tilt 2 ob j tilt

It is apparent that the distance dtilt is determined by the used objective. For the objective used in the setup with fob j = 0.31 mm (0.9 NA) and considering 4.5 Implementation and experimental setup 61 the maximum angle of 1.6 mrad of our xy-piezo stages, we obtain a limited scanning area of approximately 5 µm × 5 µm.

Figure 4.9: Schematic illustration of the red confocal microscope setup.

Figure 4.10: Schematic illustration of the setup with the two correction lenses with similar focal lengths.

Figure 4.11: Illustration of the relation between the incident beam and the location of the illumination spot. 62 Confocal Microscopy

Calibration and testing The calibration and testing procedures and steps for the red setup are similar to those described above for the green confocal setup. To test the performance of the confocal microscope, we used a grating with a periodicity of 1507 nm. Figure 4.12 shows an image of a confocal scan of the grating clearly revealing the structure of the grating. The observed unsharpness of the image is due to the used objective with the relatively low numerical aperture (0.75 NA).

Figure 4.12: A 5 µm × 5 µm confocal scan image of a grating with a periodicity of 1507 nm.

4.6 Beyond confocal microscopy - STED microscopy As discussed in section 4.3.1, the diffraction of light poses a fundamental limit to the resolution of a confocal microscope (or any other imaging system in general). The diffraction limit, given by Ernst Abbe’s formula (Eq. (4.3)), prevents the existing confocal microscope from reaching a lateral resolution below a fifth of a micrometer, thereby obstructing the operator from both imaging single NV centers and addressing individual electronic spins separated by distances smaller than the diffraction limit. A technique that allows to bypass the diffraction limit and the individual optical localization of NV centers, as well as the manipulation of single electron spins with a nanoscale resolution was provided with the introduction of stimulated emission depletion (STED) microscopy [89,90]. The concept behind the STED microscope was first pro- 4.6 Beyond confocal microscopy - STED microscopy 63 posed and experimentally demonstrated by Stefan W. Hell in 1999 [91, 92], for which he was awarded the Nobel Prize in Chemistry in 2014. Essentially, a STED microscope requires the same components as a confocal microscope. However, instead of using only one laser (for excitation), the STED microscope requires two lasers, as shown in Figure 4.13a. While the first laser (excitation laser) allows for the excitation of the fluorescent sample, the second laser (STED laser) depletes it, thereby canceling out the fluorescence in the overlapping regions while leaving a zero-intensity mode active to emit fluorescence. The zero field at the focal point can be generated by placing a phase modulator in the path of the depletion laser beam to create a doughnut-shaped beam pattern.

4.6.1 Principle of operation As the name indicates, the principle of operation of STED microscopy is based on a depletion due to a stimulated emission. In principle, fluorescence occurs when a fluorophore, after excitation to a higher energy state, spontaneously relaxes to the ground state by emitting a fluorescence photon. This process can be interrupted before the photon is released by adding a depletion beam that induces a stimulated emission process. In this process, the depletion photon is absorbed by the fluorophore at the excited state, which then relaxes to the ground state by releasing two photons with the same wavelength as the depletion photon, as illustrated in Figure 4.13b. Thus, by inducing a stimulated emission, the depletion beam ultimately suppresses the fluorescence because the electrons are quenched back to the ground state by the STED pulse. Due to vibrational relaxation, the wavelength of the released photon is always red- shifted and thereby allows to distinguish between excitation and depletion photons. Hence, the wavelength of the photons created due to the stimulated emission can be controlled to be significantly different from the excitation wavelength. The tail of the emission spectrum is usually the preferred choice in order to prevent an interference of the absorption and emission lines. The time delay between the two laser pulses is also relevant since it must be ensured that every depletion pulse immediately follows an excitation pulse. Moreover, the pulse length of the depletion beam has to be shorter than the lifetime of the excited state of the fluorophore, but longer than the pulse length of the excitation laser. To ensure that the inhibition of the fluorescence only occurs in the periphery region and not at the center of focus, the STED beam has to possess a zero-field node at the center of focus with exponentially increasing intensity, reaching a maximum in the periphery. A common technique to achieve this intensity profile is to use the vortex phase plates for engineering a doughnut- shaped wavefront. The vortex phase plate is composed of spiral phase steps, 64 Confocal Microscopy

Figure 4.13: a) Illustration of the STED setup featuring a depletion laser and a phase modulator as the essential additional parts compared to a confocal microscope. Simu- lation of the produced PSF of the laser beams (inset). The excitation laser beam (green) is superimposed on the doughnut-shaped depletion laser beam (red) thereby producing the effective PSF, where the laser beam size is dramatically reduced. b) Comparison of the energy diagrams for confocal (ﬂuorescence through spontaneous emission) and STED (depletion through stimulated emission) microscopy. The dashed short arrows represent the non-radiative relaxations.

and by varying its thickness to produce a winding staircase structure, it determines the phase of the transmitted beam. Speciﬁcally, after being tuned into a linearly polarized beam by passing through a half-wave (λ/2) plate, the phase of the Gaussian beam impinging on the spiral phase plate will continuously change from 0 to 2π in the angular direction. By subsequently passing through a quarter-wave (λ/4) plate, its polarization will change to circular polarization before passing the objective lens. As a result, the beams will cancel each other at the focal point where a zero ﬁeld will appear at the center of the focus surrounded by a doughnut-shaped illumination pattern. 4.6 Beyond confocal microscopy - STED microscopy 65

The increase in STED resolution is proportional to the power of the depletion laser. Particularly, by increasing the STED pulse intensity above a certain threshold level, the depletion becomes complete as the stimulated emission fully dominates the spontaneous emission. This leads to a complete deacti- vation of the fluorescence in the periphery, effectively narrowing down the doughnut hole with the focal fluorescence remaining unaffected, thereby over- coming the diffraction limit. A simulation of the produced focal point is shown in Figure 4.13a. The lateral resolution has been reported to reach values down to ∼ 3 nm [93]. Thus, by overlaying the STED doughnut-shaped beam with the Gaussian excitation beam profile, we can achieve a sub-λ resolution. To account for the sub-λ resolution achievable with STED, Abbe’s equation must be modified to

λex D = q , (4.15) 2NA 1 + ISTED Isat where λex is the excitation wavelength, ISTED is the intensity of the STED laser pulse, and Isat is the saturation intensity of the ﬂuorophobe. While STED microscopy offers super-resolution in the lateral direction, the axial resolution does not change compared to confocal microscopy.

4.6.2 Implementation Since we are mainly concerned with sub-diffraction spin diffraction and the control of the NV center, we combined optical spin polarization techniques with the STED approach. More specifically, by optically illuminating the NV center with a doughnut-shaped beam just before the spin readout, the spins located in the doughnut region are re-polarized whereas those in the zero- intensity field at the center of the beam, separated only by few nanometers, remain unaffected. While this technique enhances the spatial resolution, it also allows for a selective manipulation of the spins within the zero-field (the doughnut center). This STED-related approach is commonly referred to as the spin-RESOLFT10 technique and was first introduced by P. C. Maurer et al. [90]. Figure 4.14 shows our implemented setup, where we modified the green setup by adding an STED laser with a wavelength of 532 nm and a vortex phase plate11 with a topological charge12. In order to prevent a distortion of

10RESOLFT stands for ’reversible saturable optical linear ﬂuorescence transitions’ and is considered an adaptation of the STED approach based on enabling ﬂuorophobes with at least two distinguishable states to be reversibly switched on and off. 11Procured from RPC Photonics, Inc. 12The topological charge refers to the number of 2π cycles printed around a 360 degree turn of the surface. m=1 if one staircase cycle covers the entire 360 degree turn. 66 Confocal Microscopy

the doughnut center caused by the focusing objective, a quarter-wave (λ/4) plate was placed just before the objective changing the polarization of the beam to circular polarization. The independent switching of both beams was ensured by using acousto-optic modulators (AOM13). Although the setup is only a prototype and its performance has yet to be tested, the detailed characterization of the setup could prove useful for the future identiﬁcation of individual emitters and the manipulation of single electron spins with a nanoscale resolution.

Figure 4.14: a) Spin-RESFOLT setup utilizing two green lasers (532 nm); one with a Gaussian mode proﬁle, the other serving as an STED laser thereby providing a doughnut-shaped beam. Both beams are combined at a polarized beam splitter (PBS) before passing through a λ/4 plate and onto the objective. b) Spin manipulation and readout sequence where the spin state of the NV center is initially prepared into the |0i state by spin-polarization via a Gaussian beam pulse, followed by microwave manipulation. The 532 nm doughnut-shaped beam is then applied, re-polarizing the outer ring into the |0i state, providing a nanoscale imaging contrast between the spins within the zero-intensity ﬁeld and those located in the doughnut region, ultimately allowing for an independent readout of the dark inner region.

13Procured from Cystal Technology, Inc. 67

5. Spin manipulation and readout setup

In this chapter, the experimental setup for the spin polarization, manipulation and readout of single spin states of the NV center is described. More speciﬁ- cally, the chapter starts with a description of the utilized microwave and magnetic resonance hardware setup, followed by a description of the double-pass acousto-optic modulator setup for controlling and modulating the incoming excitation pump. The chapter ends with a description of the complete setup, including the confocal microscope with the microwave coupling and magnetic ﬁeld control along with the timing control sequences.

5.1 Microwave and magnetic hardware setup

Ω C u C u Ω

C u C u Figure 5.1: Schematic illustration of the microwave setup consisting of both a MW and RF signal generator, switches to realize the TTL-pulsing behavior of the signal generators and amplifiers, followed by a diplexer to mix the amplified signals. In order to prevent harmful back reflections from the sample, a circulator is placed before the sample.

Figure 5.1 shows a schematic illustration of the setup used for microwave coupling and magnetic field control. The microwave setup consists of two separate signal generator sources, allowing for the generation of both radio frequency (RF) and microwave (MW) signals. More specifically, a generator1 with a frequency range of 9 kHz to 6 GHz was used for generating the MW signals, whereas a generator with an output range from 9 kHz to 3.2 GHz was used for generating the RF signals. While the zero-field magnetic resonance at the ground state occurs at 2.87 GHz, the Zeeman splitting occurs at frequencies ranging from hundreds of MHz to values larger than 3.2 GHz, depending on the applied external magnetic field Bz. Thus, the use of both

1Rohde & Schwarz SMA 100A generators were used for both MW and RF generation. 68 Spin manipulation and readout setup

MW and RF signal generators is motivated by the aim to control both transitions: |0i → | ± 1i and | − 1i → | + 1i, respectively2. High speed external switching modules (ZASWA-2-50-DR+, MiniCircuits, TTL pulse-controlled) with a rise time of 5 ns were used for fast amplitude modulation in order to allow for the pulsing of both MW and RF signals. Since the output power3 of both signal generators is low, ranging from around 60 to 250 mW, an amplified signal is necessary in order to generate sufficiently large oscillating magnetic fields Bx (> 30 Gauss) strong enough to drive the spin transitions. Thus, two separate amplifiers4 were used to amplify both the MW and the RF signals up to levels of about 25 and 30 W, respectively. Both amplified signals were then combined through a diplexer (K&L 3IZ10-1/QTC3000-0/0) before being guided to the sample. Strong microwaves were applied to the sample through the use of a planar resonator or by placing a thin copper wire (∼ 20µm) across the surface closely located to the NV centers. Experimen- tally, we observed a strength of around 3 Gauss for the oscillating magnetic 5 field Bx at an applied MW frequency of 2.85 MHz using a MW power of ∼ 8 Watt after amplification. In order to prevent back-reflections from reaching the amplifiers and causing damage, a circulator6 was used to direct the reflected power towards a 50 Ω load. Further, a termination of 50 Ω was used to close the microwave circuit. For the Zeeman splitting experiments, an external static magnetic field Bz was applied to the sample by using a permanent mag- net, mounted on a three-axis translation stage and placed a few centimeters away from the sample. The magnetic field was measured through a custom- built Hall-sensor mounted closely (<1 mm) to the sample. In addition, when the z-component of the magnetic field was aligned with the z-axis of the NV, the NV center serves as a magnetometer giving a more accurate value of the magnetic field for the Zeeman splitting.

5.2 Double-pass acousto-optic modulator setup A fast control of the off-resonant pump laser pulses and the generation of short pulses with a rise time shorter than the polarization process (i.e., shorter

2In this thesis, however, only the MW generator has been used for controlling |0i → | ± 1i. For future applications, the RF source can be used for driving the transitions | − 1i → | + 1i. 3The output power depends on the operating frequency. In general, the lower the operating frequency, the higher the power. For instance, at 900 kHz, the output power is 28 dBm (∼ 60 mW), whereas it is 24 dBm (∼ 250 mW) at 6 GHz. 4A model 25S1G4A amplifier with a frequency response (800 MHz - 4.2 GHz) was used for the MW signals, whereas a model 30W1000B amplifier (1- 1000 MHz) was used for the RF signals. Both amplifiers were manufactured by Amplifier Research. 5Under resonance conditions, the oscillating field can be expressed and calculated as a function of the Rabi frequency: Bx = ΩR/γ. 6 Model D3C2060 from DiTom. 5.2 Double-pass acousto-optic modulator setup 69 than the life time of the intermediate dark state (< 300 ns)), is essential for the spin state polarization of the NV center and readout purposes. Further- more, ensuring a strong ratio between the off and on states of the modulated laser intensity is equally important in order to prevent a re-polarization of the spin state into the ms = 0 ground state. Figure 5.2a shows the custom- built compact double-pass acousto-optic modulator (DP-AOM) setup utilized to comply with these requirements. Particularly, the AOM module (Brimose TEM 400-100-687) with a tellurium dioxide crystal used as the comprising optical element, has a rise time of 5.5 ns and was used to modulate the CW 532 nm laser. The AOM is driven by a TTL-pulse controlled frequency driver (Brimrose FFA-400-B2(100)-F1.25.) with a rise time below 3.5 ns. The rise time tAOM scales with the beam diameter d and the acoustic velocity vAOM in the modulator crystal, i.e., tAOM ∝ db/vAOM. Thus, the smaller the diameter of the incoming beam, the shorter the obtained rise time. Since the waist of a focused beam is determined by the lens focus f and the beam diameter Db prior to focus, i.e., db = 4 f /πDb, a small beam in the AOM is ensured by expanding the beam before focusing it into the AOM, as illustrated in Figure 5.2b. Hence, the laser beam is initially broadened by a telescope configuration (L1 and L2) before getting focused by L3 into the AOM. After passing the first telescope system, the collimated and linearly polarized light is rotated into a horizontal state after passing a half-wave (λ/2) plate and transmitted through a polarizing beam splitter (PBS) to the second telescope system (L3 and L4). Through a process similar to Bragg diffraction, the zero-order beam, which is simply transmitted through the AOM, is blocked by a plate, while the diffracted amplitude-modulated first-order beam is transmitted and reflected back by the last mirror (M4). The reflected beam’s amplitude is modulated by focusing the beam onto the AOM once again, with the zeroth-order beam being blocked while the first-order diffracted beam is allowed to pass. This double pass serves as a filter, eliminating the beam displacements due to con- comitant changes in frequency without compromising the rapid laser power switching and modulation. However, while the double pass configuration effectively removes the appearing beam steering, it poses another challenge of how to separate the path of the reflected beam from that of the input beam. By placing a quarter-wave (λ/4) plate before M4, the linear polarization of the light is transformed to circular after the first pass. When reflected from mirror M4, the circularly polarized light returns to linear polarization after ◦ passing the λ/4-wave plate again, but is instead rotated 90 . Thus, the double pass through the λ/4-wave plate effectively changes the beam polarization to a vertical polarization. Since the light is orthogonally-linearly (vertically) polarized with respect to the first pass, it is refracted by the PBS, thereby allowing the two beam paths to be separated. The refracted light is then coupled to a single mode fiber (SMF) which is connected to the confocal microscope. 70 Spin manipulation and readout setup

The pulse-rise time of our DC-AOM setup was measured to be approx. 18 ns −6 and the Io f f /Ion ratio was < 10 [94].

Figure 5.2: a) Double-pass acousto-optic modulator (DP-AOM) setup. The first telescope consists of two lenses, L1 and L2, with focal lengths f1 = 25.5 mm and f1 = 50 mm, respectively, whereas the second telescope consists of two lenses, L3 and L4, with equal focal lengths, i.e., f3 = f4 = 100 mm. While the first telescope system is used to expand the beam for an optimal focus into the AOM, the second telescope system both focuses the beam during the double pass and ensures a collimated output beam. The first pinhole (PH1) blocks the zeroth-order (0. order) light while allowing the diffracted first-order (1. order) beam to pass. Similarly, this applies for the second pinhole (PH2), by which the reflected zeroth-order beam is blocked whereas the first- order beam is let through. The λ/2-wave plate rotates the linearly polarized laser light into horizontally polarized (h. p.) light, thereby allowing it to get transmitted through the PBS. The beam polarization is transformed to circular by the first pass through the λ/4-wave plate and, whilst staying circular when reflected by the mirror (M4), it now rotates in the opposite direction. By a second pass through the λ/4-wave plate, the circular polarization is transformed into vertical polarization (v. p.) and refracted by the PBS and coupled into a single mode fiber. b) Beam propagation before and after the lens system illustrating the relationship between the diameters of the incoming beam and the focused beam, db = 4 f /πDb. 5.3 Integrated setup and timing control 71

5.3 Integrated setup and timing control A schematic illustration of the complete integrated setup, including the time controlling system, is shown in Figure 5.3a. Particularly, the integrated setup consists of the green confocal microscope, the microwave coupling circuit, the double pass AOM setup and, more importantly, the coincidence unit with the pulse generator as the time controlling system. The programmable pulse generator controls the entire setup with high temporal precision (with a time resolution of 5 ns), including the control of the amplitude modulation of the laser with the AOM, the microwave switches, as well as the gating and splitting of the detection counts. Together with the coincidence unit, the pulse generator is thus able to control the timing of all signals while simultaneously controlling the data acquisition timing (the counting and collection of data) and triggering the sweep of the MW signal. The pulses can be programmed in a self-written TCL (also known as TK) based interface, allowing for the design of experimental sequences with complicated timing. A typical measurement sequence is presented in Figure 5.3b. During an experiment, a laser pulse of green light with a length between 1 and 5 µs is initially generated by the AOM, through TTL pulse-triggering at the output O1, in order to prepare the spin state by spin-polarizing the NV center into the |0i ground state. A pulse from output O2 is then generated towards switch SW1, allowing a microwave pulse to be applied. It is this pulse length that can be varied and designed into various timing sequences because this is the variable that we can sweep over. To read out the spin, another laser pulse is generated at output O1 during which two pulses are generated at output O4, gating the APD by creating two florescence detection windows through switch SW3. At the same time, another pulse is generated at output O5 overlapping the second pulse from output O3, thereby causing switch SW3 to split the two measurements into two different channels on the coincidence unit. While the first recorded pulse serves as the real measurement data, the second is used as a reference. The reference measurement is recorded after a few milliseconds of laser illumination, when the microwave radiation effect is destroyed and the spin state system is polarized into |0i again. The reference signal is usually used to normalize the signal but can also be used to compensate for a reduction of the NV fluorescence due to drift in alignment or any other factors influencing the fluorescence rate. Since the voltage recorded by the coincidence unit for the pulses from the switches SW3 and SW4 is rather low, comparators are used before inputs I1 and I2. This measurement sequence is repeated a few thousand times for each point of the microwave pulse length, and the average value is then calculated. This automated timing control of all implicated signals allows not only to perform the measurement sequence for Rabi oscillation demonstration but also for the design of any experimental sequences, e.g., Ramsey and Hahn echo sequences. 72 Spin manipulation and readout setup

5 I

5 U O

5 U O I N

NCΩ 5 8 F : 0 8CC F I3U 0 U 8 F O3U 0 85 F 5 0

82ν0

Figure 5.3: a) Illustration of the complete setup including the MW and RF setup, the green confocal microscope, the double pass AOM system, and the detection setup along with the timing control system represented by the pulse generator and the coincidence unit. The black arrows represent digital signals, the grey arrows represent the MW signals, and the green and red arrows represent the green and red laser, respectively. b) Illustration of the general experimental procedure for the preparation, manipulation and read-out of the NV center. 73

6. Experimental results - NV center characterization

Having demonstrated both the performance and functionality of the confocal microscope and described the incorporated spin manipulation and readout set, we are now ready to proceed with the characterization of the NV center. The chapter is introduced with a brief description of the diamond sample preparation process, followed by a presentation of the results of the scanning of selected NV centers with the green confocal microscope setup. Furthermore, the obtained NV optical ﬂuorescence spectra are presented. The chapter concludes with a demonstration of both antibunching and Rabi oscillations.

6.1 Diamond sample preparation In order to identify isolated NV centers, various types of diamond samples with different forms, ranging from mm-sized bulky crystals, through nanosized grain powder, to slurry mixtures of diamond power and water were examined. The samples are listed in Table A.1. Besides the demanding radiation and annealing treatments required for creating NV centers in bulk diamond, another signiﬁcant limitation is the high refraction index of the material (nd=2.4), causing refraction at the interface and thereby limiting the extraction of light, as discussed in section 3.4. In principle, using nano-sized diamond powder circumvents this problem if individual nanocrystal particles containing single NV centers are provided. However, the diamond powder samples generally suffered from aggregation1 of the diamond particles and quite often required both a thorough chemical and ultrasonic treatment2 to achieve the desired single-particle dispersion. The so-called Liquid Diamond GAF3, however, proved to be the easiest sample to work with. This sample consists of a diamond concentrate suspended in deionized water. The term GAF stands for guaranteed agglomerate-free and refers to the preceding pro- prietary treatment of the sample, which ensures that all diamonds are dis-

1Due to adhesion forces, the diamond particles form agglomerates often 10 to 20 times the size of an individual particle, making them extremely difﬁcult to break up. 2A cleaning and treatment procedure used for cleaning and preparing the diamond nanopowder is described in Appendix A.2. 3Procured from Microdiamant AG [95]. 74 Experimental results - NV center characterization persed in a single-particle distribution and that the sample is free of agglomerates. More speciﬁcally, we used synthetic type-Ib monocrystalline (MSY) diamond grown via conventional high-pressure, high-temperature (HPHT) procedures with a median diameter of 50 nm and an upper limit of 90 nm. The synthetic type-Ib diamond is estimated to contain between 0.01 and 0.05 % nitrogen impurities [55]. Due to the HPHT production process, the nitrogen impurities predominantly occur in the form of single substitutional atoms distributed throughout the crystal on isolated sites of which a small fraction will trap the vacancies4 produced during the growth process. Since the lattice constant of diamond is 3.57 Å, for each single 50 nm big nanocrystal, we expect 1403 ∼ 3·106 unit cells in total. Considering the relatively low rate of nitrogen impurities and the even lower expected amount of vacancies, most of the un- treated Ib synthetic GAF single particle diamonds will contain exactly one NV center, and as such provide an apposite concentration of NV centers suitable for addressing them individually. The Liquid Diamond GAF solution was supplied with a high diamond concentration corresponding to 100 ct/kg of water5 (conc. 2%). In order to achieve the desired concentration, the product was diluted with deionized water. After several attempts, for identifying isolated dots during the scan, the appropriate concentration was found to be 0.02 ct/kg of water (conc. 0.4 per mil). The microscope cover-slip was cleaned with acetone in an ultrasonic bath prior to dispensing the diluted liquid diamond on top of it.

