QUANTUMENHANCEDMICROSCOPY

Catxere Andrade Casacio

B.Sc., B.Eng., M.Sc.

A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020

School of Mathematics and Physics, ARC Centre of Excellence for Engineered Quantum Systems (EQUS) Abstract

In optical microscopy, as in any biological measurement performed with light, there is a compromise between increasing power to improve resolution and decreasing power to prevent photodamage to the biological structure. Quantum optics allows this compromise to be overcome, enabling improved precision without increased illumination intensity. This thesis demonstrates, for the first time, absolute quantum advantage in microscopy, with a specific focus on Stimulated Raman Scattering (SRS) microscopy. SRS microscopy is a powerful tool widely used in many fields, especially in biomedical sciences. It uses a two-photon process where the light is downshifted in frequency by being absorbed and subsequently inelastically scattered by the intrinsic molecular vibrations in the sample. Each element or molecule has a different response, allowing selective imaging of biological systems. SRS microscopy is particularly useful because it is label-free (no addition of dyes, beads or any implanted tracer), meaning that imaging contrast is achieved without modification of, or interference with, the specimen. Here I present our newly built state-of-the-art shot-noise limited SRS microscope. I also characterize the Raman microscope, describe the developped imaging system and show SRS spectroscopy and imaging of both polystyrene beads and living yeast cells. The quantisation of light introduces a fundamental uncertainty, or quantum noise, in both the amplitude and phase quadratures of an optical field. A squeezed state of light is a state of the optical field where the uncertainty of one of these quadratures is reduced below the quantum noise. Therefore, it provides an approach to reduce the noise level below this quantum noise limit and consequently increases measured signal-to-noise ratio. Here I describe the concepts involved in this technique and present our newly built light squeezer. I characterize the squeezing and show up to -1.3 dB of noise floor reduction for a 6 picosecond pulsed laser, which is the pulse duration that maximises the Raman interaction. In this thesis we apply squeezed states of light in SRS, developping a quantum-enhanced micro- scope. Our SRS Raman intensity noise is ∆I/I ≈ 10−7 and the measured quantum efficiency of the built photodiode is η = 72%. In this proof of principle we show a reduction of the noise floor of at least 13% below the quantum noise limit for Raman imaging of polystyrene beads and living yeast cells. This enhancement allowed us to resolve the cell membrane where with conventional microscope would be unresolvable. It also allowed sub-micron spatial resolution. The improved image contrast and reduced imaging time, while avoiding photodamage in the sample, surpasses the current state-of-the-art Raman microscopes and opens opportunities for new discoveries in biophysics. Declaration by author

This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, financial support and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my higher degree by research candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis and have sought permission from co-authors for any jointly authored works included in the thesis.

Catxere A. Casacio COVID-19

This thesis was completed during the 2020 worldwide corona-virus pandemic. Despite the resulting disruption to work locations, health, routines, and reduction in working time, the thesis was completed on schedule, with no additional allowances or any adjustment to the pre-pandemic deadlines. Publications during candidature

Conference abstracts

1. C. A. Casacio et al., Quantum enhanced non linear microscopy, 23nd Australian Institute of Physics Congress (AIP), Perth, AUS, December 2018 - oral presentation accompanied by abstract.

2. C. A. Casacio et al., Velocity measurement in optical tweezers for biology, 3rd Australian and New Zealand Conference on Optics and Photonics (ANZCOP), Queenstown, NZL, December 2017 - poster accompanied by abstract.

3. C. A. Casacio et al., Velocity measurement in optical tweezers for biology, 10th Ions KOALA (Conference on Optics, Atoms and Laser Applications), Brisbane, AUS, November 2017 - oral presentation accompanied by abstract.

4. C. A. Casacio et al., Velocity measurement in optical tweezers for biology, EQuS Annual Workshop, Hunter Valley, AUS, September 2017 - poster accompanied by abstract.

5. C. A. Casacio et al., Quantum enhanced non linear microscopy, Joint 13th Asia Pacific Physics Conference and 22nd Australian Institute of Physics Congress (AIP), Brisbane, AUS, December 2016 - oral presentation accompanied by abstract.

6. C. A. Casacio et al., Quantum Enhanced Microscopy, EQuS Annual Workshop, Noosa, AUS, December 2016 - poster accompanied by abstract.

7. C. A. Casacio et al., Ultra-high Bandwidth Tracking of Micro/Nano Particles in Fluid, EQuS Optomechanics Incubator, Brisbane, AUS, December 2016 - poster accompanied by abstract.

8. C. A. Casacio et al., Quantum Enhanced Microscopy, EQuS Optomechanics Incubator, Brisbane, AUS, December 2016 - poster accompanied by abstract.

9. C. A. Casacio et al., Quantum Enhanced Microscopy, Gordon Research Conference: Lasers in Medicine and Biology, West Dover, USA, July 2016 - poster accompanied by abstract. Publications included in this thesis

1. [1] Catxere A. Casacio, Lars S. Madsen, Alex Terrasson, Muhammad Waleed, Kai Barnscheidt, Boris Hage, Michael A. Taylor, and Warwick P. Bowen, Quantum correlations overcome the photo- damage limits of light microscopy, under review; preprint available at ArXiv:2004.00178.

Contributor Statement of contribution % C. Casacio data collection 80 data analysis 75 experiment design 25 experiment construction 80 microscope design and construction 5 detector design and construction 5 text writing 20 L. Madsen data collection 5 experiment design 25 experiment construction 20 microscope design and construction 5 detector design and construction 5 text writing 20 A. Terrasson data collection 10 data analysis 25 text writing 5 M. Waleed microscope design and construction 90 text writing 5 K. Barnscheidt detector design and construction 40 text writing 5 B. Hage detector design and construction 40 text writing 5 M. Taylor data collection 5 experiment design 25 initial concept 50 text writing 20 W. Bowen experiment design 25 detector design and construction 10 initial concept 50 text writing 20 Contributions by others to the thesis

Supervision throughout my candidature

Prof Warwick P. Bowen and Dr Lars S. Madsen

Assistance with proof-reading and feedback

Prof Warwick P. Bowen (Chapters 2, 4 & 5), Prof Jacquiline Romero (Chapters 4 & 5), Dr James Bennett (Chapter 3), Dr Martin Stringer (Chapters 1-6)

Thesis examination

Dr Costanza Toninelli and Prof Shigeki Takeuchi

Contributions to the experimental setup

Ulrich Hoff made the platform for the nonlinear crystal, and Alex Terrasson made the code for the microscope scan and post-processed some microscopy images used (both acknowledged throughout the text). All other contributions are as acknowledged in “Publications included in this thesis”.

Statement of parts of the thesis submitted to qualify for the award of another degree

None.

Research involving human or animal subjects

No animal or human subjects were involved in this research. Acknowledgments

Here I say a true thank you for all your help and support. To my supervisors, Warwick and Lars, who taught me all they could in and out of the laboratory. A Nico pour etreˆ disponible a` m’aider chaque fois que necessaire´ et a` Alex pour arriver au milieu du chaos et des` le debut´ plonger dans les tachesˆ du travail acharne´ - specialement´ pour faire le scan pour que ma these` soit plus el´ egante.´ To James for the physics discussions that always so easily enlightened