6.2 Confocal scans of NV centers Searching for NV-centers is typically done by initially scanning a large area. Figure 6.1 shows a typical initial 70 µm × 70µm area fluorescence scan, performed with a step-width of 200 nm, revealing many bright dots of which each is either a potential NV center, a cluster of NV centers, or other fluorescent impurities, or just dirt. Since we are looking for a single NV center, a rule of thumb is to focus on a dim isolated dot, as the very bright ones are likely to be groups of many NV centers. A good initial test to quickly distinguish between NV centers and other particles before testing for antibunching is to first switch from confocal to wide-field mode, and move the emitter candidate in and out of the position of the pump beam. An NV center will show a higher fluorescence when placed in the path of the pump beam and get fainter when moved

4According to K. Iakoubovskii et al. [59], the vacancy concentration in type-Ib MSY diamond grown via an HPHT process can be as low as 0.1 ppm. 5This is not to be confused with the unit used to measure the purity of gold. For gemstones, the carat is a unit of weight. In this case, the diamond concentration is measured in carats per kg of total liquid weight. An alternative measure of concentration is the weight percentage of diamond with respect to the total weight of the liquid. 6.2 Confocal scans of NV centers 75 out. Also, any other particles will probably bleach after some time when exposed to the beam, while an NV center wont. After zooming into a smaller area of 30 µm × 30µm, two ﬂuorescent emitters, indicated as 1 and 2, were identiﬁed as potential NV center candidates.

Figure 6.1: A 70 µm × 70µm scan image of liquid nanodiamond particles, with a step-width of 200 nm. The colored circles in the zoom-in image indicate the position of the identiﬁed NV center candidates.

As an initial test, the bright fluorescent dot (1) was examined at first through a highly resolved scan with a step-width of 50 nm, as shown in in Figure 6.2a. The scan revealed a diamond crystal with a size of approximately 1.5 microns containing two regions, indicated as (a) and (b) with the high-intensity photon emission suggesting two NV center candidates. In order to estimate both the signal, the background levels and the FWHM maximum of the NV center candidates, a line scan was performed along each fluorescent region, as displayed in Figure 6.2b. While it is clear that both fluorescent regions do show high count rate peaks around 20 kcps, they are both surrounded and flooded in background and scattered light, likely from the micron-sized host crystal. The FWHM of the cross-section taken along the line cut reveals the size of region (a) and (b) to be 450 and 240 nm respectively. The scan image also demonstrates the resolving strength of our confocal microscope. Furthermore, 76 Experimental results - NV center characterization the two NV centers separated by a distance below 500 nm could be easily and clearly identified by confocal microscopy. In contrast, a high-resolution scan of the bright dot (2), shown in Figure 6.2b, revealed a diamond nanocrystal containing a single NV center with a FWHM of around 200 nm, which is close to the diffraction-limited spatial resolution of the confocal microscope. The size of the fluorescent spot suggests that the emission center is smaller than the resolution of the confocal microscope with a slightly higher count rate of around 25 kcps.

Figure 6.2: High-resolution confocal scan images of diamond nanocrystals containing a) two NV center candidates labeled as NV 1a and 1b, and b) a single NV center labeled as NV2 (left). The results of the corresponding cross-section line scans along the luminescent regions are shown on the right. The step-width was 50 nm and the integration time per pixel was set to 10 ms. The count rate corresponds to one detector only. 6.3 Optical ﬂuorescence spectrum 77

6.3 Optical fluorescence spectrum Another way to confirm that the identified nanocrystals are NV centers is to measure their optical florescence and establish that the recorded spectra appears mainly within the PSB as expected. Figure 6.3 shows typical spectra of NV1 and NV2, recorded with a self-built 780-spectrometer 6 with a step- width of around 2 nm. The observed wide and clearly visible photoluminescence spectra with the PSB appearing at the lower energy side (between 630 and 800 nm) is in accordance with the expected result for a room temperature spectrum, suggesting that the observed fluorescence stems from NV centers. While the spectrum obtained for NV1 is highly pronounced, it shows no in- dication of ZPL at 637 nm, most likely because the scan was performed at room temperature and due to the background contributions from the two NV emitters (a and b). The latter is probably also the reason why the spectrum appears smooth. Though noisier and less smooth, the spectrum obtained for NV2 seems to reveal a small spike around 640 nm, suggesting the occurrence of ZPL. However, as discussed in section 3.4), the absence or a hardly distinguishable ZPL is expected because, at room temperature, the NV fluorescence spectrum is strongly influenced by the phonons in the diamond lattice. Since ZPL only accounts for a few emitted photons, the entire photoluminescence contribution between 630 and 800 nm from the NV center was collected in the typical experiments for the demonstration of antibunching.

Figure 6.3: Photoluminescence spectra recorded for a) the ﬂuorescent dot NV1 corresponding to two NV centers (a and b) and b) for the single NV center NV2.

6.4 Demonstration of antibunching Before commencing with a further examination of the selected NV center candidates shown in Figure 6.2 and the demonstration of antibunching, we start

6The self-built 780-spectrometer is presented in AppendixC. 78 Experimental results - NV center characterization by recalling that Eq. (2.4) expresses the second-order correlation function in terms of coincidences between photon count rates given by

hn (t)n (t + τ)i g(2)(τ) = 1 2 . (6.1) hn1(t)ihn2(t + τ)i

The collected raw correlation data C(τ) differs from Eq. (6.1) by not including the normalization (given by the dominator) and by reporting the total coincidence counts N1,2 during a total time period T within a time bin w, rather than the count rates n1,2 recorded on each detector. The raw coincidence rate C(τ) can therefore be expressed as

C(τ) = whN1(t)N2(t + τ)i. (6.2)

Therefore, in order to evaluate the intensity correlation function of the NV center, Eq. (6.2) was normalized to yield the corresponding equation for a Poissonian source and then transformed into the intensity correlation function:

c(τ) CN(τ) = . (6.3) wThn1(t)ihn2(t + τ)i Furthermore, the normalized coincidence count rate was corrected for the background, and we obtained the second-order correlation function

C (τ) − (1 − ρ2) g(2)(τ) = N , (6.4) ρ2 where ρ = S/(S + B) relates the signal (S) and background (B) levels measured during each measurement. Figure 6.4 shows the measured second-order correlation functions for the two selected nanocrystals. Compared with the second channel, the ﬁrst channel leading to the auto-correlator was delayed by 70 ns by adding an additional 14 m long co-axial cable. This is clearly visible in the graph, as the g(2)(0) dip is shifted and occurs at 70 ns. Figure 6.4a shows the measured second-order correlation function of region (a) and reveals a clear minimum at g(2)(0) ∼ 0.6. As discussed in section 2.2.3, while we expect g(2)(0) = 0 for an ideal single (2) 1 quantum emitter, the condition g (0) < 2 is used as the upper limit to identify (2) 1 photon antibunching, since a two-photon state is characterized by g (0) = 2 . (2) 2 Furthermore, using Eq. (2.7) we calculated the expected g (0) value to 3 for photon number states with n = 3, which suggests an upper limit for the two- 1 (2) 2 photon state at 2 < g (0) < 3 . Thus, the dip at 0.6 indicates the emission of two independent emitters. This result was expected as it is due to the signiﬁ- cant background light contribution from both the host grain and probably also the adjacent NV center, increasing the probability of observing two photons. 6.5 Demonstration of Rabi oscillations 79

The correlation function obtained for NV2 in Figure 6.4b-c clearly indicates (2) 1 a dip occurring at g (0) ∼ 0.2; well below the limit of 2 required for antibunching, suggesting the presence of a single photon emitter. In addition to antibunching, we also notice bunching shoulders (g2(τ) > 1) at intermediate times, before it decays to 1. As discussed in section 3.4, this effect is considered evidence for the third metastable state in which the system couples into the trapping shelving state due to high pump powers, resulting in photon bunching [50,71,96]. The bunching shoulders are less pronounced and the dip is slightly wider in Figure 6.4c compared to Figure 6.4b, due to the relatively low excitation power. Further characterization would require a mapping of the count rate as a function of the pump power. This would allow for a three-level model ﬁt to the second-order autocorrelation function and an extrapolation of the lifetime of each NV. A rough estimation from the autocorrelation function suggests a lifetime of τnc ∼ 20 ns for both NV2 and NV3. This is in good agreement with the τnc ∼ 25 ns reported in literature [50, 97].

6.5 Demonstration of Rabi oscillations Still under the presence of a small While applying a small magnetic field, we focused on the transition |0i → | − 1i, which constitutes a two-level system. Following the manipulation sequence in Figure 5.3b, the initial spin-polarization of the |0i ground state has been achieved by a ∼ 3 µs green laser illumination followed by a waiting period of ∼ 1 µs to allow for the relaxation and deshelving of the dark state. This relaxation time was chosen because the life time of the dark state was observed to be ∼ 800 ns [94]. Our timing control setup allowed to perform pulsed microwave experiments with manipulation sequences where either the microwave was frequency varied while keeping the pulse duration fixed or vice versa. However, for the demonstration of Rabi oscillation, a single microwave pulse with a frequency ν01 = 2.85 GHz resonating with the transition |−1i [94], was applied with varying duration t, and the remaining population in the |0i state is subsequently read out by once again applying a second laser pulse with a duration of ∼ 1.5 µs while recording the fluorescence intensity. Figure 6.5 shows a typical Rabi oscillation curve where roughly 106 measurement cycles have been acquired and averaged to obtain smooth curves. While CW ODMR experiments allow to calibrate the resonant frequency to one of the transitions, the Rabi oscillation allows to calibrate the adequate pulse length before applying a specific desired spin manipulation sequence and as such is a key for the operation and control of two-level quantum systems. Furthermore, the identification of the maximum (p = 1) and minimum (p = 0) fluorescence levels enables a calibration of excitation and readout tools 80 Experimental results - NV center characterization

Figure 6.4: Normalized ﬂuorescence intensity correlation function (corrected for background) obtained for a) NV1a and b-c). The laser power impinging the sample was around 7 mW for both measurement a) and measurement b), whereas it was only 2 mW for measurement c). in units of population p in the |0i ground state. However, due to the interaction with the environment, we expected to observe a damping of the Rabi oscillations for long pulses over time, which can be characterized by the ensemble dephasing time T ∗. To account for this dephasing caused by the spin environ- ∗ ξ ment, we added a Gaussian decay envelope e−(τ/T ) with ξ as the exponential factor, such that Eq. (3.5) was transformed to:

1 h −( τ )ξ i P (t) = 1 − cos(Ω t) · e T∗ , (6.5) 0→1 2 R Based on Eq. (6.5), the following function was ﬁtted to the observed oscillating ﬂuorescence counts (ct ): ΩRt −( t )ξ c(τ) = c · cos · e T∗ + c , (6.6) k 2 0 6.5 Demonstration of Rabi oscillations 81

Figure 6.5: Rabi nutations. The normalized ﬂuorescence intensity (blue curve) plotted as a function of the microwave pulse duration was ﬁtted by Eq. (6.6) (red) and reveals ∗ a Rabi frequency of ΩR = 2π · 7.65(5) ∼ 50 MHz, a dephasing time T = 629(88) ns and an exponential decay factor of ξ = 1.9(8). Data taken from [94].

where ck is the oscillation amplitude and c0 is the off-set level. Thus we obtained a Rabi frequency ΩR = 2π · 7.65 MHz ∼ 50 MHz for a microwave power of approx. 8 W. The extrapolated dephasing timescale is T ∗ ∼ 630 ∗ ns. In order to correctly determine the origin of the decoherence (T1,T2,T2 ), more sophisticated protocols are required. Future experiments could address this problem by applying various spin spectroscopy techniques, e.g., energy relaxation measurements, Ramsey fringes and Hahn echo techniques, as discussed in section 3.5.

Part III: Superconducting Single Photon Detectors

7. Background and basic concepts

7.1 Superconductivity and working principle of SSPDs 7.1.1 Superconductivity Superconductivity is a phenomena where certain materials show the remark- able behavior of zero electrical resistance, or a resistance sufficiently close to zero, so that persistent electrical currents flow without attenuation when cooled below a characteristic temperature. This phenomenon was discovered by Heike Kamerlingh Onnes in 1911 at the University of Leiden subsequent to his first success in liquefying helium. For all metals and alloys, whether superconducting or not, the electrical resistivity decreases when they are cooled. This is due to the inhibition of both the thermal vibrations of the atoms and electron scattering. However, for certain metals, when they are cooled to a specific transition temperature, they lose all trace of electrical resistance. The transition is abrupt and they are then said to have passed from normal state into a superconducting state. Hence, a material is defined as a superconductor when it shows superconductivity when cooled. As discussed later, it is exactly this transition that is the basic underlying process for particle detection in SSPDs. The phase transition temperature, also known as the critical temperature Tc, is typically in the liquid helium range, ranging from 20 to less than 1 K. Because niobium is the metallic element with the highest critical temperature of 9.3 K [98], niobium alloys are the most practical choice for superconducting applications.

7.1.2 Energy gap The ﬁrst theory to explain the electrodynamics of superconductors was the London theory introduced by Fritz and Heinz London in 19531. However, only when the concept of an energy gap ∆ of order kBTc between the ground and excited states of the system was introduced, a more profound understanding of superconductivity was established. This was later extended in the classic 1957 paper of Bardeen, Cooper, and Schrieffer [99], who proposed the celebrated

1In addition to perfect conductivity, another extraordinary feature of superconductors was observed by Meissner and Ochsenfeld in 1933: perfect diamagnetism. It was these two unique and basic electrodynamic properties of superconductivity that the London theory aimed to explain by introducing the two equations for microscopic electric and magnetic ﬁelds. 86 Background and basic concepts microscopic pairing theory, now known as the BCS theory, as an explanation of superconductivity2. They argued that even a weak attractive interaction between electrons can lead to a separation of the ground state from quasi-particle excitation states by an energy gap ∆. This weak attractive interaction leads to the formation of bound pairs of electrons, also known as Cooper pairs, at low temperatures, occupying states with equal and opposite momentum and spin. According to BCS theory, the pair may break up into two electrons which be- have almost like free electrons with no equal and opposite momenta, hence the term ’quasi-particles’. The BCS theory further predicted that a minimum energy Eg = 2∆(T) is required to break the Cooper pair. In addition, it stated a dependence of the energy gap ∆(T) at a temperature T on the critical temperature Tc, which is given by the relation:

Eg(0) = 2∆(0) = 3.528kBTc (7.1) for T Tc, where kB is the Boltzmann constant. These predictions of BCS theory are in quantitative agreement with the experimental data obtained through spectroscopic measurements [100]. From the point of view of SSPDs, it is in light of these discoveries that we can understand the detection mechanism that occurs when the detector is illuminated with light of an appropriate wavelength. Because the energy of a striking photon is typically 2 to 3 orders of magnitude higher than the energy gap of the superconductor, it is expected to break the Cooper pairs, thereby initiating a detection event.

7.1.3 Phase transition and resistance As previously discussed, the detection mechanism of a superconducting detector is based on the transition from the superconducting to the normal state, i.e., a temporary disruption of superconductivity, essentially manifested in the relation between the resistance and the operational temperature of the superconductor. This strong resistance dependence of the temperature is schematically illustrated in Figure 7.1a. At temperatures higher than the critical temperature (T Tc), the resistance shows a linear dependency and thus the detector is normally conducting, whereas at temperatures well below the critical temperature (T Tc), the detector becomes superconducting. However, over a narrow temperature range, ∆Tc, the resistance shows a sharp drop. This is the resistivity state in which the detector simultaneously exhibits both resistive and superconducting zones. Also referred to as transition width, the detector

2Although the purpose of this section is to give a brief overview of the main concepts for understanding superconductivity as well as the detection principle, rather than a theoretical review, it seems worth mentioning yet another theory with equal paramount importance as the BCS theory, i.e., the Ginzburg-Landau (GL) theory. A short discussion of the GL theory and its potential significance for explaining the particle detection in an SSPD is presented in appendixD. 7.1 Superconductivity and working principle of SSPDs 87 is operated at temperatures around this steep transition region in order to obtain a detection event. By operating the detector at a bias current (Figure 7.1b) and a temperature both below their respective critical values (Ic and Tc), an incident particle with sufficient energy will cause the temperature3 of a localized region of the nanowire to increase so that the superconductivity is broken. This temporary resistive state gives rise to a voltage signal across the superconducting nanowire and is in principle the signature of a particle detection. Besides an efficient detection mechanism, this operation technique also offers a low-noise and a highly sensitive detector.

∆

Figure 7.1: (a) Superconducting resistance transition. The transition width, ∆Tc, is de- ﬁned as the difference in temperature between the start of the decline in resistance and the point where zero resistance occurs, and is usually only a very small fraction of a degree. (b) Typical voltage versus applied bias current Ib (V-I) diagram of a superconducting detector.

3In contrast to temperature-dependent bolometer detectors, the electrons are heated in an SSPD and not the material itself. 88 Background and basic concepts

7.1.4 Microscopic absorption model A microscopic description of the detection mechanism of an SSPD is based upon the energy down-conversion occurring in a superconductor following the absorption of an elementary particle or a photon. More speciﬁcally, after a particle with energy larger than the band gap hν 2∆(T) is absorbed in the superconducting ﬁlm, a chain of high energy excitation events is produced. This relaxation process that restores superconductivity (equilibrium) in the superconductor, schematically illustrated in Fig- ure 7.2, is generally divided into the following three distinct stages [101–104]:

1) The first stage begins when a particle with energy larger than the band gap 2∆ is absorbed by a superconducting film, resulting in the breaking of Cooper pairs and the release of highly excited electrons with energy E0 close to the incident particle. Due to the relatively large coherence length4, the energy of the incident particle is absorbed by one electron only. The result is a very fast excited (hot) electron and a slow low-energy quasi-particle. At this stage, the excited hot electron very rapidly decays (on a tens-of-femtoseconds time scale), spreading its energy among a larger number of excitation events via electron-electron (e − e) scattering and initiates the creation of secondary quasi-particles, resulting in a redistribution of energy within the quasi-particle subsystem. This e − e process continues until it thermalizes to an energy E1 of the average energy of the excited electrons. However, there is little agreement on the actual value of E1. According to Van Vechten and Wood [105], E1 is reached when the energy of the hot electron has become indistinguishable from the energy of electrons in the conduction band. However, Ovchinnikov and Kresin [106] proposed the Debye energy ΩD as the characteristic energy, i.e., E1 = ΩD = 0.1 eV. 2) The second stage occurs when the energy of the electrons is sufficiently reduced for the electron-phonon (e− p) scattering to dominate and the energy down-conversion process releases a large number of phonons. Since the mean free path of these phonons is very small, they efficiently break more Cooper pairs and create a large number of quasi-particles. As the average energy of quasi-particles approaches the energy gap5 ∆, (i.e., around 1 mV at T = 10 K), they continue to increase in number reaching hν/2. However, at this stage, their further multiplication is no longer due to phonon absorption but rather e − e collisions. This process is essentially one of thermalization among electrons, resulting in an increase of the electron temperature Te to values above

4Also referred to as the physical size of the Cooper pair. 5A clear specification of the end of this stage in terms of energy can again not be given. Whereas Van Vechten and Wood suggested that it corresponds to the point in time by which the excitation energy reaches a value of only a few mV, Ovchinnikov and Krestin defined E2 to be in the order of a few ∆. 7.1 Superconductivity and working principle of SSPDs 89 the critical temperature. A typical energy from an optical photon is about 1-2 eV, whereas the energy gap 2∆ of a typical superconductor is much smaller (2∆ ∼ 5 meV for NbTiN at T Tc), leading to an efficient detection by the SSPD. A theoretical estimation of the avalanche effect for an incident photon with a wavelength of 790 nm suggested that more than 300 quasi-particles are created [107]. This avalanche effect of quasi-particle production leads to a local suppression of superconductivity, followed by the formation of hotspots and, finally, the subsequent generation of a measurable electrical pulse, which allows for the detection of an impinging particle. Therefore, this stage is regarded as the operational stage and essentially determines the detection output of the SSPD. 3) In the final stage, the superconductivity is restored due to the relaxation of the strongly nonequilibrium system with its mixed distribution of quasi- particles and phonons and the diffusion of the quasi-particles. While the hot phonons escape from the superconducting film and couple to those in the substrate, thereby removing the energy from the film, the nonequilibrium quasi- particles may diffuse or recombine to form Cooper pairs. The SSPD system, hereby, returns to its initial equilibrium state, once again becoming superconducting and ready to detect another incoming particle.

7.1.5 Hotspot formation A schematic illustration of the hotspot formation process is presented in Fig- ure 7.3. The initial diameter of a hotspot is 2Rm, which is in the order of the coherence length ξ of the superconductor [102,108]. As the hotspot keeps growing during the e− p thermalization process, reaching a final cross-section 2 area π(Rm + LE ) with LE being the diffusion length [109], the applied supercurrent flowing in the SSPD nanowire is expelled and forced out by the diffus- ing quasi-particles of the resistive hotspot region towards the film edges. This leads to an increased current density j in the sidewalks near the edge of the stripe. If the nanowire diameter is sufficiently small and the bias current Ib is close to the critical current Ic, the current density j exceeds the critical current density jc, which leads to the creation of so-called phase-slip centers (PSCs) across the film, and a resistive barrier Rk is formed across the entire width w of the superconducting film [110]. This induces a voltage between the contacts of the structure. The time-integral of the voltage contains the photon-energy information. According to Jukna et al. [111], the absorption of a ∼ 1.55 µm photon in a ∼ 3.5 nm thick NbN film at a temperature of 4.2 K results in a coherence length ξ = 11.2 nm and a diffusion length LE = 13 nm, hence a total final diameter of the hotspot of ∼ 50 nm. The hotspot cross-section area 90 Background and basic concepts

νΔ

Figure 7.2: Schematic illustration of the avalanche process initiated by photon absorption in a superconductor. During the ﬁrst stage (a), a photon with energy larger than the energy gap is absorbed, resulting in the breakup of a Cooper pair. During the second stage (b), the quasi-particles recombine and distribute their energy among a large number of phonons. Towards the end of the second stage (c), an additional breakup of Cooper pairs by phonons occurs. At the end of the ﬁnal stage (d), the superconductivity is restored due to a recombination of the Cooper pairs and the escape of the phonons into the substrate. TF and TD denote the Fermi and the Debye temperature, respectively. 7.1 Superconductivity and working principle of SSPDs 91

Figure 7.3: Schematic illustration of the hotspot formation mechanism: (a) Equilib- rium state. A uniform Ib current flows through the superconducting nanowire. Af- ter photon absorption, a localized hotspot with an initial diameter of 2Rm with suppressed conductivity is formed. (b) The hotspot grows until reaching a final diameter of 2(Rm + LE ) before it diffuses (c) and expels the current towards the edges of the wire. (d) A resistive state is formed, interrupting the current flow. 92 Background and basic concepts is proportional to the incident particle energy6 [113]. The higher the energy of the particle, the larger the cross-section area of the hotspot. This dependency is utilized for photon-energy-resolving measurements [109, 114]. Once the hotspot has reached its final size, it will then diffuse due to the cooling process as the quasi-particles lose their energy and decay, thereby heal- ing itself and restoring superconductivity. The time evolution, also referred to as the intrinsic recovery time, depends on the relaxation time of the quasi- particles and was measured to be in the order of ∼ 30 ps for ultrathin NbN nanowires [103]. The formation time of the PCS is referred to as the delay time and was measured to be around ∼ 70 ps [110]. Combining both the intrinsic recovery and delay time values ((302 + 702)1/2 ≈ 75 ps) [115] in order to estimate the SSPD response time might suggest a rather high counting rate of ∼ 13 GHz. However, it has been demonstrated by Kerman et al. [116] that another parameter limits the SSPD response time to a few nanoseconds, i.e., the kinetic inductance of the superconducting meander. This is discussed in more detail in the following sections.

7.1.6 Phenomenological model For an intuitive understanding of the operation of the detector, however, a simple phenomenological model, illustrated in Figure 7.4, is sufficient. Here, the electronic behavior of the detector is modeled equivalent to a circuit consisting of a switch S, a kinetic inductance Lk and a resistor Rn. An open switch corresponds to the absorption of a particle resulting in the detector becoming resistive (Rn > 1kΩ), and thus a voltage pulse of V = IbRAA can be measured, provided that Rn RA, where RA is the amplifier input impedance and A the amplification. When the switch is closed, the resistance of the resistor Rn is equal to zero and the detector is in a superconducting state. The kinetic inductance is the central aspect of the model and represents the conductance of the nanowire and is given by

wl L = λ 2µ , (7.2) k p 0 d

2 where l is the length of the wire, w the width and d its thickness. λp denotes the penetration depth of the material and µ0 the vacuum permeability. The switching behavior of the detector does not result in a stepwise response of the current but rather an exponential decay. After absorption of a particle the initial current value Ib will decay with a time constant [116]

6Besides the incident particle energy, the size of a hotspot also depends on other parameters, such as the 2∆ of the superconductor, the electron thermalization time and the electron diffusiv- ity [112]. 7.2 Quantiﬁcation of the performance of an SSPD 93

Figure 7.4: Electrical circuit of an SSPD according to the phenomenological model.

Lk τ f all = (7.3) RL + Rn towards a final value RL In = Ib , (7.4) RL + Rn where RL is the input impedance. However, when the self-heating of the 2 nanowire due to the current, given by P = I(t )Rn, is sufficiently reduced, the decay is interrupted and the switch closes, returning the nanowire to the superconducting state. This causes the current in the nanowire to exponentially recover to its initial value Ib with a time constant L τ = k . (7.5) RL According to Eq.(7.3) and Eq.(7.5), the time characteristics are strongly affected by the kinetic inductance, and thus Lk determines the recovery time. I shall return to the kinetic inductance in section 7.2.2, where I discuss in more detail the dead time and the trade-off between the counting rate and either the active area or the detection efficiency.

7.2 Quantification of the performance of an SSPD When addressing the performance of the SSPD, a series of characteristics are typically considered. These are the detection efficiency, the dead time, the dark count and the jitter. In the following subsections, I will address these features in more detail, as well as their relevance to different aspects of the field of quantum communications (QC). 94 Background and basic concepts

7.2.1 Detection efficiency The detection efficiency (DE) is defined as the overall probability of register- ing an event if a radiation quanta impinges on the detector. The DE is probably the most fundamental characteristic of a detector, and a high efficiency value is considered of paramount importance and highly desirable in most photon- counting applications. The DE is a function that describes the sub-processes influencing the detection event and can be expressed as the product of three factors [117]

DE = ηabs × ηd × ηc (7.6) where ηabs is the absorption efficiency of the superconducting nanowire (i.e., the NbTiN layer), ηd is the likeliness that an absorbed photon causes a voltage pulse that is measurable, and ηc is the optical coupling efficiency: the probability that incident light reaches the active area of the SSPD. The term ηabs × ηd is referred to as the device efficiency and depends on the physical properties of the device whereas ηc only relies on one external factor, i.e., coupling techniques. More specifically, the first factor ηabs depends on the absorption properties of the nanowire, the chosen material composition and the geometry of the wire, which themselves depend on the surrounding layers, e.g., the substrate and coating layers. The second factor is called the intrinsic quantum efficiency of the device and gives the probability of the generation of a pulse once a photon is absorbed. The probability of generating a pulse depends on a number of parameters such as the applied bias current, the system temperature, the incoming particle energy and the geometry of the nanowire (width and thickness). These parameters are worth addressing: Applied bias current. The detection efficiency shows a sigmoidal dependence on the bias current. Figure 7.5, depicting the detection count rate versus the bias current, reveals a very low sensitivity at lower bias currents (Ib Ic). Only around 0.95Ic, the sensitivity increases exponentially and saturates at higher currents (Ib > Ic). For more narrow nanowires and a higher photon energy, it has been shown that the sensitivity increases, resulting in a shift of the curve towards lower bias currents and a steep exponential slope in the transition region [118]. For lower energy photons, the curves become less steeper and more displaced towards higher bias currents. System temperature. The first studies on the temperature dependence were aimed at understanding the origin of dark counts [119–122]. As the operation temperature is lowered, the number of dark counts significantly decreases for any given bias current, as expected. Shortly afterwards, all experimental results showed that the system temperature not only influenced the number of dark counts but also the DE [123–125]. More specifically, lowering the system temperature from the conventional 4.2 to ∼ 1.6 K, results in a shift of the cut-off wavelength λc towards longer wavelengths [126]. Absorbed pho- 7.2 Quantification of the performance of an SSPD 95

8 ] s p

c 6 M [

e t a r

n 4 u o c

n o i t c

e 2 t e D

0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 R e l a t i v e b i a s c u r r e n t

Figure 7.5: Detection efﬁciency of a detector as a function of the normalized bias current.

tons with λ ≤ λc are detected with an increased intrinsic DE, whereas the DE rapidly decreases for low-energy photons with a wavelength larger than λc. For λ = 635 nm, a reduction of the temperature from 4.2 to 2 K resulted in an increase in efficiency by a factor of 3, for instance [125]. However, a further reduction of the temperature (T = 300 mK) did not result in another increase of the intrinsic efficiency. Particle energy. During the initial stages of the DE spectral sensitivity characterization of photon detectors, the studies were more focused on wavelengths important for fiber-optic QC systems and the commercial near-infrared (NIR) telecommunication wavelengths, i.e., 1.3 and 1.5 µm [112,119,127,128]. Shortly afterward, several photon wavelengths in the range from visible light to the far-IR were examined, and it was observed that the DE depends exponentially on the incoming photon energy, i.e., the DE increases exponentially with the photon energy [113]. This is likely due to the increased size of the hotspots generated by photons with a higher energy in the narrow detector stripe. Recently, the spectral range was extended again and the devices were found to very efficiently detect high-energy particles, namely α- and β-particles. A detailed description and review of the various examined nuclear particles and their associated DEs is given in chapter 10. Nanowire geometry. Early detectors [107,112] were based on a single ∼ 1 µm-long superconducting stripe with very low DE values. To optimize the DE, the sensing element of the detector needs to fill the optically illuminated area as compactly as possible. Since the optical illumination can be focused on very confined areas (in the order of 100 µm2), a meander pattern was found to be the most suitable compact structure. All detectors presented in this thesis 96 Background and basic concepts consist of a long meandering wire with a rectangular cross-section, approx. 100 nm wide and 5 nm thick, and a fill factor7 of 50%. The geometrical layout of the detector has also been shown to influence the DE. Not only does an increase of the fill factor (corresponding to a larger active area) leads to higher DE values; decreasing both the width and thickness of the wire also lead to an increase of the DE. This is likely due to the increase of the hotspot diameter relative to the decrease of the film thickness, which in turn promotes event detection. A high uniformity of the superconducting wire is also required in order to ensure a proper operation of the detector and an even DE. A variation of the cross-section area along the wire will mean that different segments must be characterized by different values of Ic. This will introduce different DE values for a given bias current and may cause the detector to switch to the normal state since the wire is being biased far from its critical value [112]. For the end-user with no means to influence the device efficiency, it is not of much concern, as long as the coupling losses are not taken into account. The coupling losses are represented by the last factor in Eq. (7.6). These losses occur when photons are coupled to the detector through free-space optics (i.e., the microscope objective) or optical fibers. In chapter 11, various conventional optical coupling techniques are discussed, and a design for an alternative technique, which allows to enhance the coupling factor, is proposed. Since it is difficult to exactly quantify each factor in Eq. (7.6), the DE function is not very practical for the end-user. In literature, often the more practical and simple system detection efficiency (SDE) is used and defined as

R − R SDE = detected dark . (7.7) Φ

SDE is a measurable dimension that quantiﬁes the relation between the actual number of detection events, Rdetected, and the number of photons Φ directed towards the detector, where the measured count rate is corrected for the ﬁnite dark count rate Rdark. In contrast, the DE is not directly measurable but can be deduced from the SDE by rewriting Eq. (7.6):

DE = SDE × ηc (7.8)

The detector samples mentioned in this thesis were all reported to have a DE around ≤1-5% for λ = 1.3 µm at 4.2 K. The best DE achieved for this type of detector and wavelength was reported as 20% [125]. Nevertheless, the low DEs of our samples did not signiﬁcantly affect the measurements presented in this thesis.

7The fill factor is the ratio between the line and space defined as f = (w)/(w + s), where s is the space. In our case s = w. 7.2 Quantification of the performance of an SSPD 97

7.2.2 Dead time The dead time τ of the detector, also known as the reset- or recovery time, is defined as the time interval after the absorption of a particle, during which the detector is unable to detect another particle. The dead time behavior is not treated as a sharp step-like function, but rather as a parameter for the probability ηr that a resistive state is formed after the detection of a photon, that decreases in time and recovers exponentially to the initial state. The reset response is typically modeled as a dynamic interaction between the electrical and thermal properties of the SSPD [129–131]. For the reset to occur, the resistive state needs to be unstable. This is only the case if the electrical time response is slow enough compared to the associated thermal time constants. For the SSPD, this means that the time to cool down after a detection event has to be sufficiently fast compared to the time it takes for the current to nearly drop to zero and then return to the superconducting state. For our devices, a very fast cooling rate (compared to the electrical time constants) is ensured by using a NbTiN nanowire with a meander structure. As mentioned in section 7.1.6, the electrical circuit has been modeled as a kinetic inductor Lk connected in series to a resistor. The dead time, given by Eq. (7.5), is the primary factor limiting the maximum count rate of the SSPD. The maximum count rate can be increased by reducing the Lk/RL time constant. Increasing the resistance RL seen by the detector by adding a resistor in series is an alternative to decreasing τ [129]. However, the detectors used in this study were operated with the load impedance of the RF amplifier fixed to 50 Ω. Another option is to reduce the kinetic inductance. Since the kinetic inductance is proportional to the length of the nanowire divided by the cross- sectional area of the nanowire, as implied by Eq. (7.2), shortening the wire length will result in a faster reset time, thereby increasing the maximum count rate of the detector. However, this also implies a smaller active area or a lower fill-factor of the meander structure, both of which are harmful and a limitation to the over-all DE of the detector. Thus, there is a trade-off between the DE and the maximum count rate. A third alternative to decreasing the inductance is to connect more detectors in parallel, resulting in a total inductance 1/LK,Total = 1/LK,1 + 1/LK,1 + ... As mentioned earlier, methods to increase the speed of the SSPD through a modification of the electrical time constants have been intensively studied and deemed possible. However, the thermal constants governed by the properties of the NbTiN nanowire and the sapphire substrate also put a limit to the recovery time. Although so far no fast device has been reported where the thermal properties have been modified, alternative conducting and substrate materials are still being actively investigated. Attempts to increase the speed of the response in an effort to increase the count rate of the SSPD cannot go on indefinitely, since a too short response time will result in the negative 98 Background and basic concepts electrothermal feedback becoming fast enough to counterbalance the Joule heating, resulting in an effect known as latching, where the device becomes locked in a stable resistive state and can no longer detect photons [131]. In the specific case of our device, with a 100 nm wide, 5 nm thick and 500 µm long NbTiN wire, the kinetic inductance is approximately 250 nH. For a typical input impedance of 50 Ω, the dead time is τ = 5 ns, resulting in a maximum count rate of 200 MHz.

7.2.3 Dark counts A dark count is the undesired phenomenon of a false count, resulting from the completely spontaneous formation of resistive states when no photons or particles are absorbed. Next to the detection efﬁciency and the dead time, the dark count rate (or noise level) is perhaps the most important property of an SSPD. A high dark count rate will drastically decrease the noise−equivalent power (NEP) parameter of the detector, thereby limiting the security in the envisioned quantum cryptography applications. Dark counts are usually expressed by a rate in hertz, and are measured with the detector already embed- ded in the experimental setup and its unique environmental conditions. The dark count rate Rdk can be suppressed by reducing the bias current. However, this also results in a reduction of the DE. Thus, there is a trade-off between the DE and the dark count rate. This trade-off is expressed in terms of the NEP and has proven useful for optical power measurements. For quantum detectors, the NEP is deﬁned as [132]:

hν p NEP = 2R , (7.9) SDE dk where hν is the photon energy. The smaller the NEP, the better the detector. Experimental results have shown that the dark count rate strongly depends on the bias current and the temperature8. Despite thorough studies, the mechanism leading to the dark counts is still unclear and yet debated. However, two models have been proposed as an explanation of the observed current and temperature dependence. Vortex anti-vortex pairs. The Ginzburg-Landau (GL) coherence length for a thin NbN ﬁlm at zero temperature is ξ(0) = 5 nm. Since the width of our nanowire is much larger than the coherence length (w ξ) but the thickness is comparable (d ≈ ξ), the detector can be regarded as a two-dimensional (2D) superconducting ﬁlm. The thermal unbinding of a vortex anti-vortex pair

8Background radiation, i.e., black-body radiation, was initially suspected as a possible source for dark counts. However, blocking all incoming radiation by locking the detector in a µ- metallic shield did not prevent the occurrence of ﬁnite sporadic voltage pulses. Thus, the background radiation was ruled out as a potential source [133]. 7.2 Quantiﬁcation of the performance of an SSPD 99

(VAP)9 is intimately linked to the so-called Berezinskii-Kosterlitz-Thoules (BKT) phase transition within a 2D superconducting film topology, occurring at the critical temperature TBKT . This model predicts [122, 134] that below TBKT in a zero magnetic field, in which the resistance is zero, the formation of bound VAP is energetically favorable and a VAP is generated. If the temperature is between the BKT transition temperature TBKT and Tc, both bound pairs and thermally unbound VAPs coexist. A transport current, however, can break them. When a bias current is applied to the nanowire, the vortex and anti-vortex of a VAP will feel a Lorentz force in the opposing direction resulting in a reduction of the VAP binding energy. Thus, the combined action of an applied current and thermal activation may lead to the unbinding of the VAP, which manifests itself as a spontaneous resistive state. Single vortex crossing. Another possible origin is a vortex crossing the nanowire perpendicular to the bias current, resulting in a dissipation of heat due to the magnetic self-field of the applied bias current. According to Bulaevskii et al. [135], when a single vortex crosses from one edge of the nanowire to the other, enough heat is released to create a belt-like resistive state region across the strip, leading to the generation of a detectable voltage pulse. A more thorough description of the single vortex crossing model is described in [135, 136].

A last possible origin of the dark counts is the phase-slip center which exists in one-dimensional (1D) nanowires. However, since we are considering a 2D superconducting ﬁlm, the phase-slip centers are only expected to play a minor role. So far, experimental data [137] points to the VAP unbinding model as the dominating dark count mechanism. Notwithstanding, for the realization of dark-count-free SSPD devices, it seems clear that addressing the unbinding of VAPs and/or the vortex crossing is the solution. In general, the dark count rates of SSPDs are rather low [32] compared to other single photon detectors with a similar DE.

7.2.4 Timing jitter The detection process of an impinging photon is not indefinitely fast. The variation in the time interval between the two significant events, i.e., the absorption of a photon and the generation of an electrical pulse from the detector, is known as timing jitter. Detectors with an ultra low timing jitter are very attractive and can be used in increased bit rates in quantum key distribution (QKD) applications, allowing to achieve a higher timing resolution or an improved spatial resolution in time-of-flight applications such as LI-

9Vortexes are topological defects in the order parameter. 100 Background and basic concepts

DAR10 [32, 138, 139]. The maximum count rate is determined by the timing resolution, and a dominant timing jitter will cause counts to become lost, thereby limiting the actual maximum count rate. However, in the case of our detectors, the timing jitter is not a limiting factor because it is much lower than the reset time. Although the nature of the timing jitter is not well understood, it surely depends on both the electrical constants of the detector and the details of the readout electronics setup, i.e., the time distribution of the optical pulse, the electronic components, the readout noise and the dispersion in the ﬁber [139]. However, an intrinsic timing jitter of the detector is believed to be induced by the variation in time delay of the formation of resistive areas due to the different positions of absorption, which most likely is caused by a variation of the nanowire-width and defects in the ﬁlm. The intrinsic timing jitter is much smaller than the overall timing jitter of a detector. Compared to conventional photon detectors (Si APD), the timing jitter of SSPDs is significantly lower, making them a promising candidate for the detection of single photons [138]. The timing jitter is in principle measured by analyzing the variation in the time interval. Timing jitters as low as 18 ps have been reported. However, for the detectors used in this thesis, the typical timing jitter is ∼ 60 ps [140].

10Acronym for Light Detection And Ranging which is a remote sensing technology. 101

8. SSPD design and measurement setup

Since the first realization of an SSPD in 2001 by Goltsman1 et al. [107], niobium nitride (NbN) alloys have been widely used for the fabrication of SSPDs. Currently, many groups working on SSPDs are using NbN films deposited on a sapphire substrate, either adopting or varying the fabrication method and design first introduced by Goltsman et al.. The devices presented in this thesis were fabricated together with Sander Dorenbos and Esteban Ureña from the Quantum Transport Group at Delft University of Technology (TU Delft). They are based on a 5-6 nm NbTiN thin film on a silicon substrate as an alternative to the more conventional NbN films deposited on sapphire substrates. A motivation for the choice of the NbTiN superconducting film, as well as the substrate, is discussed in the next section. The device fabrication process is described in explicit detail in Ureña’s and Dorenbos’ theses [140, 141] and elsewhere in literature [112,142]. However, in the following sections the considerations and requirements for a high-quality SSPD device are discussed, followed by a short review of the fabrication methods and steps. Finally, the setup used for the SSPD measurements presented in this thesis and the basic characterization tests are described.

8.1 Design and fabrication requirements In order to determine the requirements for a functioning SSPD and the req- uisites that need to be met during the fabrication process, an understanding of the operational principles of the SSPD must be achieved. Therefore, the main principles of SSPD detection are briefly summarized. A crucial precon- dition of the single particle detection model is the ability of the conducting film to absorb a particle. Furthermore, the thickness of the conducting film must be lower than the electron thermalization length and can be maintained at temperatures much lower than the transition temperature Tc of the superconducting film. Another important condition is the hotspot dimension. Only

1Actually, the very first realization of NbN film-based devices was already achieved in 1998 by Ilin et al. However, the NbN film device they used showed significantly different properties when compared to current state-of-the-art SSPDs and was based on a different structure and readout scheme. 102 SSPD design and measurement setup when the detector stripe film is sufficiently narrow compared to the size of the hotspot and when the bias current is close to Ic, can the superconductivity be destroyed and an easily detectable voltage transient be generated. The above mentioned conditions determine the 2∆ value of the superconducting film. It depends on the critical temperature Tc, the critical current Ic and the choice of the substrate. All these prerequisites lead to a number of design and fabrication requirements.

8.1.1 Particle absorption To determine the most suitable material for the superconducting film, as well as the underlying substrate, for the absorption of single photons, let us first consider the behavior of the radiation absorption coefficient of a metallic conducting film given by [143]

4(RS/Z0) ηabs = 2 , (8.1) [(RS/Z0)(nsub + 1) + 1] where nsub is the refractive index of the used substrate, Z0 = 377 Ω is the free- space impedance, and RS is the surface resistance of the considered conducting ﬁlm measured just above transition Tc.

Figure 8.1: Theoretical particle absorption for two thin substrate materials.

In Figure 8.1, the absorption coefficient is plotted as a function of the thin film surface resistance for the two most commonly used substrate materials, i.e., sapphire (n = 1.72) and silicon (n = 3.48). The sapphire substrate clearly shows a higher absorption efficiency compared to silicon, which is the reason why it is considered the substrate material of choice. However, even though the absorption efficiency is lower, silicon substrates exhibit other competitive 8.1 Design and fabrication requirements 103 properties, making silicon a promising candidate material as well. We will return to the discussion of the substrate material after considering the superconducting film materials in the following section.

8.1.2 Advantages of a nano-structured superconductor Two suitable superconductor materials with a short electron-phonon interaction time are niobium nitride (NbN) and niobium titanium nitride (NbTiN). Both materials posses a comparatively high critical temperature and ﬁlm resistivity. Table 8.1 compares several relevant properties of the two alloys.

Compound Energy gap Critical temperature Coherence length Resistivity

2∆ [meV] Tc [K] ξ [nm] ρ [µΩcm] NbN 3 10 5 160 NbTiN ∼ 5 15 3.8 90

Table 8.1: Comparison of selected physical properties of NbN and NbTiN ﬁlms [98, 144, 145]. Resistivity measured at 300 K.

Since our device is based on the particle absorption in a thin conducting film, in order to achieve a desired surface resistance, the cross-section to length ratio of the conducting film is determined by the film’s resistivity ρ according to the following equation: ρ R = . (8.2) S d where d is the film thickness. For a film thickness of around 5 − 6 nm, the associated surface resistance for both materials lies around the values corresponding to the maximum absorption efficiency shown in Figure 8.1: RS(∼ 5.5 nm) = 150 Ω for NbTiN and RS(∼ 5.5 nm) = 320 Ω for NbN. The wire dimension needs to be comparable to the size of the hotspot for the entire cross- section of the SSPD wire to become resistive. A simple geometrical criteria for this condition is given by [119] w R ≥ (1 − I /I ) . (8.3) m b c 2 Depending on the energy of the impinging particle, calculations and experiments performed on the hotspot both estimate its final diameter to be in the order of several tens of nanometers. In section 7.1.5, we have shown that Rm ∼ 50 nm for a photon with a wavelength of 1.55 µm. Considering the typical operation bias ratio Ib/Ic ∼ 0.8 − 0.9, criteria (8.3) suggests a wire width with an upper limit of a few hundred nanometers. However, since the goal 104 SSPD design and measurement setup was to fabricate a superconducting detector that allows to efficiently detect a broad spectral range of incoming particles, a further reduction of the width is the most sensible approach. Therefore, for practical fabrication reasons and due to the required uniform width of the wire, a width of w ∼ 100 nm was the best choice.

8.1.3 NbTiN on silicon - an alternative to the NbN on sapphire-based SSPD In 2009, Barends et al. reported that the observed noise was up to an order of magnitude higher when using sapphire instead of silicon as substrate material [146]. Additionally, since a deposition on silicon is now possible at room temperature, detectors based on silicon substrates enable an easy integration with advanced electronic circuits. As for the conducting film, NbN has thus been the favored material for the fabrication of SSPDs due to the possibility of depositing high-quality ultrathin films [112, 147]. However, Sander et al. [125] reported a reduction of the dark count rate by a factor of 10 for an SSPD with a NbTiN conducting film compared to identical NbN-based detectors. Furthermore, the DE values match those of NbN detectors, resulting in an improved signal-to-noise ratio, probably because the thin NbTiN layer is less affected by the surroundings than other superconducting films [148]. In addition, when compared with NbN-based detectors, the homogeneity of the superconducting parameters in NbTiN-based detectors has been suggested as an explanation for the lower dark count rates [125]. Consequently, this suggests that an SSPD consisting of a NbTiN film on a silicon substrate is a highly effective device. The devices presented in this thesis are all silicon substrate-based detectors with a 100 nm wide, 500 µm long and 5-6 nm thick NbTiN wire folded in a circular2 area with a diameter of 10µm with a filling factor of 50 %, yielding a compact active area of 50 µm2.

8.1.4 Fabrication The detectors were fabricated using standard nanofabrication techniques, employing electron beam (e-beam) lithography and reactive ion etching (RIE) on an oxidized silicon substrate. The prepared detector was then placed between two gold contacts, which are arranged in a co-planar waveguide with an impedance of 50 Ω. The deposition of the ultrathin NbTiN ﬁlm was ﬁrst carried out at room temperature by sputter-cleaning the silicon substrate followed by NbTiN sputtering. The existence of a native oxide (SiO2) layer on the Si substrates seemed

2Other commonly used active areas are square-shaped with a side length of 10 µm. 8.1 Design and fabrication requirements 105 necessary to ensure a high-quality of the ultrathin NbTiN films with an amorphous layer. The ratio of ∼70 % Nb to ∼30 %Ti in the NbTi target was found to yield the best trade-off between the critical temperature Tc and the resistivity [145]. Our NbTiN films were deposited via reactive ion sputtering using a single Nb0.7Ti0.3 alloy target in an Ar and N2 atmosphere at room temperature. The film sputtering was performed by Tony Ziljstra and Dr. Eduard Driesen from the Physics of Nanoelectronics group at the Kavli Institute of Nanoscience at TU Delft. Next, the gold contacts, which allow the connection to external electronics, were written by e-beam lithography followed by an application of the standard metal deposition and lift-off technique to define the metal contacts. The nanowire meander was then fabricated on the substrate through RIE, after the deposition of a negative resist (HSQ) and e-beam expose. The negative resist ensured that the exposed areas remained on the substrate. A schematic illustration of the SSPD fabrication process is shown in Figure 8.2. The SSPD chip was then glued onto a printed circuit board (PCB) with an SMA-type coaxial connector, and the contacts were bonded. A scanning electron microscopy (SEM) image of the active area of an SSPD pasted onto a PCB can be found in 8.3.

Figure 8.2: Schematic illustration of the SSPD design and fabrication process: (a) A 5-6 nm NbTiN superconducting ﬁlm (gray) is sputtered onto a silicon substrate with a 225 nm thick native oxide layer (red). (b) Nb and 60 nm Au (yellow) contacts are written by e-beam lithography and lift-off techniques. (c) The ﬁnal meandering nanowire is obtained after e-beam lithography and RIE. 106 SSPD design and measurement setup

Figure 8.3: A sequential zooming in (by means of SEM) on the SSPD mounted on a chip carrier reveals the meandering nanowire structure. The circular shape of the active area ensures an optimal coupling overlap with an optical ﬁber. 8.2 Readout electronics and experimental setup 107

8.2 Readout electronics and experimental setup 8.2.1 Measurement setup

00 000

0 0

Figure 8.4: Schematic illustration of the conventional SSPD setup.

A schematic illustration of the conventional measurement and readout setup for an SSPD is shown in Figure 8.4. The chip carrier with the glued SSPD is mounted on a dip-stick and then immersed into a liquid helium (He) bath cryostat at 4.2 K well below the liquid He surface to ensure a stable operation. A coaxial cable connects the detector to the electronic readout system, which is located outside the cryostat and is operated at room temperature. The electronic readout system consists of a custom-designed Bias Tee (1 MHz - 5 GHz) connected to the detector through the AC+DC port and to a computer- controlled constant current source through the DC component. A bias voltage can be applied via a data acquisition (NI DAQPad-6015) box through the Bias Tee and converted into a current by a built-in resistor. Depending on the electronics configuration, either a 200 or 500 kΩ built-in resistor was used. The readout voltage over the SSPD was monitored by the DAQPad box through the DC port of the Bias Tee to ensure a continual observation of the superconductivity state of the device. Because the DAQPad box is too slow to register 108 SSPD design and measurement setup the counting events, the output signal of the AC port was fed into a cascade of low noise amplifiers with a total gain of ∼ 54 dB and a bandwidth of ∼ 1 GHz. The amplified detection pulse was either sent to a high speed oscilloscope (1 GHz bandwidth, LeCroy LC574AM) or to a pulse counter (Stanford Research SR400 Photon Counter). The DAQPad card and the counter were both computer-controlled through a LabView program, in which all the necessary parameters, such as the bias voltage and the trigger level, can be set and monitored. Depending on the measurement, the optical illumination of the SSPD was provided by various means, such as: 1. an optical fiber pigtail, 2. light focused onto the active area via a coupling lens, 3. optimizing the optical coupling to the fiber tip of the SSPD by mounting it on a 3D piezo positioner system, 4. or by placing high-energy particle emitters slightly above the detector. Each of these illumination and excitation methods will be described and discussed in the following sections. Furthermore, any alteration of the setup will be mentioned when discussing each experiment. Figure G.3 shows a photo of the complete setup built and used in our lab at KIKO. Although it is not the exact setup used for all of the experiments, it represents the typical setup.

8.2.2 Characterization After preparing the setup and immersing the detector into the cryostat, prior to the experiments, a sequence of tests were carried out to characterize the performance of the detector. These tests included verifying the superconductivity state and determining the associated critical current value of the device, the pulse shape of the detection event and the recorded dark counts rates. Fig- ure 8.5 shows the results of the screening of four different SSPD devices by measuring the voltage as a function of the applied bias current Ib. According to the I-V curves, all devices are superconducting, showing no voltage below their associated critical current values, after which the voltage rises abruptly and continues to increase proportionally to the applied bias current, following Ohm’s law. This trend is clearly visible for the SSPD samples #3 and #4. The critical current value indicated by the sudden increase in voltage, however, is slightly different for each detector. Samples 1-3 all seem to have comparable Ic values in the 8-9 µA range, whereas sample #4 has a significantly lower critical value at around 5 µA. Since the geometry of the active area of all devices is identical, the low critical current value may suggest that the quality of the thin film in detector #4 is not optimal. More specifically, a possible explanation for the poor film quality is the non-uniformity of the sample’s mi- crostructure, leading to constriction in the nanowire and thus a limitation of the critical current value. 8.2 Readout electronics and experimental setup 109

S S P D # 1 1 . 5 S S P D # 2 S S P D # 3 S S P D # 4 ]

V 1 . 0 [

e g

a t l o V 0 . 5

0 . 0

4 5 6 7 8 9

B i a s c u r r e n t I B [ m A ]

Figure 8.5: Voltage drop across the SSPD as a function of the bias current for four different samples recorded to check the superconductivity. The measurements were all performed in a low-temperature probe station at 4.2 K.

When operating the detector, i.e., applying a bias current just below the critical value while detecting impinging particles, a check of the pulse shape of a recorded detection event also helps to conﬁrm the detection functionality of the SSPD and suggests a dead time value. Each detection event generates a pulse, as shown in Figure 8.6. Since the rise time is negligible compared to the decay time, the dead time is mostly dominated by the decay time. As discussed in sections 7.1.6 and 7.2.2, the DE recovers exponentially with time after a detection event. By ﬁtting an exponential decay model to the recorded detection pulse in Figure 8.5, the dead time τ was estimated to around 5 ns for all our detector samples, implying a maximum count rate of 200 MHz. Figure 8.7 shows the measured dark count rates for normalized bias current values. The recorded dark count rates are around two orders of magnitude higher compared with the dark count rates of the best SSPDs reported in literature [26]. The similarity of the slopes for samples #1 − 3 indicates a comparable dark count sensitivity, whereas sample #4 shows both a sensitivity range and a count rate that are noticeably broader and higher. Although a low dark count rate is a property usually aimed for, the relatively high dark count rates obtained for our detector samples did not prevent the successful demonstration of the proposed read-out schemes and the characterization of the DE of the detectors towards high-energy particles, as discussed in chapters9 and 10. 110 SSPD design and measurement setup

R e c o r d e d d e t e c t i o n e v e n t 2 E x p o n e n t i a l f i t ] V m [

e 1 g

a t l o V

0 2 0 4 0 6 0 8 0 1 0 0 T i m e [ n s ]

Figure 8.6: A typical detection pulse recorded by the oscilloscope after ampliﬁcation. The exponential ﬁt suggests a time constant τ ∼5 ns for the recovery of the detector.

1 0 6 S S P D # 1 S S P D # 2 1 0 5 S S P D # 3 S S P D # 4 4 ] 1 0 1 - s

[ 3 1 0 s t n

u 2

o 1 0 C

k 1 r 1 0 a D 1 0 0

1 0 - 1

1 0 - 2 0 . 7 0 0 . 7 5 0 . 8 0 0 . 8 5 0 . 9 0 0 . 9 5 1 . 0 0

B i a s c u r r e n t I B [ m A ]

Figure 8.7: Dark count rate as a function of the normalized bias current at 4.2 K for 4 devices recorded for a trigger level value of 0.025 V. 111

9. Capacitive readout and gating of the SSPD

9.1 Introduction In this chapter1,a new readout scheme for superconducting single photon detectors is proposed, based on a capacitive integrating circuit would relax in the need for large bandwidth amplification and result in voltage steps that are proportional to the number of absorbed photons. This scheme may prove beneficial for a number of applications, including imaging-based SSPD arrays and biomedical applications such as fluorescence lifetime measurements [138]. The integrating readout scheme is introduced in section 9.2 starting with a brief motivation followed by a presentation of the simulation and experimental results of the capacitor voltage readout. The only disadvantage of this approach, the loss of time information, is compensated for by a fast-time gating technique to filter scattered light in time and reduce the number of dark counts, potentially leading to a higher signal-to-noise ratio. The gate pulse is generated upon the detection of a photon and created by a spontaneous parametric down-conversion source, heralding the presence of a second photon. The fast- time gating technique is demonstrated in section 9.3. Finally, the chapter is concluded by a discussion of the two presented operational schemes and their potential applications in 9.4.

9.2 Capacitive readout scheme As previously discussed, conventional SSPD operation involves counting voltage pulses triggered by single photon detection events. This requires high-gain ampliﬁers with a large bandwidth (> 54 dB, ∼ 1 GHz) and pulse counting electronics. The high-frequency ampliﬁcation stage was replaced with a capacitor functioning as an integrating element to simplify the operation. The use of a capacitor requires less power in operation. Most importantly, this also allows to build SSPD array systems by using low-temperature multiplex- ers [149–151] and sequentially reading out the capacitors corresponding to

1Most parts of this chapter have been previously published in Review Of Scientiﬁc Instruments 84 053108 (2013). 112 Capacitive readout and gating of the SSPD the individual pixels. This in turn allows to detect all photons and to determine their position.

Simulation The electronic model used in the program, Micro-cap 9, is schematically illustrated in Figure 9.1. The SSPD behavior was modeled as a current controlled (CC) switch, and a photon absorption event was modeled by integrating a pulse source into the circuit. In the model, the system is biased with a DC current IDC (Vb over a 100 kΩ resistor) and a pulsed current IP (voltage drop Vp over a 250 kΩ resistor). The sum of these currents is monitored by measuring Isense and used to control the CC switch. The switch operates in hysteresis mode around 10 µA, which means that it opens when the current reaches 12µA and closes when it drops below 8 µA. Since the critical current IC for our detector was measured to be just below 10 µA, the DC bias component was set to 7.5 µA and the pulsed component to IP =5 µA. The pulse width was set to 0.3 ns and the repetition rate was ﬁxed at 16 MHz, yielding events separated by 62.5 ns. At the initial phase of the simulation, the current is small and the CC switch is therefore closed, representing the SSPD in the superconducting state. The pulsed source increases the current to above the threshold of 12 µA and causes the CC switch to open. The current then ﬂows through the 6 kΩ resistor representing the hotspot resistance. When the current decreases to 7.5 µA, the CC switch closes again, corresponding to the restoration of the superconducting state. The model values are based on measurements and literature. According to the pulse detection illustrated in Figure 8.6, the measured value of the recovery time τ is ∼ 5 ns, implying a kinetic inductance of Lk ∼ 250 nH. The hotspot resistance RSSPD was estimated to be around 6 kΩ in [129].

22 22 2 22Ω

2 2 2

Figure 9.1: Schematic illustration of the experimental setup model for the capacitor readout. For the co-axial line, the transmission delay was set to 5 ns and the corresponding impedance to 50 Ω.

A capacitor, which constitutes the main element in this scheme, was then added to the circuit. This yields an RC-time τRC of (50Ω + Rd)C seconds, 9.2 Capacitive readout scheme 113 where 50 Ω corresponds to the termination resistance required to match the coaxial line impedance and Rd is the resistance of the discharge resistor (∼ 10 Ω), which sets the time constant. The readout voltage was probed at the node labeled ’Capacitor Readout’. The simulation results obtained for various capacitors with a capacity in the range from 10 to 0.3 nF are shown in Figure 9.2. According to the simulations, for n detected photons, n steps will sequentially be formed on top of the capacitor voltage readout measurement indicating n detected photons. In principle, decreasing the capacitance values down to orders of picoFarads results in an increase of the readout amplitude to the order of millivolts. However, as shown in Figure 9.2, the characteristic integration behavior of the capacitor, which allows for a differentiation between 1 or n detected photons, diminishes when the capacitance drops below 1 nF. Thus, in order to obtain an optimal readout amplitude and a reasonable RC-time constant of ∼ 60 ns, the capacitance was chosen to be 1 nF for the experiment.

8 0 0 . 3 n F

] 0 . 5 n F V m

[ 6 0 0 . 7 n F

t 0 . 9 n F u

o 1 n F d

a 3 n F e 4 0 r 5 n F e

g 1 0 n F a

t l

o 2 0 v

r o t i c

a 0 p a C

- 2 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 T i m e [ n s ]

Figure 9.2: Capacitor voltage readout for various capacitance values.

Experimental results A schematic illustration of the experimental setup is shown in Figure 9.3. The measurements were performed in a liquid helium bath cryostat at 4.2 K. A 633 114 Capacitive readout and gating of the SSPD nm pulsed laser diode was used for optical excitation and coupled through a single mode fiber (SM600 from Thorlabs) with a ∼ 10 µm mode field diameter, and was focused onto the aligned active area of the detector by a collimating lens (NA = 0.25, f = 11 mm, F220FC-B from Thorlabs). SSPD sample 1 (shown in Figure8.5) was mounted onto a circuit board and connected through a coaxial cable to the electronics readout box as described in section 8.2.1. The bias voltage was applied by the data acquisition box through the Bias T and converted into a current by a 500 kΩ resistor before continuing to the SSPD. The output signal was connected to the capacitor at room temperature, after which it was amplified and measured on an oscilloscope. Assuming an SSPD pulse length of τLR ∼5 ns, we expected the capacitor readout voltage prior to It the amplification to be in the order of tens of microvolts (V = C , where I ∼ 10 µA). Figure 9.4 shows both experimental and simulation results obtained for

Figure 9.3: Schematic illustration of the experimental setup used for the capacitor readout. Instead of using a 54 dB amplifier as described in section 8.2.1, the capacitor was connected through the AC port in series with a 44 dB amplifier (ZX60-33LN) before monitoring the output signal on the oscilloscope. the capacitor readout. Within the 120 ns time window that the detector was biased with ∼ 10 µA, two laser pulses were applied to the SSPD with a repetition rate of 16 MHz. The capacitor voltage readout of five events recorded by the oscilloscope shows the expected integrating behavior and contains two distinct peaks separated by around 60 ns, corresponding to two detection events. The five noticeable noise signals are mainly due to the quantization noise of the oscilloscope. The delay between the laser pulses and the detection events is determined by the length of the coaxial cables and the optical fiber. The simulated curve Vsim is in good agreement with the measured capacitor read- 9.3 Gating behavior 115

out Vcap. Most of the recorded events (∼ 75%) showed only one peak on the capacitor readout curve, indicating a single photon detection event. A fraction of the recorded events (∼ 20%) showed a double peak. Thus, a distinction between 1 and 2 detection events based on the readout amplitude is possible.

6 0

S c a l e d d o w n b y V b a f a c t o r o f 1 0 V 5 0 l V s i m V 4 0 c a p ) V m (

l 3 0 a

n g i

S 2 0

1 0

0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 T i m e ( n s )

Figure 9.4: The bias voltage (Vb), the voltage pulses driving the laser diode (Vl), an average of of ﬁve capacitor voltage readout measurements (Vcap) and the simulation result (Vsim) for a capacitance of 1 nF. The bias voltage is scaled down by a factor of 10.

9.3 Gating behavior As previously discussed in section 7.2.1, both the DE and the dark count rate increase with the bias current. However, in some implementations, the bias current must be limited to avoid large dark count rates. Time gating can increase the signal-to-noise ratio by enabling the application of a larger current (and hence a higher DE) during a short time window when a photon is expected, without suffering from large dark noise when no photon is expected, a technique that is similar to the one employed for avalanche photo-diodes. The gate pulse is generated upon the detection of a photon and created by a spon- 116 Capacitive readout and gating of the SSPD

Figure 9.5: (a) Setup for the gating experiments. The electronic circuit box consists of a pulse stretcher (providing a 50 ns wide TTL signal) connected in series to an inverter (PicoQuant SIA 400, In TTL, Out ∼ 300 mV, an 80 dB attenuator (Mini Circuits ZX73-2500), a low pass filter (Mini Circuits, BLP25) and a 500 Ω resistor. (b) Gating and measured signals. The APD detection pulse (APD), scaled by a factor 0.02, was reshaped by the electronics box into a 50 ns inverted gate pulse (Gate). The gate pulse is scaled up by a factor of 100. For comparison, both a regular detection event without gating the SSPD (Regular) and an event occurring when a gate pulse is applied (Gated) are shown. 9.3 Gating behavior 117 taneous parametric down-conversion source, which heralds the presence of a second photon. The gating enables an efficient synchronization and allows to control the detection events while suppressing the occurrence of dark counts. Figure 9.5a shows the setup used for the gating experiments. Here, a single mode fiber was pigtailed2 to the SSPD 4 (cp. Figure 8.5) to allow for an efficient optical illumination. The pigtailed detector was mounted on a dip-stick and immersed in liquid helium. It was electrically connected similarly to the setup described in the previous section 9.2, but, instead of sending the output signal to the capacitor, the signal was directly amplified by 54 dB and then sent to the oscilloscope. A constant DC bias current of ∼ 4 µA, about 80% of the critical current, was applied. The optical illumination in the schematic illustration shown in Figure 9.5a was provided by a spontaneous parametric down-conversion (SPDC) source. A continuous-wave 532 nm pump laser drives a collinear SPDC process in a 2 cm long KTP crystal cut for degenerate type-II phase-matching3. After the crystal, a polarizing beam-splitter separated the generated photon pairs (coherence time ∼ 2 ps), and the individual correlated 1064 nm photons were collected using single-mode fibers. One of these fibers was connected to an avalanche photodiode detector (APD) to provide the gating pulse. A detection event of this detector heralds a photon in the other fiber, which was connected to the pigtailed SSPD. The APD signal was converted to a proper gating pulse with a pulse stretcher (to create a 50 ns wide TTL signal), a 80 dB attenuator, and a low pass filter (∼ 13 ns rise time). The filter is required to decrease the direct cross-talk between the gating pulse and the AC-coupled high-frequency pulse detection electronics. The pulse was then applied across a 500 Ω resistor to add it to the DC bias current. The processing of the APD signal caused a delay of ∼ 10 ns. This gating pulse provided only a fraction (∼ 20%) of the required bias current. The main DC component was provided by the driver (IAPD IBias,IAPD + IBias = ITotalBias). However, IBias could be kept smaller than usual, resulting in the absence of dark counts when the detector was not gated on. The involved signals, the APD pulse, the gate pulse, a regular detection event, as well as a gated detection event are shown in Figure 9.5. To measure the correlation between photons detected by the SSPD and the APD, both output signals were sent to a time-correlated single photon counter module (PicoHarp 300, resolution set to 256 ps). Figure 9.6a shows the measurement where the heralded photons were delayed by adding pieces of 1 m optical fiber patches at a time. Figure 9.6b shows the results when the gate pulse was delayed by adding pieces of a 1 m coax line at a time. The correlated photons show up as a sharp peak, indicating that the detection of a

2The ﬁber pig-tailing was done by R. H. Hadﬁeld (School of Engineering and Physical Sciences, Heriot-Watt University). 3A more detailed description of the setup of the SPDC source is provided in appendixE. 118 Capacitive readout and gating of the SSPD photon by the APD heralds the presence of another photon at the SSPD. Since the timing jitter of the APD and SSPD are much larger than the coherence time of the photon pairs, the width of the peak is determined by the jitter. The envelope of the ∼ 50 ns wide curve where detection events occur is caused by both background light and dark counts. It indicates the shape of the gating pulse applied to the SSPD, and is thus a good hint for the photon DE.

Figure 9.6: Gated operation of the SSPD. (a) Detection events as a function of the optical delay of the heralded photon. The reference shows detection events for a 7m ﬁber optical delay without gating. (b) Detection events as a function of the gate pulse delay. When the heralded photon falls outside the gate window (lowest trace) there are no correlated detection events. 9.4 Conclusion 119

9.4 Conclusion To summarize, the implementation of a capacitor-based voltage readout has been demonstrated, allowing us to resolve the number of incoming photons within the RC-time of the capacitor and relax the amplification requirements. Simulations were performed using a circuit model with two photon pulses and confirmed by measurements. I. E. Zadeh et al. reported the first attempt to practically implement a multiplexing array of large arrays of SSPDs [152]. Combining an SSPD array with a low-temperature multiplexing readout will allow to detect all photons and to determine their position, resulting in a single-photon imaging detector with a low noise that is sensitive over a broad wavelength range. Furthermore, we have shown that it is possible to gate an SSPD to provide some of the time-information that is lost when using a capacitive readout. For future projects, additional work is needed to improve and increase the detection efficiency within the small time-windows when photons are expected, while preventing the occurrence of dark counts outside this window. Further research on multiplexing arrays may prove beneficial for a number of imaging applications based on imaging sensors.

121

10. High-energy particle detection

10.1 Introduction Since the first detection of β-particles with photographic films by Becquerel [153], detectors with a higher efficiency, a lower noise level, a better energy resolution and higher saturation rates have been developed [154]. The detection of α- and β-particles is of paramount importance in a wide range of applications, playing an important role in biochemistry [155], in the precise measurement of thin layers [156], in radiotherapy [157], in dating [158], in security systems [159] and for targeted radiotherapy [160–162]. Prevalent detection systems include gas proportional counters, high-purity semiconduc- tors, scintillation detectors, and micro-scale transition edge sensors. Scintil- lation [163] and semiconductor counters [164] provide a high detection efficiency albeit at the cost of a large detection volume. Micro-calorimeters based on superconducting transition edge sensors are currently among the smallest radiation detectors, with absorber dimensions as small as (400 × 400 × 250) µm [165]. The readout time of these devices is of the order of milliseconds, limiting the detection rate to ∼ 100 Hz. Additionally, low operating temperatures [166] around 10 mK further reduce their applicability. A superconducting microstrip made of NbAl has previously been shown to switch from the superconducting to the conducting state under an intense α-particle flux (740 kBq) [167]. However, single particle detection at the nanometer scale has not yet been demonstrated, although it has been shown that superconducting nanowires are capable of detecting single photons [107] and single electrons [168]. In this chapter1, this concept is extended to the detection of high energy particles in the MeV energy range. We experimentally demonstrated an efficient single α- and β-particle detector with a DE close to unity. In addition, we observed that our nanoscale detector exhibits a blindness towards γ- and X-rays. The chapter is introduced by a brief description of the sample preparation processes and the mounting methods in sections 10.2 and 10.3. Selected detection results for the different α-/β-particle and γ-/X-ray emitters are presented in section 10.4. The chapter is concluded by section 10.5, where the obtained results are discussed.

1Most parts of this chapter have been previously published in AIP Advances 2, 032124 (2012). 122 High-energy particle detection

10.2 Sample preparation α-particle emitter 210Po isotopes were chosen and prepared as a pure α-particle source with a sufficiently high activity to be detected by the SSPD. The 210Po activity for the plated stainless steel disk source was produced by irradiating 591 mg of natural metallic bismuth (in the form of < 0.5 mm beads sealed in a quartz tube) in the central irradiation facility of the Hoger Onderwijsreactor (HOR) at the Delft University of Technology (φ = 3.7 · 1013 n/cm2·s). This produced an initial 210Po activity of ∼ 618 kBq and an initial 210Bi activity of ∼ 54 MBq. After a cooling period of ∼ 15 days, the 210Po activity had increased 1 to ∼ 2.2 MBq. The quartz tube was opened and ∼ 2 the bismuth metal was dissolved in a combination of 0.5 mL concentrated nitric acid (HNO3) and 1.5 mL of 30% hydrogen peroxide (H2O2). This solution was dried and then re-dissolved in water three times to get rid of the excess HNO3 and H2O2. The solution was then dissolved in 0.5 M oxalic acid (H2C2O4). Plating was carried out following the procedure described by Ordoñez-Regil et al. [169]. In an effort to minimize the effect of any 210Bi co-plated on the metal disk, the measurement was started five days later (an additional half-life) to further reduce the 210Bi activity. After the measurement, the activity of the 210Po plated on the disk was measured using a Hidex 300 SL liquid scintillation counter (LSC). The source was mounted in a standard LSC vial and submerged in LSC fluid (UltimaGoldTM XL). Activity measurements were made in standard counting mode, alpha double coincidence mode, and alpha triple coincidence mode. Figure 10.1 shows a simplified decay scheme for 210Po: an α-particle- emitting radionuclide, with the α-particle emission being rarely (a probability of 0.0012 %) accompanied by γ-ray emission. The 210Po source showed an activity of 41.4 kBq, as measured with a scintillation counter, with an average α-particle energy of 5.3 MeV and a half-life time t 1 = 138.38 days [170]. 2

β -particle emitters Two different β-emitting samples, 42K and 31Si, were prepared by irradiation of potassium hydroxide (KOH) and a high-purity quartz bead (SiO2), respectively. The irradiation was again performed using the pneumatic tube system at the HOR (ϕ ≈ 4.6 · 1012 n/cm2s). The 220 mg quartz bead was irradiated for 9 hours, which resulted in an initial 31Si activity of ∼ 26 MBq. The 53.7 mg of KOH were poured into a small polyethylene cup, capped, and irradiated for 2 hours, producing an initial 42K activity of ∼ 40 MBq. Figure 10.1 shows simpliﬁed decay schemes for both sources. It is important to note the different γ-ray emission probabilities for each of these decays: while the emission of a β-particle is accompanied 17.64% of the time by a 1.524 MeV γ-ray in case of 42K, 31Si is a relatively pure β-particle source [170]. The half-life values 10.3 Sample mounting and setup 123

42 31 for the used sources are t 1 = 12.36 hours for K and t 1 = 2.62 hours for Si. 2 2

Figure 10.1: A simpliﬁed decay scheme for all three isotopes, i.e., 210Po, 42K and 31Si. 210Po and 42K are relatively pure sources, both of them decaying 99.9% of the time through α- and β-particle emission, respectively, whereas 42K decays only 81.9% of the time through β-particle emission.

γ-ray emitter Since α-particles are much easier to block than β-particles, an 241Am source was chosen for the test measurements. 241Am is an α-particle-emitting radionuclide whose decay is accompanied by signiﬁcant amounts of other events (e.g., conversion and Auger electrons, and X- and γ-ray emissions). A few of the relevant emission probabilities are: a conversion electron intensity no less than 60% (of various energies between 3.9 and 76 keV), ∼ 35% Auger electron emission (10.1 keV), X-ray emissions totaling no less than 37%, and γ-ray emissions totaling no less than 38% [170]. We counted an electroplated 241Am source (a legacy source previously removed from a smoke detector) at approximately the same geometry as the 210Po source. This source was soldered to a threaded rod which helped to ensure a reproducible geometry.

10.3 Sample mounting and setup The 210Po source was mounted onto a metallic holder on top of the detector to prevent the detection of scintillation events from organic materials. Further- more, the 210Po-source was placed as close as possible to the detector without damaging the bonding wires, as shown in Figure 10.2a. The distance from the 124 High-energy particle detection top of the bonding wires to the sample surface is known from the standard bonding parameters to be ∼ 20 µm and was checked by measuring the variation of the focus distance in a conventional microscope. We estimated the sample to be a few microns above the bonding wires, which corresponds to a distance of ∼ 25 µm from the sample to the detector, with an uncertainty of ±3 µm. The 241Am source was mounted in a way similar to the 210Po source. Both β-particle sources (42K and 31Si) were ﬁrst placed in small cups, leading to a slightly different mounting method. A plastic holder on top of the detector contains the β-particle sources. The arrangement is shown in Figure 10.2b. The height of the holder was relatively easy to adjust (i.e., the distance between sample and detector), which was measured with a vernier caliper with an uncertainty of ±0.1 mm. Three detectors were used in this experiment to measure each of the different sources. Each detector was mounted onto a circuit board with a coaxial connector and inserted into a metallic housing. The metallic housing is a sealed capsule, specially made and tested to comply with the no-radiation-leakage safety requirement set by the reactor authorities. The metallic housing was then mounted onto a dip-stick and immersed in liquid helium (4.2 K). The used readout setup was similar to the setup described in section 8.2.1. For photos of the metallic housing, and additional pictures of the setup and sample mounting, see appendixF.

Figure 10.2: Illustration of the mounting of (a) the α-particle sources attached to a screw and (b) the β-particle sources placed on top of a plastic holder. 10.4 Particle detection 125

10.4 Particle detection We successively tested our detectors with a pure α-particle source (210Po), two β-particle sources (31Si and 42K) and a γ-ray source (241Am). The used samples are listed in Table 10.1. For each source, the bias current was ramped close to the critical current while the detection count rates were recorded, with the process repeated over several hours of measurement.

α-particle detection Figure 10.3 shows the α-particle detection rates versus time for a given current bias. Because of the long half-life, we did not observe a decrease in the count rate over our limited measurement time. Instead, we observed a constant count rate with an average of 582 ± 43 cps, as shown in Figure 10.3. In this arrangement, the detector occupied a fraction ηd of the isotropic radiation sphere given by A/4πd2, where A is the active area. For the estimated distance of d ∼ 25 µm and a source intensity of A0 ∼ 41 kBq, the detection ef- ﬁciency of the SSPD was calculated to be ∼ 78±18% (407±55 cps corrected for background counts). Since an α-particle is a relatively massive particle, it could damage the active NbTiN layer [171]. After more than 1.7 · 108 detection events during the 95 hours of measurement with the α-particle source, the detector showed no decrease in count rate, no increase in noise level and no modiﬁcation of the critical current, thus demonstrating a high radiation hardness.

β -particle detection To demonstrate the β-particle detection capability, two different sources were 42 31 used: K(t 1 = 12.36 hours) and Si (t 1 = 2.62 hours). Figure 10.4a shows 2 2 the detection events recorded for the 42K source measured over a time period of 26 hours. The single exponential ﬁt (solid blue line) yields a half-life time of 12.4±3.4 hours. The detector noise ﬂoor is indicated by the dashed blue line. Adopting the same procedure for the shorter lived 31Si source, the exponential decay in Figure 10.4b gives a half-life of 2.9 ± 0.5 hours. The half-life values measured for both 42K and 31Si are in good agreement with published data [170], and thereby demonstrate the capability of the detector for single β- particle detection. The distance d between source and detector was set to 1 mm for 42K and 2 mm for 31Si. Combined with the initial activities of each source (cp. Table 10.1), this yields an SDE of 95 ± 14% and 106 ± 12% for 42K and 31Si, respectively.

Insensitivity towards γ-rays Experiments were carried out to determine the sensitivity of the detector towards γ-rays. The measured count rate depicted in Figure 10.5 for the bare 241Am was 5.75 ± 0.43 kcps and the dark count level (without the 241Am 126 High-energy particle detection

Figure 10.3: Results of the α-particle detection experiments. The detection count rates 210 were recorded at Ib/Ic ∼ 0.91 for the Po source (red circles) and the background counts (dashed blue line). The average count rate for the source is 582 ± 48 cps, and 175 ± 26 cps for the background. Detector sample 2 (shown in Figure8.5) was used for this experiment. source) was measured to be 2.07 ± 0.20 kcps. In order to measure only the contribution of the γ-rays to the count rate, we introduced a shield to block the α-particles (and the conversion and Auger electrons) from reaching the detector. A small piece of aluminum foil (∼ 0.2 mm thick) was used to cover the surface of the source and then folded upward around the shaft of the threaded rod. The count rate was then recorded for the shielded 241Am to determine the γ-ray DE. The detection count rates dropped down to the dark count level, indicating that no X- nor γ-rays were detected. 10.4 Particle detection 127

Figure 10.4: Results of the β-particle detection experiments. a) β-particle detection count rates as measured for the 42K source. The detection count rates recorded at Ib/Ic ∼ 0.95 are depicted as a semi-logarithmic plot versus time (red dots) together with an exponential fit (solid blue), which yields a half-life time t 1 = 12.4±3.4 hours. 2 Detector sample 3 (shown in Figure8.5) was used for this experiment. b) β-particle detection count rates measured for the 31Si source. Detection count rates recorded at Ib/Ic ∼ 0.88 are depicted as a semi-logarithmic plot versus time (red dots) together with an exponential fit (solid blue), yielding a half-life time t 1 = 2.9 ± 0.5 hours. 2 Detector sample 1 (shown in Figure8.5) was used for this experiment. The detector background level for both measurements is indicated by the dashed blue line. The half-life for both isotopes was calculated through t 1 = ln(2)/Λ, where Λ is the slope 2 of the exponential fit. 128 High-energy particle detection

Figure 10.5: Results of the γ-ray detection experiments. The detection count rates 241 were recorded at Ib/Ic ∼ 0.95 for the bare long lived Am source (red circles). The α-particles emitted from the 241Am source were then blocked and the count rate was recorded again to determine the γ-ray DE (green triangles). Background counts (blue squares) were recorded in absence of the 241Am source. The dashed blue line indicates the average count rate for the bare source, whereas the overlapping black and red lines indicate the average values for the γ-particle-ﬁltered and background counts. 10.5 Conclusion 129

10.5 Conclusion Table 10.1 presents the DE of our superconducting nanowire detector for single particles, ranging from single photons at optical frequencies to α- and β-particles in the MeV range. We have demonstrated an efﬁcient nanoscale detector for single α- and β-particles. The DE is close to unity for both particles, and the half-life values determined for both β-particle sources are in good agreement with published data, which indicates a good capability of the detector for single particle detection. We note that no radiation damage was observed after more than 4 days of α-particle irradiation, demonstrating the robustness of the detector. Furthermore, the nanoscale detector exhibits a blindness to γ- and X-rays. The increasing demand for radiation particle detectors insensitive to saturating γ- or X-rays [172] makes our detector a good candidate for a γ-discriminating detector. However, whether this insensitivity is due to the nanoscale thickness or the absorption properties of the active area has yet to be investigated. Likewise, a theoretical explanation of the presented high-energy particle detection principle has yet to be formulated, and a systematic analysis of the optimal combination of superconducting ﬁlm and its underlying substrate must be carried out to optimize the DE. In the future, arrays [152] of these nanowire detectors could be operated. In principle, a high energy resolution may be achieved by analyzing the change in count rate as the bias current is changed relative to the critical current. This has already been demonstrated at optical frequencies with this type of detector [109]. The detector could be mounted on a scanning probe to allow for particle detection measurements with an unprecedented spatial resolution. The use of nanoscale detectors for particle detection is expected to enable a wide range of new applications where the high time and spatial resolution and high counting rates will be essential.

Source Type Initial Average Published Half-life Detection Reference

Activity Energy (t 1 ) Efﬁciency (DE) for SDE 2 210Po α 41.2 kBq 5.30 MeV 138.38 days 0.78 ± 0.18 Present work 42K β − 40 MBq 3.52 MeV 12.36 hours 0.95 ± 0.14 Present work 31Si β − 26 MBq 1.49 MeV 2.62 hours 1.06 ± 0.12 Present work 241Am γ, X − ∼ 5.95 keV − 0 ± 0.10 Present work SEM e− − 10 keV − ∼ 1 [168] Laser hν (photon) − ∼ 1 keV − [email protected] nm [125]

Table 10.1: Comparison of the detection efﬁciency for the different irradiation sources based on experimental and published data for a wide range of particle energies.

131

11. A multi-purpose testing station

11.1 Introduction One of the biggest challenges for an efficient detection of photons (or any other particle for that matter) is the optimization of the coupling between the optical fiber and the small active area of the SSPD. Current conventional setups differ in design and make use of various coupling techniques, e.g., placing the fiber in close proximity to the detector [107, 119], directing the beam onto the active area through a focusing lens [125, 138], or by gluing the tip of the fiber onto the detector [115], a technique known as pig-tailing. Despite the fact that these techniques can ensure that a fraction of light is coupled to the detector, the coupling efficiency has generally proven to be relatively poor. Moreover, the cooling process required to cool down the system to the operating temperature in the cryogenic regime can easily result in a thermal misalignment due to the different expansion coefficients of the materials used for the coupling, adding to the inefficiency of the coupling and making the used setup unreliable. These challenges are usually related to the inherent properties of the utilized testing setup. One approach to address these challenges is the development of a novel detection setup that, besides providing an optimal coupling efficiency, also proves robust and able to sustain continuous and repeated cooling processes without the occurrence of a misalignment. Furthermore, when designing a low-cost and user-friendly testing setup, a low helium consumption, a compact size and a system that is easy to operate are abilities that are worth aiming for in an ideal testing setup. A promising proposal for such a setup was presented by Orgiazzi and Ma- jedi [173], who fixed both the fiber and the SSPD to a casing. Their casing was made of a metal with an extremely low expansion coefficient which allowed to achieve a very reliable coupling efficiency. However, both the proposed alignment and mounting procedures are rather time-consuming processes, thereby preventing an accessible and rapid interchange of either the detector or the fiber if one of them gets damaged or shows a drop in performance. In this chapter, the design and fabrication of a reliable SSPD testing system for an efficient characterization of the SSPDs under optimal coupling conditions is presented. The good coupling between fiber and detector is ensured by using a 3-axis nanopositioner system, which aligns the fiber-tip to the active area and can be operated at cryogenic temperatures. For measurements that 132 A multi-purpose testing station would either require a swap of the fiber or the detector, the assembly is designed to allow for a fast replacement of both. A general outline of the design considerations and the fabrication of the dipstick used for the testing system is given in the next section (Section 11.2), followed by a description of the principle of operation of the scanning system in section 11.3. A calculation of the expected coupling efficiency and preliminary experimental results as proof of principle are presented in section 11.4. The conclusions are presented in section 11.5. Additional data, pictures, and specifications can be found in ap- pendixG, whereas further information regarding the design, fabrication and the utilized software applications and procedures (LabVIEW and Matlab) is available in the bachelor thesis of Klaus Hueck [174].

11.2 Dipstick construction 11.2.1 Design considerations and fabrication Since no cryogenic-free systems were available in our lab for cooling the detectors, we decided to use a liquid helium transport dewar in which a dipstick with the attached detector could be submerged. Thus our design effort and attention was primarily focused on developing a dipstick able to comply with our main criteria for a suitable system. The first requirement was the efficient coupling of the photons from the fiber to the detector. Second, the system needed to be user-friendly, which involved a quick and easy replacement of both the optical fiber and the detector. An active coupling system whose optimization process could be controlled in real-time was introduced to resolve the coupling efficiency problem while enabling the operation of the detector at low temperatures. More specifically, by attaching the end of the fiber to a ferrule that was mounted on a 3D attocube piezo-positioner that allowed to move the detector in all directions, we were able to achieve an optimized alignment of the fiber even when the system was cooled down to 4.2 K. Both the detector and fiber were located in a compartment at the bottom end of the dipstick, as shown in Figure 11.1. To allow for the fast and accessible replacement of the detector, a two-step mounting system was designed. The board with the glued and bonded detector, previously described in section 8.1.4, was mounted on an aluminum block which in turn was placed inside the bottom compartment. However, these criteria, together with the setup involving the dewar, put some constraints on the design of the system. Firstly, the dipstick geometry was determined by both the size of commonly available liquid helium dewar tanks and the utilized coupling system. The minimum attainable diameter of the coupling system was around 40 mm, thus a dewar with a 50 mm diameter neck was chosen. More- over, to reduce the heat conductivity between the bottom compartment of the 11.2 Dipstick construction 133

Figure 11.1: Photograph showing the compartment at the bottom of the dipstick which contains the coupling system. More pictures of the bottom compartment can be found in appendix G.3.

dipstick and the top-housing with the electrical and optical feed-throughs at room temperature, a stainless steel rod was selected. The wall thickness of the rod was 1 mm and the outer diameter of the tube was chosen to ∼ 19 mm (3/4”) to ensure that there was enough space inside the dipstick tube for all the necessary electrical and optical cables1. The length of the stainless steel tube was determined by the height of the dewar and was therefore chosen to have a dipping length of 1320 mm. Hence, when the dipstick was fully immersed, its bottom end was only 110 mm above the bottom of the vessel. Secondly, the upper seal of the compartment had to be helium-tight when submerged in the dewar. However, because of the very compact and space-saving design of the compartment, there was not enough space for the indium wire seals which are typically used [175]. Therefore, we decided to test an alternative solution: a low-profile indium wire seal, presented in [176]. The 75 mm thick indium wire was cut in such a way that both ends fit the circumference of the compartment, thereby shaping an o-ring. Before inserting the indium o-ring, a small amount of cryogenic vacuum grease2 was applied to the mating surfaces of the seal. This allowed to re-use the indium o-ring at least three times. Although the leak rate of the seal could not be quantified, a good sealing quality was achieved during the experiments. The top-housing contained all the required optical and electrical connectors, i.e., an RS232 connector for driving the attocubes, an SMA-connector for both applying the bias voltage and for the signal readout, and a feed-through for the

1Three pairs of wires for the attocube system, one semi-rigid co-axial cable for the electrical signal and one optical fiber. 2Apiezon N Ultra High Vacuum Grease. 134 A multi-purpose testing station optical fiber. While all these connectors had to be airtight at room temperature, the optical feed-through required special attention due to the frequent replacement of the optical fiber. Before describing the optical feed-through in more detail in section 11.2.2, it is worth to briefly mention the measures taken to ensure a proper sealing of the RS232 and SMA-connectors: • RS232 connector: the used RS232-connector was sealed with epoxy glue which, except for small air bubbles inside the epoxy glue, proved to provide a high-quality sealing. The sealing quality can be further improved by using an electrical feed-through designed for vacuum usage. • SMA connector: a hermetic SMA-adapter with an o-ring seal was used for high-vacuum compatibility3. An additional challenge during the dipstick design process was the probability of condensation in front of the detector, potentially leading to a reduced coupling efficiency. Therefore, besides the necessity to reduce the thermal stress to a minimum during cooling, the compartment also had to be evacuated. Therefore, just below the top-housing, a T-piece was added to the tube to provide access via a vacuum flange through the entire tube and all the way down to the compartment. A pump4 was then attached to the flange to evacuate the system, while monitoring the system pressure with a Thermovac5 with a measuring range of [5 · 10−4,1 · 103] mbar and inserting the exchange gas. The exchange gas supports the cooling of the detector and helps to prevent condensation inside the stick. Inserting 20 mbar of pure helium into the evacuated system proved to be sufficient. Close to the T-piece, the electrical readout setup (similar to the one described in section 8.2.1) was mounted. The attocube controller was separated from the electrical readout system, but was partly controlled by the same LabView program to execute the scanning and alignment procedures while recording the count rate of the detector. Photos of the entire setup are shown in appendix G.3.

11.2.2 Optical fiber vacuum feed-through6 The majority of current optical fiber vacuum feed-through designs focus on simplicity and achieving a low optical loss, and are therefore based on encap- sulating a short piece of fiber so that it can be made vacuum tight [177, 178]. Fibers are then connected to both sides of the encapsulated fiber using standard optical fiber connectors. The major drawback of these systems is that the selection of the encapsulated fiber will then dictate which fiber and wavelengths can be used. As a result, if a wide range of wavelengths are required,

3Procured from CMR-direct. 4Oerlikon Trivac D 2.5 E. 5Oerlikon TTR 91. 6Most parts of this section have been submitted in paper III. 11.2 Dipstick construction 135 then either a MMF must be used or more than one feed-through. In addition, because these designs require fiber-to-fiber connections at both sides of the vacuum system, they will naturally exhibit a higher optical loss compared to other designs. A number of alternative designs have been proposed that allow to change the fibers without requiring a change of the feed-through; so-called demount- able designs [179–181]. However, these designs either still suffer from limitations in terms of the fibers that can be used [179] or require a special preparation of the fibers [180,181], which again might limit their suitability for certain experimental situations. To solve all of these problems, we have developed a new design that offers the user the ability to connect standard fibers utilizing normal fiber connectors, in this case FC/PC connectors, and other connectors as well (such as FC/APC or SMA). Our design is based on the modification of commonly available standard fiber bulkhead connectors so that they become suitable for an application as vacuum feed-throughs when combined with a rubber o-ring seal, resulting in a simple and highly flexible fiber feed-through.

Feed-through fabrication

Figure 11.2: Schematic illustration of the modified mating sleeve and construction of the optical fiber vacuum feed-through. The edges marked in red were removed to achieve a good acceptance geometry for the o-ring [174]. (a) Cross-sectional view of the unmodified bulkhead adapter. (b) Exploded view of the fiber connector, o-ring, and modified bulkhead adapter assembly. The modifications made to the bulkhead are outlined in red. (c) Final assembly of the adapter attached to a blank.

Figure 11.2 shows a schematic illustration of the modified bulkhead connector and the o-ring seal that formed the basis of our adapter. When fibers are inserted into the connector, the o-ring is deformed so that it seals the fiber into the adapter. We have selected small diameter NBR o-rings for this work, but 136 A multi-purpose testing station a wide range of vacuum-grade o-rings are available, and any of these should be suitable. The feed-through was fabricated using a countersink drill bit to carefully remove a small amount of material around the top and bottom of the inner metal tube that encloses the ceramic sleeve which centers the fiber ferrules. This was done to ensure that a good seal was achieved when the o- ring was compressed between the fiber connector and the bulkhead adapter. The use of a countersink bit offered the advantage of being somewhat ‘self- centering’ which helped to improve the accuracy of the milling process and hence the seals effectiveness. To seal the bulkhead adapter against the vacuum chamber, the feed-through was glued in place on the top-housing with a high-performance epoxy glue7. Figure 11.2c shows the complete assembly with a fiber attached. To realize the maximum sealing performance of the adapter, it is advisable that a fiber is attached on both sides at all times. Although this may be problematic in some cases, we have found that the use of a blank fiber (an old FC/PC connector with a very short piece of fiber still attached) was suitable where the use of a full length fiber would be problematic.

Experimental setup To test the feed-through’s leak rate, all of the components were connected to a small (2.3±0.3) L vacuum chamber which was determined to have a base leak rate of 4.8 ± 0.6 · 10−6 L·mbar/s, measured by timing the change in pressure using a cold-cathode pressure gauge8. The chamber was evacuated using a pumping station consisting of a turbo pump9 backed by a diaphragm pump10. With this setup, the chamber could be pumped down to a base pressure of ∼ 5 · 10−6 mbar. The layout of the system employed for the leak rate tests is shown in Figure 11.3.

Figure 11.3: Schematic illustration of the vacuum system used for the leak rate measurements. 1) Diaphragm pump, 2) Turbo-molecular pump, 3) Manual valve, 4) Pirani gauge, 5) Cold cathode gauge, 6) Helium container, 7) Vacuum chamber, 8) Test port.

7An alternative approach is to use a simple NBR rubber washer of suitable size compressed against the ﬂat surface of a vacuum blank ﬂange, as described in paper III. 8Pfeiffer Balzers IKR 050 gauge and TPG-300 vacuum gauge controller. 9Pfeiffer HiPace 80. 10Pfeiffer MVP 015-2. 11.2 Dipstick construction 137

The leak rates were determined in two different ways. Analogous to the chamber leak rate measurement, the first technique simply involved measuring the rate at which the system pressure increased once the turbo-pump had been valved off. This method was used when it was impractical to sur- round the tested component (e.g., the whole chamber) with helium. Since this first technique likely results in less accurate rates due to the inclusion of virtual leaks, the gauge reaction time and other factors, a second technique was also applied which involved surrounding the tested component (e.g., the feed-through) with helium, and then measure the leak rate using a commercial helium leak detector system11. In this configuration, the pump station was replaced with the leak detector system, which had its own turbo pump setup. The optical loss measurements were then performed using NIST-traceable calibrated power meters12 and a range of laser sources and fibers, which are listed in Table 11.1. For reasons of simplicity, the measurements were conducted prior to attaching the modified and unmodified adapters to the vacuum chamber. However, additional measurements made when the adapters were attached to the chamber revealed no significant change in the measured losses. To determine the loss, each fiber and wavelength combination was measured at a series of different input powers. The acquired data was then fitted employing the method of least squares. In all cases we have tested the loss between identical fiber types; the investigation of losses resulting from the coupling of dissimilar fibers is outside the scope of this work.

Leak rates and optical losses Figure 11.4a shows the rate of change of the chamber pressure with and without the modified adapter. The measured rates are listed in Table 11.1. The measurement of the leak rate of the modified adapter was made to test the accuracy of this method compared to the standard helium leak rate measurement. The leak rate of our modified adapter was also determined by measuring the helium leak rate as described in the experimental section. The measured rates and their uncertainties are listed in Table 11.1 as well. Assuming the system was operating in the molecular flow regime (which seems reasonable considering the basis of the base system pressure and the measured leak rate) and by converting the helium rate for the modified adapter to an ’air’ value, we obtained a leak rate of 7.94 ± 1.8 · 10−6 L·mbar/s, which is in good agreement with the value obtained by simply measuring the change in pressure. Calculating the average of these two values resulted in a final leak rate of 6.6 ± 2.1 · 10−6 L·mbar/s, making the adapter suitable for an application in high-vacuum (HV) systems.

11Pfeiffer Qualytest HLT260. 12Thorlabs S120C and S122C. 138 A multi-purpose testing station

Figure 11.4: a) Vacuum chamber pressure vs. time with and without the modiﬁed feed-through. b) Measured attenuation values vs. wavelength for different types of ﬁbers. The red and black dashed lines represent the average loss values for each of the adapters.

Timed Helium leak Detection system [10−6L·mbar/s] [10−5L·mbar/s] Rate Unc. Rate Unc. Chamber 4.76 0.61 - - Chamber + modiﬁed adapter 10.08 1.26 - - Modiﬁed adapter 5.16 1.31 2.06 0.47

Table 11.1: Measured leak rates and corresponding uncertainties for the chamber and the modiﬁed feed-through.

Since one of the major performance requirements for an optical feed-through is a low optical loss, the overall optical loss was measured over a range of wavelengths and using a series of different fibers. The stated insertion loss for this kind of fiber bulkhead adapter, without modification, is < −0.5 dB, and by averaging all the values in Figure 11.4b for the unmodified adapters, an insertion loss of −0.44 ± 0.13 dB was obtained, which is in good agreement with the reported value. For the modified adapters, the average loss across all the measured wavelengths and fibers was determined to be −0.41 ± 0.17 dB. As this is both nearly identical to the loss measured for the unmodified adapter and within the experimental error of the reported loss for an unmodified adapter, the result suggests that the modification process did not have a significant effect on the adapter’s optical performance. 11.3 Scanning system 139

11.3 Scanning system The idea of using a scanning system emerged from the need of being able to actively optimize the coupling efficiency. The scanning system used in this study consisted of a stack of three linear attocube piezo positioners13 mounted on top of each other. The fiber used to couple light to the detector by a ferrule was mounted as shown in Figure 11.1. However, the available system had no position feedback mechanism, inducing the risk of damaging the electrical bonding if the fiber tip was getting too close to the detector surface (< 20 µm) when scanning in the x-y plane. To eliminate this risk, it was necessary to implement a position feedback in the z-direction.

Cavity distance measurement - scan in the z-direction By considering the arrangement between the tip of the fiber and the surface of the detector as a Fabry-Perot (F-P) interferometer, more specifically, as a cavity consisting of a pair of highly reflective mirrors, the absolute distance between the fiber and the detector could be measured by using a white light source or a wavelength-tunable laser [182].

Figure 11.5: Schematic illustration of the setup utilized for measuring the distance between the ﬁber tip and the detector.

A schematic illustration of the experimental setup used to measure the distance in the z-direction is shown in Figure 11.5. In this setup, the light generated by the tunable laser source 14 is routed by an optical circulator to the tip of the fiber, which serves as a sensor probe. The light reflected back from the fiber is directed towards a photo-diode by the optical circulator. Typically 4% of the incident light is reflected from the tip of the fiber, whereas the remaining 96% propagates through the vacuum cavity distance d before being back-reflected by the surface of the detector and coupled back into the fiber core.

13Two ANPx51 positioners and one ANPz51 positioner. 14Santec TSL-200. 140 A multi-purpose testing station

Figure 11.6: Schematic illustration of the operation principle of the F-P cavity and√ the electric ﬁelds√ resulting from the two back-reﬂecting surfaces, where E3 = Ei TF L1 2 −iβd+iπ and E4 = Ei TF RDL2e . .

The electric fields of the reflected light beams shown in Figure 11.6 are given by √ √ 2 −i2βd+iπ E1 = Ei RF , E2 = EiTF RDL2e , (11.1) where Ei is the electric field of the incident light beam, RF + TF = 1 are the reflection and transmission coefficients at the surface of the fiber, RD is the reflection coefficient of the detector, β is the propagation constant of the air, and L2 the loss factor due to imperfections of the cavity and surface. The additional phase shift to the field E2 allowed to obtain information regarding the absolute distance. The term iπ represents the 90◦ phase shift due to the reflection from the detector. Now the normalized reflection spectrum IFP could be obtained as a function of the wavelength λ:

2 E1 + E2 √ 2 4πdn IFP(λ) = = I1 + I2 + 2 RF RDTF L2 cos − π (11.2) Ei λ where n is the refractive index of the medium, in this case vacuum, and therefore n ≈ 1. From Eq. (11.2) one can deduce that the maximum and minimum values of IFP(λ) are achieved when the term (4πdn/λ −π) fulﬁlls the following conditions: 4πdn 4πdn − π = 2mπ, − π = (2m + 1)π, (11.3) λmax λmin where the integral m represents the m-th order interference fringe. By deﬁning the wavenumber of light to be f = 1/λ, performing a fast Fourier transformation (FFT) on Eq.(11.3) yields that the frequency spectrum may be used to 11.3 Scanning system 141 calculate the absolute distance of the cavity length d since

f = 2nd. (11.4)

The resolution of the system depends on the broadness of the used light source. Particularly, since the distance d can be calculated from the positions of two adjacent fringes, e.g., λ1 and λ2, according to

λ λ d = 1 2 , (11.5) 2n(λ2 − λ1) at least two fringes within the bandwidth of the tunable source are required in order to resolve the distance. With a typical scanning range from 1510 to 1570 nm (in our case) a resolution of ∼ 20µm was guaranteed. Prior to operating the system in a cryogenic environment, a proof test of the functionality of the distance measurement system was performed by mounting the fiber tip on a µm-translational stage in front of a mirror. This is illustrated in Figure 11.7 where the measured cavity distance between mirror and fiber is plotted as a function of the relative position of the fiber tip. It is evident that the measured linearity is a stable and reproducible dependence suggesting a good reliability of the measurement system. A typical interference spectrum and its corresponding Fourier transform obtained after the detector was implemented are shown in Figure 11.8, demonstrating the functionality and the good quality of the integrated scanning system. The time required for each distance measurement run was around 30 seconds. This, however, could be dramatically reduced by utilizing a white light source with a broader spectrum together with an optical spectrum analyzer.

Active alignment - scan in the x-y plane Under cryogenic conditions and subsequent to the important superconductivity characterization test15, an active alignment process between the fiber tip and the active area of the detector was conducted in order to optimize the coupling. A successful automated alignment process is only possible when the system is able to detect a clear maximum count rate, implying a perfect positioning of the fiber tip with respect to the active area. Since the intensity distribution of a fiber output beam is considered a Gaussian distribution, the formation of a distinct peak was expected. Based on this assumption, an algorithm was developed and tested. In principle, the algorithm for the alignment involved a simple scan in the x-y plane, with the system initially moving one step in both the x- and the y- direction in order to orient itself at the count-rate landscape. The system will then scan in x-direction until a maximum count rate is reached and repeat

15I.e., measuring the voltage drop over the SSPD as a function of the applied bias current. 142 A multi-purpose testing station

5 0 0 0 M e a s u r e d L i n e a r f i t ]

m 4 0 0 0 m [

e c n a t s

i d

3 0 0 0 d e r u s a e M 2 0 0 0

0 5 0 0 1 0 0 0 1 5 0 0 R e l a t i v e d i s t a n c e [ m m ]

Figure 11.7: Linear dependence between the measured (ﬁber-mirror) distance and the relative position of the ﬁber tip.

Figure 11.8: Interference spectrum (left) and corresponding FFT (right) obtained after integrating the distance measurement system, indicating a distance of around 50 µm between fiber tip and detector. the same scan in the y-direction. Only when a position with a detected global maximum in count rate is reached, the distance between fiber and detector is manually set to a reduced value (typically 100 µm) and a new x-y scan is performed to compensate for any potential misalignment, for instance, due to a tilt between detector and fiber. Since the utilized attocubes did not provide 11.4 Estimation of the coupling efficiency 143 a position feedback, it was challenging to perform the scan in the x-y plane because the exact step size in both the forward and the backward direction varied16. Nevertheless, the scan algorithm still proved reliable and was able to measure and secure/capture the expected Gaussian peak. Even when the initial count rate was only 2 % of the final count rate, the scan algorithm was able to find the peak in less than 10 min, and thereby was able to successfully optimize the coupling. A measured count-rate distribution and a typical optimization process of the alignment are illustrated in Figure 11.9 and Figure 11.10, respectively.

Figure 11.9: Typical result of the scan in the x-y plane revealing the Gaussian count rate distribution peak obtained during the active alignment process.

11.4 Estimation of the coupling efficiency To estimate the expected coupling efficiency between the fiber tip and the active area, a calculation was performed for single mode fibers with a typical numerical aperture (NA) of around 0.13. Since the fiber tip was located in close proximity to the detector, we assumed a perfect Gaussian mode profile, not only within and outside the fiber, but near the active area as well. The mode profile in the fiber is then given by [128]

2 −2(x2 + y2) P(r) = 2 exp 2 (11.6) πw0 w0

16However, according to the data-sheet provided by attocube systems, the estimated step size is 50 nm. 144 A multi-purpose testing station

5 0 0 0 0

4 0 0 0 0 ] 1 - s [ 3 0 0 0 0 e t a

t n

u 2 0 0 0 0 o C

1 0 0 0 0

0 0 2 0 4 0 6 0 8 0 1 0 0 A l i g n m e n t p r o c e s s [ % ]

Figure 11.10: Variation of the count rate during the scan in the x-y plane performed as part of the active alignment process.

where w0 ≈ λ/πNA is the beam radius. Since the beam radius w(z) at a distance z from the fiber tip is given by s λz w(z) = w0 1 + 2 , (11.7) πw0 the mode profile at distance z from the fiber can be expressed as

2 −2(x2 + y2) P(r,z) = exp . (11.8) πw(z)2 w(z)2 Since the active area is circular in shape with a radius of a = 5 µm, the fraction K of the power incident on the detector is

  2 Z 2π Z a −2r2 K = exp rdrdθ 2 λz 0 0 2 λz πw0 1 + 2 w0 1 + 2 πw0 πw0   (11.9) −2a2 = 1 − exp . 2 λz w0 1 + 2 πw0 Assuming a perfect alignment between fiber and detector, the values calculated for K are plotted in Figure 11.11 as a function of the distance for two 11.4 Estimation of the coupling efficiency 145 different wavelengths, i.e., 800 and 1550 nm. Obviously, the highest estimated coupling efficiency calculated for a wavelength of 1550 nm and a circular active area is around 90% and was obtained at a fiber distance below 20 µm from the detector. Typically, the system was operated at distances of around 100 µm, yielding a calculated coupling efficiency just above 50%. This is also the coupling efficiency suggested by the detection count measurement when varying the cavity distance between the fiber and the circular detector for a wavelength of 1550 nm. Although not matching, the results of the z-scan17 reveal a trend similar to the calculated values, with a coupling efficiency of approx. 50% at a distance of 110 µm. For pigtailed detectors, Slysz et al. [128] calculated that the coupling efficiency rapidly decreases with increasing misalignment due to the cooling process, reaching a coupling efficiency as low as 10% for a misalignment of only ∼8 µm, even when the initial coupling efficiency was as high as 90%. Due to the flexibility offered by the sub-micron active alignment after submerging the detector into the liquid helium, the system continuously sustained its alignment after the coupling was optimized, making the estimated coupling efficiency of 50% a very competitive value. Furthermore, if an improved bonding technique can be implemented that min- imizes the risk of damaging the electrical bonding wires, the flexible scanning system might easily allow for a further reduction of the distance between the fiber and the detector and thus to obtain even higher coupling efficiencies. Although most of the detectors employed in this work possessed a circular active area of around 79 µm2, detectors with a square-shaped active area of (10 × 10)µm2 are still commonly used. Therefore, for comparison, it is worth mentioning the coupling values of the square-shaped areas as well18. As shown in Figure 11.11, for distances larger than 30 µm (and up to 150 µm), the estimated coupling efficiency is on average 10% higher compared with the coupling efficiency obtained for the circular area, which is not surprising since the square-shaped area is around 20% bigger. However, for a lower wavelength (800 nm), the coupling efficiency of the circular areas was found to improve, e.g., reaching values higher than 80% for a circular area located at a distance of 100 µm.

17The scan in the z-direction was performed manually. Since the used attocube piezo positioner featured no position feedback mechanism, it was challenging to systematically scan with a similar step length, hence the irregular scanning step gaps. 18The results obtained for the fraction of the power coupled into the square-shaped active area are presented in Appendix G.2. 146 A multi-purpose testing station

Calculation at 1550 nm for a squared area 1.1 Calculation at 800 nm for a squared area Calculation at 1550 nm for a circular area Calculation at 800 nm for a circular area 1 Measurement at 1550 nm for a circular area Measurement fit

0.9

0.8

0.7

0.6

0.5 Fraction of coupled power into detector

0.4 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Cavity distance between fiber and detctor [microns]

Figure 11.11: Comparison of the calculated and measured fractions of the emergent beam coupled from a single mode fiber into the active area of the SSPD as a function of the distance between fiber and detector. The calculations were performed for wavelengths of 800 and 1550 nm for detectors with two typical types of active areas, i.e., a circular area with a radius of 5 µm and a square-shaped are with a side length of 10 µm. The normalized detection counts (with corresponding fit) were obtained for the detector with a circular active area and a wavelength of 1550 nm.

11.5 Conclusion In summary, we have designed and developed a simple and robust testing station allowing for a fast and accessible exchange of the optical fibers, thereby enabling an efficient characterization of SSPDs for applications requiring a frequent and rapid exchange of the fiber. The versatility of the testing station was enabled by the fabrication of an HV-compatible fiber feed-through based on the modification of commonly available fiber bulkhead connectors, which offers both an optical loss and a leak rate sufficiently low enough for a variety of HV applications. The combination of a low cost, high durability, flexibility, and simplicity implies that the adapter will be extremely useful for a wide range of experiments, especially those which require a frequent (and relatively rapid) fiber exchange. Furthermore, the active alignment in all three directions and the automatic coupling scheme, both constituting the most essential parts of the setup, proved to be very stable, easy to operate and agile compared to a manual alignment with a micrometer stage. The preliminary results were in good agreement with the calculations, demonstrating a proof of principle in terms of the optimization of the coupling efficiency and consequently a reduction 11.5 Conclusion 147 of the coupling losses, thereby enhancing the detection efficiency of the detector defined in Eq. (7.6). However, a more detailed characterization of the coupling efficiency with a fully automated scan in the z-direction is essential for future projects involving a further optimization of the coupling efficiency. This also includes examining the dependence of the coupling efficiency on various combinations of active areas and wavelengths.

Part IV: Conclusion and Outlook

151

12. Conclusion and outlook

12.1 Single photon source Summary and conclusion In the first part of this work, we have designed and constructed two different single photon source setups employing diamond color centers as emitting sources and confocal microscopy to identify and select a single color center. Both confocal microscopy setups were based on a unique scanning approach and a distinct excitation wavelength (green and red). While a simple 3-dimensional scanning stage was utilized in the green setup to move the object, the red setup instead featured a 2-dimensional tilting mirror, mounted before the objective, which allowed for a fast scanning process by moving the laser beam rather than the object. For the pivotal confocal configuration, a single mode fiber was used as pinhole for both setups which allowed for a fast and easy alignment and, more importantly, served as an efficient filter both blocking out-of-focus light and suppressing other (non-fundamental) modes. Both confocal setups were characterized and showed a stable and reliable performance allowing for day-long scans without significant drifting which might have affected the image quality. In particular, the green setup exhibited an excellent spatial resolution close to the diffraction-limit of around 200 nm. Furthermore, the fast and accessible switching between the confocal and conventional microscopy modes allows to use both setups for microscopy applications beyond single photon generation. The microscope also features a self-built microwave and magnetic hardware setup, which allows to manipulate the spin properties of the emitters and to measure the Rabi oscillations. Using a diamond nanocrystal containing a single nitrogen-vacancy center as emitting source, the single photon source was realized through the demonstration of photon antibunching at room temperature with the green confocal setup. The single nitrogen-vacancy center showed a photostable emission with an estimated lifetime of around 20 ns and without any noticeable blinking or bleaching behavior. Furthermore, the spin properties of the nitrogen vacancy center in terms of Rabi oscillations, was successfully demonstrated. Combined with the microwave setup, the complete integrated setup will allow for a wide range of spin environment spectroscopy studies, including π-pulse sequence, Ramsey-fringe and Hahn echo spectroscopy. 152 Conclusion and outlook

The red setup, on the other hand, will allow to demonstrate the occurrence of antibunching for other suitable diamond centers, e.g., silicon and nickel impurities. In the final stage of this work, as an attempt to further push the resolution performance beyond the confocal limit, the STED microscope was realized by modifying the confocal microscope. Since the STED technique allows to bypass the diffraction limit, it will enable the identification of individual emitters and more importantly the manipulation of single electron spins on the nanoscale. However, a characterization of the performance of the STED setup is first required for any future projects involving applications with sub-λ resolution.

Future research Although research on SPS systems is at the frontier of QI technology, with the NV center as the leading emitter candidate, several challenges need to be addressed before SPS systems can be fully implemented in real-life quantum technology applications. Before addressing these challenges in detail, it is instructive to briefly identify some of the principle prerequisites of QI applications. A growing number of industrial QI applications require a large scalable network of interconnected quantum systems; so-called quantum networks. Fea- sible quantum networks, comprised of a few local (NV center-based) quantum bits connected via photonic channels that distribute quantum informa- tion1 have to enable the transportation of quantum information (i.e., a coherent single photon transfer) between remote separated physical systems. Photonic channels such as optical fibers, waveguides and free-space distribution links are commonly used for transmitting photons. However, for long distances, the communication is inevitably impaired by signal losses and decoherence effects because the coupling efficiency between the nodes exponentially decreases due to matter interactions and interfacing with the channels. While amplifiers can be used to heighten the signal at intermediate nodes in classical information transportation systems, this is not possible for quantum networks due to the no-cloning theorem [10]. Therefore, quantum repeaters were proposed as an alternative approach for transporting quantum information over long distances by transmitting qubits through quantum teleportation, utilizing the quantum entanglement phenomenon. For NV center-based SPS systems, the remote entanglement of the spin-photons may serve as an optical channel and might allow to replace the long optical fibers and thereby help to overcome the induced signal losses. The principle of teleportation was first realized in 2014 using two distant NV spins [183], with the nitrogen spin state of one NV

1Whereas, in quantum computing, the network nodes serve as quantum logic gates that process information and store quantum states, the quantum network can be employed to ensure a secure communication through QKD algorithms. 12.1 Single photon source 153 center being teleported to the other over a distance of 3 m utilizing the shared entanglement between the spins of the two NV centers. Shortly afterwards, an entanglement between two distant NV spins separated by 1.3 km was demonstrated by the same group led by R. Hanson et al. [184]. Since for both quantum computing and QKD the realization of quantum networks strongly relies on the generation of an entanglement, a further exploration of the remote entanglement between distant NV centers will pave the way towards more comprehensive quantum communication devices with the prospect of achieving scalability of more local quantum nodes. However, several challenges persist and remain to be solved; with the low photon collection efficiency being the main hindrance for a reliable employment of NV centers (and other color diamonds in general). With a collection efficiency of only a few percent for most confocal systems, combined with a similarly low coherent photon emission, these rates may suffice for proof- of-principle demonstrations (by generating entangled states between two NV centers with a success rate of only 10−7)[185, 186], but must be improved significantly for a useful and realistic employment in commercial QI systems. Recent collection optimization strategies and attempts focused on sculpting geometrical solutions directly on the diamond crystal surface, fabrication of nanostructures as waveguides or embedding the emitter within external optical cavities, begin to address this. Particularly, by drilling a solid immersion lens (SIL) on top of an NV center, a count rate of 1.0 · 106 cps has recently been demonstrated [187]. By fabricating a nanowire on top of an emitter, resulting in a so-called nanoantenna or waveguide pillar, the collection efficiency could be enhanced by a factor of 10 while at the same time requiring a much lower excitation power (∼ 10%) than conventional setups [188]. Embedding emitters within metallic nanocavities resonant with ZPL emission have shown much promise for both enhancing the coupling efficiency and the ZPL emission intensity [189, 190]. Furthermore, a substantial investigation and characterization of solutions involving the etching geometry and the possibility to adapt and integrate nanophotonic cavities and devices for a better collection efficiency will prove valuable. Especially applications that require a controllable generation of indistinguishable photons will benefit from an enhanced collection efficiency and a more narrow ZPL. Fabrication and engineering techniques for the deterministic generation of spectrally narrow NV centers with high emission rates are also among the desired objectives. Techniques allowing to specifically control the purity of the NV center environment, e.g., by creating the emitting sources through ion bombardment or by growing them in a controlled way, are still in active development [191]. However, with the aim of developing scalable fabrication techniques to produce diamond films on a wafer-scale, this remains a difficult task due to the statistical nature of the atomic defect creation process. 154 Conclusion and outlook

Since most QI applications employ the spin properties of the NV center, this necessitates a deeper understanding of its unique properties. Future studies could aim to explore the peculiar properties of NV centers in detail, especially 1) the origin of the equilibrium charge state, 2) the effect of a temperature variation on the ground and triplet excited states, and 3) the spin- polarization mechanism [17]. Knowledge of the first will lead to a better control over the NV center during fabrication and implantation, whereas a more thorough understanding of the second will help to define enhanced strategies for improving the coherence of the NV-spin. Finally, an understanding of the spin-polarization mechanism will facilitate an enhanced readout fidelity of the NV ground state spin, which is necessary for qubit applications. Extending the research to include other color diamond emitters with spin properties more promising than the popular NV center could prove revolutionary. Considering the recently discovered silicon-vacancy (SiV) in diamond [21, 192, 193] and in silicon carbide (SiC) [194], both with photo-luminescence and spin properties similar to the NV center (albeit with a sharper optical spectrum for the SiV center), and with the diamond hosting more than 500 potential optical emitters, the prospects of finding a suitable diamond-based source emitting at the standard telecommunication wavelength of 1550 nm are promising. A depiction of the improvement of diamond-based SPS systems in terms of count rates over the last decade indicates an increase by more than two orders of magnitude (from 104 to 106 cps) due to an improved coupling into the emitters enabled by recent advances in nanophotonics. This, according to Aharonovich et al. [14], suggests a kind of Moore’s law for the development of diamond-based single photon emitters. Thus, if this trend is to continue with similar pace, the law foresees the single-photon count rates reaching the GHz regime within the next decade. Once this is achieved, a transition towards a more commercial employment of diamond-based SPS systems in QI-related technologies will be within reach in fields where scalability can be realized through an all-integrated platform merging emitters, photonic circuits and detectors onto a single chip. In addition to quantum optical applications, we will inevitably see progress in other fields such as biotechnology [195] and metrology [196, 197]. Partic- ularly, with emission lines in the near infrared, the NV center is becoming a highly desired bio-marker due to its reliable photostability, the biocompatibil- ity of diamond nanocrystals and because it offers the possibility of avoiding interference with autofluorescent cell components. Furthermore, the excellent nanoscale magnetic sensing abilities of the NV center may prove essential for new biological applications, e.g., in neuroscience and drug delivery. Because the full potential of the NV center for sensing applications is only revealed while in close proximity to the target, addressing the challenges related to sur- 12.1 Single photon source 155 face effects and spin decoherence may revolutionize the fields of nanoscale metrology and bio-imaging. 156 Conclusion and outlook

12.2 Superconducting single photon detector Summary and conclusion In the second part of the thesis, we have examined and characterized the single superconducting photon detector through a couple of experiments. In our first collaborative work, we have demonstrated a novel capacitive readout scheme combined with fast gating enabling a simplified readout of the detector, thereby allowing to overcome the limitations of conventional readout schemes which require a large bandwidth amplification and complex counting electronics. While the implementation of the capacitor-based readout scheme preserved the detector’s ability to resolve single photons (i.e., to count the number of incoming photons within the RC-time of the capacitor), it also allowed for the multiplexing of several detectors without any complex electronics. The only drawback, i.e., a loss of time information, could be compensated for by the fast gating of the detector. The gating of the detector was demonstrated through the detection of heralded photon pairs. The gate pulse heralding the presence of a second photon was generated upon the detection of the first photon by a spontaneous parametric down-conversion source. The gating allows for an efficient synchronization and control of the detection events while suppressing the number of dark counts. Combined with the proposed multiplexing scheme, the presented gating technique should find application in advanced multi-array imaging detection systems. In our second collaborative work, we extended our concept of detection to also include high energy particles in the MeV energy range, and demonstrated not only the detector’s ability to efficiently detect single α- and β-particles but also detection efficiencies close to unity. In addition, the results of the half-life measurements for both β sources were in agreement with literature and suggest single particle detection. The detector also proved robust, showing no signs of a decline in detection efficiency during an α-particle bombardment for more than four days, and was blind towards γ and X-rays, making it a good candidate for future research and applications. However, whether this insensitivity is related to the nanoscale thickness or the absorption properties of the active area has yet to be investigated. Likewise, a theoretical explanation of the presented high-energy particle detection principle has yet to be provided, and a systematic analysis of the optimal combination of superconducting film and its underlying substrate for the most efficient high-energy particle detection must be carried out. In the future, arrays [152] of these nanowire detectors could be operated. In principle, a good energy resolution may be achieved by analyzing the change in count rate as the bias current is changed relative to the critical current. This has already been demonstrated previously for optical frequencies with this type of detector [109]. The detector could be mounted on a scanning probe to conduct spatially resolved particle detection measurements 12.2 Superconducting single photon detector 157 with unprecedented spatial resolution. Merging nanoscale detectors and particle detection is expected to open up a wide range of new applications where a high time and spatial resolution and high counting rates will be essential. Finally, a multipurpose testing station was designed and constructed for the detector with the main objective of optimizing the coupling efficiency between the optical fiber and the active area of the detector, as well as allowing for a fast and accessible exchange of the optical fiber, thereby facilitating an efficient characterization of the detector. While the optimization of the coupling efficiency was ensured by employing an active coupling mechanism that allows for the optimization in all directions, the flexibility was provided by using a simple, low-cost and durable optical fiber feed-through based on the modification of a commercially available fiber bulkhead adapters. The optimization of the coupling efficiency was demonstrated through proof-of-principle experiments. The obtained results were in good agreement with the calculated coupling efficiency and suggest a relatively high coupling efficiency around 50% when placing the fiber tip at the typical operation distance of 100 microns from the active area of the detector.

Future research With the SSPD technology maturing in recent years, research on SSPD devices is currently undergoing a transition as the detectors are now slowly being commercialized, with few emerging companies specializing in offering fully packaged detector systems. Hence, the focus is shifting from basic research to more advanced and specialized topics. As the DE is getting close to unity due to the employment of optical cavity structures [25, 27, 31], the research focus is shifting towards ﬁnding materials with a similar performance as the pio- neer NbN and NbTiN superconducting materials but at higher temperatures, a better performance concerning the other parameters, e.g., the dark count rate, response time and jitter, or which can easily be integrated into waveguide and cavity systems. While WSi-based detectors are currently the most attractive ones, with a DE of 93%, they must still be cooled down to temperatures below 2.5 K during operation, and even lower temperatures (120 mK) for optimal performance. But their comparatively high jitter (∼ 500 ps at 2.5 K) limits the usability of these detector for high time resolution applications. NbN and NbTiN were primarily selected for their high transition temperature (Tc = 16 K for bulk) and high current density. Apart from Nb, NbTiN and WSi, a number of other materials have been explored recently (such as NbSi, TaN and MgB2). However, MoSi [198, 199] and MoGe [200] are the materials gaining the most attention. Both are amorphous (similar to WSi), which is desirable for industrial fabrication due to the high degree of uniformity and allows them to be easily integrated into a range of different substrate materials without degradation. Furthermore, they both have a higher bulk Tc (∼ 7.5 158 Conclusion and outlook

K) compared to WSi (∼ 5 K), although a lower Tc than NbTiN. However, although their reported DE is lower than the DE of current state-of-the-art WSi detectors, in theory, MoSi and MoGe-based detectors are expected to achieve a DE close to unity once integrated with suitable optical cavities. Another alternative material could be MgB2 with a bulk transition temperature of ∼ 39 K[201, 202]. However, with this high transition temperature, it might prove challenging to build a detector with a good overall performance and a high DE, while the temperature is not high enough for practical applications. However, current NbN/NbTiN-based detectors still suffer from several disadvantages and their DE needs to be considerably increased, e.g., by improving the quality of the deposited material, hence the yield (i.e., the number of functioning devices per fabricated batch), or by exploring alternative ways to integrate detectors with new substrate materials. Nevertheless, to improve the overall detector performance, a stronger focus on the detailed description of the underlying detection mechanism is of paramount importance [203]. A fundamental understanding of the microscopic processes involved in the detection event will bring to light the processes responsible for the inherent linking of the parameters, e.g., the increase in dark count rate when increasing the detection sensitivity, and address the wavelength response (as a function of the detection efficiency) since each material seems to have a certain cutoff wavelength (that is probably also temperature-dependent), where absorbed photons with wavelengths shorter than the cutoff wavelength will be detected with saturated efficiency. Furthermore, with the growing number of investigated materials, a comprehensive description will prove useful for identifying a suitable material for the wavelength of interest (1550 nm) for a specified application, as opposed to the tedious trial and error approach currently employed, and possibly determine the performance limits of SSPD devices. Another important aspect is the modeling and design optimization of the detectors, and the possibility to adapt nanophotonic cavities and integrated waveguide structures in order to enhance their performance parameters apart from the DE, i.e., realizing a high DE and fast response time and a low jitter. Recent design modification attempts utilizing a reduced filling-factor (20%) and a twice as thick NbN nanowire (8.5 nm) sandwiched between two cavity layers, resulted in an enhanced DE of 80% and an improved counting rate [25]. Hence, only a relatively short nanowire would be required, which would help to improve the jitter and the response time and reduce difficulties related to the fabrication of uniform nanowires. Thus, exploring alternative optimization strategies, for instance, a different nanowire structure (narrow enough wires) and absorption thickness (thereby maximizing the interaction length), could lead to the fabrication of high-performance SSPD devices - apart from a DE close to unity. Furthermore, a DE close to unity has been achieved for a wave- 12.2 Superconducting single photon detector 159 length of 1550 nm using nanophotonic integrated waveguide circuits [204]. Further research in this direction might lead to fully scalable detectors with high interface abilities with waveguide-based platforms. The electronic readout schemes are another factor determining a detector’s usability and performance. For many applications, it is advantageous to employ SSPD arrays [205] for enabling photon number resolution, increasing the count rate, or for imaging purposes. Since this requires efficient readout schemes with a low noise level readout schemes, a lot of focus is currently directed towards exploring the possibility of developing high bandwidth cryogenic amplifiers with a high impedance to improve both the signal-to-noise performance of the detector and its response time, while simultaneously performing the signal multiplexing in a cryogenic environment in order to simplify the wiring and to reduce complexity. The recently introduced single flux quantum (SFQ) logic circuit scheme has gained much attention [206] because it can digitally support multiple arrays and multiplex signals. Although the readout scheme and the fabrication of the SFQ circuit is rather complex and still requires further amplification at room temperature, it offers an impres- sively low timing jitter (∼ 40 ps). An alternative promising candidate is a superconducting amplifier circuit providing both a large pulse amplification and a low timing jitter [207, 208]. With the recent demonstration of a reduction of the number of readout lines to only 16 for a multiplexed 64-pixel SSPD array [209], the exploration of ultra-high speed switching at cryogenic temperatures allowing multiple detectors to share a single RF line is a promising approach and could prove effective for reducing both the response time and afterpulsing effects.

Part V: Appendix

Appendices

165

A. Diamonds - utilisation and treatments

A.1 Utilised diamond samples

Name Manufacturer Appearance Type Median size and dimension Liquid Diamond GAF Microdiamant Mixture of Synthetic, type Ib 0-0.05 (GAF) powder & water 0-0.05 NAT Microdiamant Powder Natural, type Ia 0-0.125 µm (upper median: 0.33 µm) Micron MDA Element Six Powder Synthetic, type Ib 0-0.10 µm

Micron SND Element Six Powder Natural, type Ia 0-0.10 µm

MTL 252508 Element Six Bulky Synthetic, type Ib (2.5 ×2.5 × 0.8)mm3 MCC L252508 Element Six Bulky Synthetic (CVD), type Ib (2.5 ×2.5 × 0.8)mm3 Syndia SYP Van Moppes Powder Synthetic, type Ib 0-0.05 µm Syndia SYP Van Moppes Powder Synthetic, type Ib 0-0.05 µm Syndia PM Van Moppes Powder Natural, type Ia 0-0.25 µm Nanopowder Nanostructured & Powder Synthetic, type Ib 3-5 nm, max ∼ 10 nm (1320JGY) Amorphous Materials Inc.

Table A.1: Comparison of the different types and shapes of the diamonds used in this work. 166 Diamonds - utilisation and treatments

A.2 Preparation and production of the nano-diamond powder (NDP) for the Nano-Sizer measurements

1. Cleaning and puriﬁcation: Purify the NDP in an H2SO4 and ◦ HNO3 (sulfuric and nitrid acid) solution with a 3:1 vol/vol ratio at 90 C for 30 min.

2. Extensive cleaning and separation:

••While submerged in the H2SO4/HNO3 solution, centrifuge the NDP at 4.000-11.000 rpm for ∼30 min. • Remove the H2SO4/HNO3 solution using a pipette, leaving only the NDP at the bottom. Add de-ionized water to the NDP. Centrifuge again at 4.000-11.000 rpm for ∼30 min and rinse extensively with de-ionized water. Repeat this 3 times. • Remove the de-ionized water, and let the NDP dry over night. • Measure the weight of (container+NDP) and subtract the container weight to determine the weight of the NDP.

3. Suspension in different solutions: • Re-suspend the NDP in de-ionized water to a concentration of 0.1 g/ml as stock. Alternatively, re-suspend the NDP in a polymer solution (1 wt.% polyvinylpyrrolidone in propanol) and disperse the mixture in an ultrasonic bath for ∼10 min. This prevents the aggregation of the particles and their stabilization in a colloidal state. • Centrifuge at around 11.000 rpm for 30 min to obtain small nanocrystals.

4. Measurement with the Nano-Sizer: • Suspend the NDP in solution in the special-made Nano-Sizer cuvette. • Change the settings under Measurement and begin the measurement by clicking Play. 167

B. High-temperature vacuum oven for the annealing of the diamonds

As described in section 3.1, color center defects in diamond, such as nitrogen- or silicon-vacancies, are typically produced (or increased in concentration) by high-energy radiation followed by annealing at high temperatures. While the irradiation generates lattice vacancies in diamond, the annealing at temperatures above 700 ◦C facilitates the diffusion of the vacancies and their ultimate trapping by nitrogen atoms, thereby creating NV centers. In this section, the design1 and construction of a self-built high-temperature vacuum oven is described.

Oven construction Due to the high operating temperature (800-1200 ◦C) of our oven, it was necessary to perform the annealing under vacuum conditions to prevent the diamond crystal from burning and becoming covered in soot. The oven was comprised of a vacuum chamber in which the actual furnace was located. The furnace itself consisted of a heating coil produced by winding a tantalum wire2 around a ceramic tube. Tantalum was selected due its high melting point (∼ 3000◦C) and good electrical conductivity. Furthermore, due to their good mechanical deformability, the handling of the tantalum plate and wire was easy. The furnace was covered by a tantalum heat shield mounted on a stainless steel threaded rod. To ensure reproducibility, the annealing temperature could be determined via a thermocouple wire3 embed- ded within the ceramic tube during annealing. Both the tantalum heating wire and the heating sensor (thermocouple) were connected to their respective electrical feed-throughs through the circular bottom plate, which ensured both the electrical insulation and the vacuum sealing of the chamber. In Figure B.1, a schematic illustration of the electrical feed-throughs located on the bottom plate is shown.

1The design was informed and motivated by the oven described in [210]. 2The tantalum sheet and wire were procured from H. C. Stark. 3Farnell Type K. 168 High-temperature vacuum oven for the annealing of the diamonds

Threaded rod ( stainless steel) Insertion sleeve Washer

Aluminum plate c c v v

O-ring

Connector (stainless steel)

Figure B.1: Schematic illustration of the cross-section of the bottom plate with the the leak-tight electrical feed-throughs.

Loading and annealing procedure For the annealing of the diamonds, the heat shield was ﬁrst removed and then a tweezer was used to place the diamond crystal inside the ceramic tube in the furnace. The thermocouple was then placed as close as possible to the diamond crystal, and the heat shield was remounted. After sealing the chamber, a pump4 was attached to evacuate the vacuum chamber, while monitoring the chamber pressure using a Thermovac5. After a few minutes, a pressure of approx. 3 · 10−3 mbar was reached. For achieving temperatures around 1200◦C, the power consumption of the furnace was around 70 to 100 W (6-8 A at 12-13 V).

4Oerlikon Trivac D 2.5E. 5Oerlikon model TTR 91. 169

C. Single photon spectrometer

In this section, the design and construction of a highly sensitive single photon spectrometer with its highest detection efﬁciency at wavelengths near 750 nm is presented1. This spectrometer setup was mainly used for the detection of the optical ﬂuorescence spectrum of NV centers, but also for other experiments in our group. In the following subsection, the basic grating parameters and spectrometer design considerations are discussed followed by a presentation of the spectrometer setup and the calibration results.

C.1 Grating parameters and design considerations Grating principle The grating principle takes advantage of the diffraction phenomenon and the interference that occurs during this process. When a beam of light is diffracted at a slit, the interference will lead to wave-tops and wave-dips. Instead of a single slit, a diffraction grating features a periodic structure. Therefore, more light is diffracted, which results in an enhanced interference. In this respect, a spectrometer is designed to determine the wavelength of the emitted light, i.e., to distinguish between various wavelengths. The grating constitutes the decisive optical part of a spectrometer by diffracting different wavelengths at different angles, obeying the grating equation

mλ = a(sinθi + sinθm), (C.1) where m is the order of diffraction, λ the wavelength of the emitted light, a the distance between the slits in the periodic pattern, also referred to as the grating constant, θi the arbitrary angle of an incident beam, and θm is the angle at which the light beam is diffracted. Since the diffraction angle depends on the wavelength, the wavelengths of the incident light are determined by measuring the intensity at certain angles, after which the obtained angles are converted into wavelengths. However, this only holds when deal- ing with the same order of diffraction for the different wavelengths.

1A spectrometer identical in design and operation to this spectrometer was built for detecting wavelengths around 1550 nm. 170 Single photon spectrometer

Diffraction gratings are generally divided into two basic categories, i.e., ruled and holographic gratings. Holographic gratings are produced by pho- tolithography and often have a lower scatter. They are typically used to reduce aberrations. On the other hand, ruled gratings are produced by phys- ically forming periodic structures on a surface using a diamond tool, and are usually used for high-resolution spectroscopy applications as they generally have a higher efﬁciency. Ruled gratings are further divided into different types, with perhaps blazed and unblazed gratings being the most common types of ruled gratings, both of which are then further divided into reﬂection and transmission gratings.

Blazed gratings and blaze angle In our spectrometer setup, we used a ruled blazed reflection grating because it offers several advantages compared to both transmission and unblazed gratings. For instance, when using a ruled transmission grating, the detector has to be moved with high precision to measure the different angles (with each angle corresponding to a unique wavelength), as shown in Figure C.1a-b, which is both inconvenient and impractical. Furthermore, for an unblazed grating, the maximum irradiance (β = 0) occurs for the 0th order (m = 0), whereas a blazed grating allows to shift the maximum irradiance to any desired order, as illustrated in Figure C.1c-d. Another important feature of the blazed grating is the so-called ’blaze angle’. The groove profile is constructed in such a way that a blaze angle is formed to the plane of the grating. By altering the blaze angle, specific regions of the spectrum are concentrated, leading to an increased grating efficiency in that specific spectral region. Thus, depending on the setup and the desired wavelength, a certain blaze angle must be selected to keep the maximum irradiance (β = 0) in the desired order. The wavelength for which a grating diffraction occurs with maximum efficiency is known as the blaze wavelength. Thus, when moving further away from the blaze wavelength, the diffraction efficiency will decline while the polarization dependency will increase. The spectral range covered by a grating is determined by the blaze wavelength λb. As a rule of thumb, the first-order diffraction efficiency will drop to 50% at 0.66λb and 1.5λb [211].

Normal and Littrow conﬁguration To determine the most suitable blaze angle, we consider the geometrical properties of the grating by introducing two different normals: n is normal to the plane of the grating, whereas n0’ is normal to the blazed surface. As illustrated in Figure C.2, the following two conditions apply: C.1 Grating parameters and design considerations 171

θ θ β

θ θ

β Figure C.1: Comparison of different types of gratings. Left: Transmitting unblazed (a) and blazed (b) grating. Right: Reﬂecting unblazed (c) and blazed (d) grating.

θ θ

Figure C.2: Schematic illustration of the geometrical properties of a blazed grating.

1) From the perspective of n0, the relationship between the angle of incidence and the angle of reﬂection is given by

θi + θb = θm + θb. (C.2) 172 Single photon spectrometer

where θb is the blaze angle. 2) The angle of reflection of the m:th order satisfies Eq. (C.1). This allows for two possible mounting configurations, referred to as the normal and the Littrow configuration. In the normal configuration, the light is considered to be incident along or close to the normal to the plane of the grating n. Then, θi=0, and Eq. (C.2) implies that θm = −2θb. Substituting this into Eq. (C.1) and considering the sign convention, we obtain 1 mλ θ = sin−1 . (C.3) b 2 a In case of the Littrow configuration, light is considered to be incident along or close to the normal to the groove face n0, i.e., the normal to the blazed grooves. Thus, θi =θb and θm = -θb, and from Eq. (C.1) follows that mλ θ = sin−1 . (C.4) b 2a For a grating that is blazed for m = 1, we obtain m λ m λ = a(sinθ + sinθ ) ⇒ θ = sin−1 1 b = θ = θ . (C.5) 1 b i m1 m1 2a b i If the grating is illuminated with a light beam with the blaze wavelength λb, for m = 1 Eq. (C.5) implies that the angle of incidence will be equal to the angle of diffraction, i.e., the grating will reflect the beam (first order) like a mirror. Furthermore, for the Littrow configuration, if the angle of incidence is close to the blaze angle, only two orders of diffraction are allowed: m = 0 and m = 1. Hence, instead of spreading the intensity of the incident light between several diffraction orders, the maximum possible irradiance is now confined to a minimum of two orders only.

Resolvable wavelength An essential factor that determines the performance of the spectrometer setup is the resolving power, which is a measure of the grating’s ability to spatially distinguish between two distinct wavelengths. By applying the Rayleigh criteria, the minimum resolvable wavelength of a grating ∆λ can be expressed as

λ λa ∆λ = = , (C.6) Nm m where N = 1/a is the number of illuminated lines. Assuming a beam width w at m = 1, Eq. (C.6) can be modiﬁed to λa ∆λ = . (C.7) w C.1 Grating parameters and design considerations 173

Clearly, a maximally illuminated number of lines will yield the optimal minimum resolvable ∆λ. Yet, it is not always straightforward to keep optimizing the beam width because the collimating lens in the FC forms a beam with a width of around 2 mm. However, if the beam width is selected to w, the radius of the detection area must be w/2. Since the coupling lens (CL) is typically 3 mm in radius, an iris can be placed in front of the lens to adjust the beam width. In addition, the optical path has to be sufﬁciently extended so that all wavelengths above λ + ∆λ and below λ − ∆λ are diffracted out of the detection area. This way, we ensure that no other wavelengths except λ ± ∆λ are being detected. Neglecting this parameter would mean that we are not fully exploiting the resolving power of the grating, thereby lowering the actual resolution. The geometrical relation between the minimum length of the optical path L required for resolving the minimum wavelength and the beam width at the detection location, shown in Figure C.3, is given by w L = . (C.8) tanα where α is λ+∆λ λ α = θm − θm . (C.9)

λΔλ

λ α

Figure C.3: Schematic illustration of the relationship between the optical length and the resolvable wavelength.

Setup design 2 3 For our setup, we used a grating with a blaze wavelength of λb = 750 nm and a grating constant of a = 1/1200 lines/mm blazed for m = 1 in Littrow

2Thorlabs GR25-1208 with dimensions of 25 mm x 25 mm x 6 mm. 3 The choice of a grating optimized for a wavelength of λb = 750 nm was motivated by two main reasons: 1) Commercial gratings with blaze wavelengths relevant for our application were mainly optimized for either λb = 500 or λb = 750 nm, of which the latter was the most sensible choice since it was more suitable for our main application, i.e., the detection of the NV 174 Single photon spectrometer

conﬁguration. The minimum resolvable wavelength was calculated both as a function of the beam width (Eq. (C.7)) and the optical distance between the grating and the detection spot for different incident angles (Eq. (C.9) substituted into Eq. (C.8)), and the results are shown in Figure C.4. When assuming a beam width of w ∼ 1 mm occurring at m = 1, we obtained a minimum resolvable wavelength of ∆λ ∼ 0.6 nm and an optical path length of around L = 0.5 m to maintain this resolvable wavelength. The example was calculated for incident light with a wavelength of 780 nm and an angle ◦ of incidence θi = 0 , since these were the parameters the setup was based upon. If the spectrometer is used for other wavelengths in the spectral range between 495 and 1125 nm, a new estimation for ∆λ has to be made. Nev- ertheless, this must not be considered a hindrance for performing measurements at other wavelengths, as long as one is aware of the limitations of the setup and calculates the error estimate at the desired wavelength. For example, when keeping the setup parameters ﬁxed (λb=750 nm, L = 0.5 m, w = 1 mm) and recalculating the values for a wavelength of 632 nm, we found that the width-based resolvable wavelength slightly improved (∆λ ∼ 0.5 nm), whereas the optical distance-based estimated resolvable wavelength doubled to ∆λ ∼ 1.3 nm. Thus, in order to improve ∆λ for a wavelength ∼640 nm, the optical length L must be increased.

C.2 Spectrometer setup Figure C.6 illustrates the implemented spectrometer setup, providing an optical path of approximately 0.5 m between the grating and the detection spot, which is sufﬁcient for a resolvable wavelength of 0.6 nm, for incident light with a wavelength of 780 nm with a beam with of ∼1 mm. An iris was placed after and before the coupling lens (CL1 and 2) to adjust the beam width, while the grating (in Littrow conﬁguration) was mounted on a motorized OWIS rotational stage. For single photon counting experiments we used a Perkin Elmer photon counting module. Although this detector had a gating option, it was operated in Geiger mode. A PCI data acquisition card (DT304) was used and connected through a serial port to a screw terminal panel (STP300), to which 2 counter inputs, 4 analogue inputs, 2 analogue outputs and 8 Digital I/O were assigned. Both the motorized grating stage and the data acquisition card were controlled through a custom written software script based on the Tk/TCL language via a user-friendly interface.

spectrum. 2) Besides the investigation of NV centers, other experiments in our group required a detection of signals in the red spectral range (700-850 nm). C.2 Spectrometer setup 175

Figure C.4: Calculated resolvable wavelength ∆λ as a function of both the beam width w (Eq. (C.7)) and the optical distance L (Eq. (C.9) and Eq. (C.8)) between the grating and the detector for a wavelength of 780 nm (red lines) and 632 nm (blue lines), respectively, for a grating with λb=750 nm at an incident angle θi = 0. The solid lines represent the resolvable wavelength as a function of the optical distance (in m) for selected incident angles, whereas the dashed lines represent the minimum resolvable wavelength of the grating as a function of the beam-width (in mm).

An important parameter of the spectrometer for measuring different wavelengths is the so-called angle of detection, ϕ. The setup was aligned so that only light beams were detected for which the angle of incidence and the angle of diffraction obeyed the relation

ϕ = θm − θi. (C.10) Since the grating was mounted so that the angle of incidence was close to zero, the angle of diffraction was equal to the angle of detection (ϕ = θm). Hence, the distances d1 and d2 satisﬁed the relation tan(ϕ) = d1/d2. Since we had some degree of freedom due to the width of the mirror, the values obtained for these distances (d1 and d2) were only approximate. We estimated ϕ to be ∼ 69◦. However, the precise value was determined later through a more careful calibration of the grating.

Calibration of the grating After assembling the setup, the position of the grating was calibrated. The calibration was performed in two steps. For the ﬁrst step, laser light with a wavelength of 781.69 nm was coupled through CL1. As we know from Eq. 176 Single photon spectrometer

Figure C.5: 780-spectrometer setup.

Figure C.6: Photograph of the spectrometer setup for a laser light beam with a wavelength of 780 nm.

(C.1), for this type of grating, any incident light beam will be diffracted ◦ at an angle of θm = 0 (for m = 0) whenever the angle of incidence is ◦ θi = 0 , the grating was rotated until the order m = 0 was reflected back onto CL1. By specifying and requiring the incident angle to be zero for the detected wavelength of 781.69 nm, we obtained an exact value for the angle of detection corresponding to ϕ = 69.72◦. The grating was hereafter ◦ fixed at θi = 0 , and the mirror was adjusted so that light was detected at CL2. For the second calibration step, we used a different light source, i.e., a HeNe laser emitting light with a wavelength of 632.76 nm, to verify the ability of the spectrometer to detect other wavelengths accurately. For this ◦ source, the angle of incidence was calculated to θi = 7.3 (using Eq. (C.11) presented in the following subsection). If an offset was measured, it was corrected by readjusting both the grating and the mirror, and then repeating the calibration procedure. After the fine-adjustment of the grating, we obtained the calibration parameters for the setup listed in Table C.1. The acquired calibration results obtained for a laser with a wavelength of 781.69 and 632.76 nm are shown in Figure C.7 and Figure C.8, respectively.

Calculation of the wavelength After the grating has been calibrated and ϕ has been determined for the setup, one can easily mount an unknown source and start rotating the grat- C.2 Spectrometer setup 177

Wavelength (nm) Incident angle θi 632.95 7.3◦ 781.60 0◦

Table C.1: Calibration parameters for the spectrometer setup for ϕ = 69.72◦.

Figure C.7: Calibration results for a laser with a wavelength of 781.69 nm represented by measured photon counts as a function of the scanned wavelength. a) Rough sweep with a rotational step size of 0.1◦ and b) a ﬁne sweep with a step size of 0.01◦, revealing a peak at 781.58 ± 0.001 nm and an FWHM of 1.329 ± 0.002 nm.

ﬁ

Figure C.8: Calibration results for a laser with a wavelength of 632.76 nm represented by measured photon counts as a function of the scanned wavelength. a) Rough sweep with a rotational step size of 0.1◦ and b) a ﬁne sweep with a step size of 0.01◦, revealing a peak at 632.951 ± 0.001 nm and an FWHM of 1.861 ± 0.001 nm.

ing to scan over a range of wavelengths until light is detected. The relation between the wavelength and the rotation angle of the grating is obtained by substituting Eq. (C.10) into Eq. (C.1) and can be expressed as follows: 178 Single photon spectrometer

mλ = d(sinθi + sin(θi − θ)). (C.11)

The minus sign in θi −θ is due to convention. Eq. (C.11) is plotted in Figure C.9.

Figure C.9: Wavelength plotted as a function of the grating incident angle θi for ϕ = 69.72◦. 179

D. GL Theory

In 1950, a few years prior to the introduction of the BCS theory, the Ginzburg-Landau theory (GL) was devised by Landau and Ginzburg. Rather than focusing on the excitation mechanism, the GL theory focuses entirely on the superconducting electrons to successfully explain superconductivity. The application of the macroscopic GL theory, which distinguishes two types of superconductivity, proved useful in many situations where the microscopic BCS theory was difﬁcult to apply. Combining Landau’s theory of second-order phase transitions with a Schrödinger-like wave equation, the GL theory introduced a complex pseudo-wavefunction ψ to represent the local density of superconducting electrons ns given by 2 ns = |ψ(x)| (D.1) To determine ψ, the free energy F of the superconductor near the superconducting transition must be at a minimum with respect to variations in the order parameter ∆(T). The free energy is given by

∗ 2 2 β 4 1 h¯ e 2 |B| F = Fn + α |ψ| + |ψ(x)| + ∗ | ∇ − A ψ | + (D.2) 2 2m i c 2µ0 where Fn is the free energy in the normal phase, m is the effective mass, e the charge of an electron, A the magnetic vector potential, and B the magnetic ﬁeld. With Eq. D.2 in mind, the differential equation for ψ can be expressed as follows:

∗ 1 h¯ e 2 ∇ − A ψ + β |ψ|2 ψ = −α(T)ψ (D.3) 2m∗ i c which is the Schrödinger equation for a free particle with an additional nonlinear term. The corresponding equation for the supercurrent is then given by e∗h¯ e2∗ J = (ψ∗∇ψ − ψ∇ψ∗) − |ψ|2 A. (D.4) s i2m∗ m∗c The GL equation, however, is only valid under equilibrium conditions, for instance, in case of a persistent current in a superconducting state. Since the particle detection mechanism in an SSPD is a highly non-equilibrium process, we need a more generalized GL dynamic equilibrium (or a more 180 GL Theory

time-dependent) formalism taking into account the fluctuation of the high current density source (i.e., the transition between the superconducting and the normal state). This leads to a modified GL differential equation for the space and time dependence of the order parameter. Solving this modified GL differential equation near Tc yields [100]

2 2 2 2 [(T − Tc)/Tc + β(∆ /Tc ) − ξ (0)∇ ]∆ = −(π/4Tc)τE ∆(∂∆/∂t) (D.5)

where τE is the inelastic scattering time. Although Eq. (D.5) seems to most accurately describe the detection process in our detector, to date, there is no (theoretical) work conﬁrming the applicability of Eq. (D.5) to SSPDs. 181

E. Single photon down conversion source

At the very beginning of my PhD, I was assigned a project to build a compact single photon down conversion source for both research and laboratory courses related to Bell state studies. Later, and during my visit at TU Delft, I built a similar setup for the QT lab as part of our collaboration. Although the intended plan was to use my spontaneous parametric down conversion (SPDC) setup for the gating readout measurement (cp. Section 9.3), a different SPDC source1 was used due to logistic and planning reasons. Nevertheless, since the used setup described in Section 9.3 is conceptually similar to the one I built both in Stockholm and Delft, it is worth presenting in this thesis. Thus, in the following, a description of the components of the source is presented, as well as the setup of the compact source of polarization-entangled photon pairs.

E.1 Optical and setup components Pump laser and detectors. The heart of the experimental setup is a source for producing a pair of photons by SPDC; a non-linear effect that produces two photons of lower frequency from one pump photon of higher frequency. The input is referred to as the pump, while for historical reasons the two outgoing photons are usually called the "idler" and the "signal" photon. We use subscripts p, i and s to refer to the pump, idler, and signal photons, respectively. The laws of the conservation of energy and momentum require that

ωp = ωs + ωi, (E.1) and

kp = ks + ki. (E.2) where ω is the angular frequency of the photon and k the vector of its wave number in vacuum.

1The collinear SPDC process was driven by a 532 nm pump laser in a 2 cm long KTP crystal cut for the degenerate type-II phase matching. This setup was built by my colleague Reinier W. Heeres. 182 Single photon down conversion source

For the successful detection of the photons produced by down-conversion, a high detection efficiency is essential, thereby limiting the range of suitable pump beam wavelengths. For the detection of the photons, we used avalanche photo diodes (APDs) optimized for a high quantum efficiency. When used as single photon detector, an APDs is also referred to as a single photon avalanche diode (SPAD). It generates a 20 ns wide pulse when a photon is detected, with a dead time of 60 ns between the pulses. The APDs used in this work had a specified peak quantum efficiency of ∼ 80 and ∼ 60% for photons with a wavelength of 700 and 810 nm, respectively. The efficiency drops rather quickly to 10% when the wavelength increases to 1000 nm. To operate the detectors at their peak efficiency, we want the produced down-conversion photons to have wavelengths in the range from 700 to 800 nm. Since ks = ki = kp/2, the pump laser wavelength must therefore be in the range from 350 to 400 nm. We employed a continuous wave (CW) violet Toptica laser diode to pump the beta-barium-borate (BBO) crystal used in our experiments. Our laser diode was specified to exhibit a center wavelength of 405 nm and a line- width of typically less than 1.5 nm. Therefore, the resulting coherence c length of our pump laser was lc = ∆ν = 0.1 mm and the output power was ∼40 mW. To increase the power density within the BBO crystal, a lens system was chosen in order to focus the pump beam to a waist w◦ below ∼100 µm in diameter. The utilized lens system consisted of two cylindrical lenses ( f1 = 300 mm and f2 = 250 mm), with the first placed horizontally and the second vertically. The cylindrical lenses were used to compensate for the elliptical shape of the laser beam in both directions. Both lenses were coated with an UV anti-reflection coating to minimize the losses due to internal or external reflections. BBO crystal. For the generation of entangled states we used a beta-barium- borate (BBO) crystal with dimensions of 7 mm x 7 mm x 2 mm. The BBO crystal was cut in such a way that the axes were oriented at an angle of 41.8◦ from the normal to the large face. The crystal was mounted on a holder and aligned to the laser beam direction. Due to the non-linear optical properties of the crystal, a small fraction of incoming laser photons spontaneously decayed into pairs of photons via the SPDC process. The above mentioned laws of conservation of energy and momentum (Eq. E.1 and Eq. E.2) lead to phase-matching conditions that had to be fulfilled in order for the down-conversion to occur. This was achieved by balancing dispersion and birefringence against each other by orienting the optical axis of the crystal at a certain angle against the laser beam. We used type-II phase matching, i.e., the down-converted photons showed a different (orthogonal) polarization. The down-converted photons left the crystal in two cones at E.1 Optical and setup components 183

±3◦ to the pump-beam axis, with each polarization restricted to one of the cones: the signal cone carried the vertical, the idler cone the horizontal polarization. At the intersubsection points of these two cones, a two-particle superposition then occurred, with the entangled states given by

1 √ (| HV > ±eiα | VH >), (E.3) 2

where the relative phase α could be changed with compensator plates. The optimal distance for the coupling of the down-conversion photons was estimated to be at ∼35 cm from the BBO crystal. Waveplates. A waveplate is a birefringent material that exhibits one refractive index for light polarized along the optical axis of the material, and another refractive index for light polarized perpendicular to the optical axis. Since the speed of light going through a medium is inversely proportional to the refractive index, photons with one polarization will travel faster through the material than light with the other polarization, so that the phase between the two polarization components continuously changes. A half-wave plate (HWP) is made of a birefringent material with a thickness and orientation chosen in such a way that light of a speciﬁc wavelength is subjected to a phase shift corresponding to half a wavelength (180◦), whereas for a quarter-wave plate (QWP), the light is retarded by 90◦ in phase. By rotating the waveplates with respect to each other in our measurement setup, any basis state could be produced. Compensator. Due to the birefringence of the BBO crystal, a transversal walk-off of the extraordinary beam and longitudinal walk-off occurred in our experiments. The transversal walk-off produced a shift between the or- dinary and extraordinary cone while the longitudinal walk-off introduced a time delay between horizontally and vertically polarized photons. Both walk-off effects allowed to distinguish the photon polarization, thus de- stroying the entanglement. Placing two additional BBO crystals (one in each path) with half the thickness of the original one and oriented in the same way compensated for the walk-off effect; hence the name compen-

sators. After the compensation, the two possible processes (|Hi1 |Vi2 and |Vi1 |Hi2) at the intersubsection of the down-conversion cones could no longer be distinguished by comparing the arrival times of individual photons. Polarization control modules. The down-conversion photons were coupled into the single-mode fiber (SMF). However, the optical fibers acted like birefringent elements. For short SMFs (a few meters), this can lead to a rotation of the polarization state. This polarization rotation depends on external conditions, e.g., the temperature and the stress caused by bending the fiber. In order to stabilize the fiber, a so-called fiber loop compensator 184 Single photon down conversion source

was used. By rolling the ﬁber around the three loops, the rotation caused by the ﬁber could be controlled. Coincidence counting electronics unit. Since we were interested in measuring the polarization correlation between the photons of an entangled pair, we had to determine which detection events at the different detectors belonged to a single photon pair. For this purpose, we used a coincidence counting unit with a coincidence window of 2 ns. The coincidence window is a certain time interval in which a coincidence can be detected. If the coincidence window is too large, the probability that two signals which are not caused by a single photon pair are accidentally recognized as a photon pair is too high. On the other hand, if the coincidence window is too narrow, the actual entangled photon pair will not be detected.

E.2 Setup of the SPDC

Figure E.1: Photograph of the photon generation and state preparation setup that constituted the ﬁrst part of the compact down-conversion photon source.

Figure E.1 shows the setup used for the analysis of polarization-entangled photons. The setup consisted of two parts. The ﬁrst part was responsible for the generation and preparation of two entangled photons in a certain Bell state. The second part was an analysis station measuring the polarization of each of the entangled photons for a selected basis. Brieﬂy, the pump beam was focused onto the BBO crystal by two lenses, and the photon pairs created by the SPDC source left the crystal opening with an angle of 6◦. E.2 Setup of the SPDC 185

By passing an HWP, the polarization of the photons was flipped 180◦ before they reached the two compensation crystals. To optimize the coupling for the 810 nm-photons, an RG filter (RGF) cutting all wavelengths below 710 nm and a narrow filter (NF) with a 5 nm-window centered at 810 nm were placed into the beam path before the photon pairs were coupled into the SMF via a coupling lens (L3 7.5 mm). To compensate for an arbitrary polarization rotation within the fiber, a PCM was connected to the end of the SMF. The photons were then coupled to the SMF and guided to two analysis stations (one for each photon).

Figure E.2: Photograph of the analysis stations that constituted the second part of the compact down-conversion photon source.

The analysis stations simply consisted of one HWP followed by a QWP, as shown in Figure E.2. Each arm after the QWP was fed into an APD that created an electric pulse for each impinging photon. All APDs in both analysis stations were connected to a coincidence unit that counted the hits registered by each detector, as well as coincident hits registered across multiple detectors. By rotating the half-wave plate we could measure the polarization for any basis of linear polarization. The total propagation length from the BBO to the detector was adjusted to be equal for both paths so that coincidence events from the entangled photons could be registered.

187

F. Setup and mounting for high-energy particle sources

Figure F.1: Photographs of the sample mountings used for the (a) α-particle and (b) β-particle sources. 188 Setup and mounting for high-energy particle sources

Figure F.2: Photographs of the SSPD and its metallic case. (a) The detector was connected to the detection electronics via a coaxial cable (SMA connector). The case consisted of anodized aluminum. (b) The detector was enclosed in a tight aluminum cylinder. The top ﬂange was screwed onto the body and an o-ring was used to seal it. 189

Figure F.3: Setup used for the detection of high-energy particles. (a) The metal case was mounted onto a holder. The sample holder consisted of a top ﬂange on which two rods were mounted. The metal was is then taped to the two rods. A co-axial cable was fed to the metal case (containing the detector) through the top ﬂange. Side views are shown in (b) and (c). (d) The liquid helium vessel into which the sample holder (with the metal case) was dipped. (e) The sample holder (with the metal case) dipped into the liquid helium vessel. (f) Schematic illustration of the experimental setup used for detecting the impinging α- and β-particles and γ-rays.

191

G. Additional information and photographs illustrating the coupling system

G.1 Operation manual for the SSPD dipstick system Important precautions!

• Always close the vacuum-valve before turning off the pump, and turn on the pump before opening the vacuum-valve. Otherwise the oil might get sucked into the pump. • Make sure the attocube is always grounded when not in use. This is done by switching all the knobs to Gnd.

For changing the ﬁber:

• Carefully remove the small screws on the top-flange (on the top-housing) where the fiber is mounted. • On the top-flange, the following connectors can be found: an SR232 connector, a fiber connector, an SMA connector and a dummy fiber connector (Figure G.1). The dummy fiber connector is intended to be replaced by a temperature sensor. All the fiber connectors should be sealed with o-rings. • For the top-flange: If the o-ring (black rubber ring) falls off, it has to be cleaned with methanol, and so should the inner side of the lid. Then apply the smallest amount of vacuum-grease, before attaching it and closing/tightening the system. • For the bottom-flange: After three uses, the indium ring needs to be replaced with a new one. Before mounting the new indium ring, clean it with acetone and isopropanol. When placing the indium ring, apply a bit of grease to the ring and the inner metallic wall.

Mounting of the SSPD:

• Place an indium plate beneath the aluminum detector mounter. 192Additionalinformation and photographs illustrating the coupling system

• Tighten the two screws. The indium plate should be between the base and the SSPD. • Mount the cover and tighten it with the wrench key. • Glue the detector onto the board using UV glue and epoxy resin.

Prior to submerging the detector into the cryostat:

• Connect the tube to the pump. • Close the valve connecting the balloon. • Open the vacuum valve. • Switch on the pump. • Remove the balloon and the valve flange, and mount them onto the dewar. • Connect the electrical wires to the readout setup. • To clean the balloon for later use, fill it with helium gas, and then empty it. • Refill the balloon and remove it from the dewar while keeping it full. Clutch (with a scissor) at the end of the balloon to prevent a leakage of the helium gas. Mount the flange systems back onto the dewar. • Re-mount the balloon onto the pump. Open the valve to the balloon to make sure that there is no air between the balloon and the interior of the pump. • Wait until the pressure reaches ∼ 10−2 mbar. A pressure of 5 · 10−2 should be achievable. Apply some methanol to the dipstick (both to the bottom and the upper parts). If the pressure remains constant, there is no leakage in the system. • After the pressure has stabilized, close the pump valve, open the balloon valve (filled with He) to let the gas into the system (detector and attocube) before dipping it into the liquid helium. Close the balloon valve and open the vacuum valve again and measure the pressure, which should be around 2.3 mbar.

Submerging the dipstick into the liquid helium and test of superconductivity

• Slowly (and carefully) submerge the dipstick into the liquid helium vessel. A slow dipping process (around 20-30 minutes) reduces both the risk of a potential mechanical shock to the system caused by differences in temperature and the helium liquid consumption. • On the attocube driver, to check whether the attocubes are cold enough, switch the knob to capacitor. The displayed value should read around G.1 Operation manual for the SSPD dipstick system 193

170 when dipped in He, compared to a value of ∼ 1000 at room temperature. • Perform an IV-check to conﬁrm the superconductivity of the detector by executing the LabVIEW program IV−simple.vi.

Distance measurement and attocube test: z-axis • To measure the distance between the detector and the ﬁber, start the LabVIEW program scan−laser.vi. • Switch on the tunable laser source (1550 nm-laser). • Set the attocube controller to ccon (computer control) mode. • Run a scan through the program. The distance will now be measured and displayed.

x-y plane

• Start the LabVIEW program SSPD-continous.vi. • The laser is set to remote. To disengage it, press on the lamp. Analo- gously, for the photon counter, press save/print for manual operation. • On the attocube controller, set the voltage to 30 V and the frequency to 400 Hz. When set to Run, the system is in manual operation mode. • At the beginning, maximize the counts manually. When optimized, switch the attocube controller to ccon-control mode. • To perform a scan in the x-y plane, start the LabVIEW program align.vi, and perform the measurement. Counts as high as around 28000 cps can be achieved initially.

Removing the dipstick

• When done with the measurements, switch off all the equipment and turn the attocube-knobs to Gnd. • Disconnect the ﬁber and slowly take out the dipstick while pumping. Open the pump valve. 194Additionalinformation and photographs illustrating the coupling system

G.2 Calculated coupling value for a square-shaped active area Using Eq. 11.8, we can calculate the fraction K of power incident on the square-shaped active area of a detector with a side length a = 10µm:   2 Z a/2 Z a/2 −2(x2 + y2) K = exp dxdy 2 λz −a/2 −a/2 2 λz πw0 1 + 2 w0 1 + 2 πw0 πw0  2 (G.1) 2 = Er f   . q λz w0 1 + 2 πw0 Eq. G.1 is plotted in Figure 11.11 for two wavelengths, i.e., 800 and 1550 nm. G.3 Additional photographs of the coupling system 195

G.3 Additional photographs of the coupling system

Figure G.1: Photographs of the bottom part of the dipstick and the top compartments. a) Closed and sealed bottom compartment. b) Open bottom compartment containing the attocubes without the aluminum detector mount. c) A sideview of the complete dipstick. d) Below the top-housing (1) a T-piece (2) is located on the tube. e) A zoom- in on the top-housing with the mounted electrical readout parts: (1) the bias-T and (2) the amplifiers. f) A top view of the top-housing flange showing all the feed-throughs to the optical and electrical connections: (1) optical fiber, (2) RS232 for the attocubes, (3) SMA for both biasing and readout and (4) temperature sensor for future experiments. g) Top-housing flange with all the feed-throughs connected. 196Additionalinformation and photographs illustrating the coupling system

Figure G.2: Photographs of the control and acquisition apparatus. a) The attocube driver (1), the tunable laser source (2), the power supply (3), the oscilloscope (4) and a counter (5). b) A zoom-out view showing the PC, the pump (1) and the thermovac (2).

Figure G.3: A photograph showing our SSPD measurement setup in Stockholm. The SSPD was mounted on a dipstick that was immersed into the liquid helium vessel. In this setup, the readout electronics were mounted on top of the dipstick. Part VI: Bibliography

199

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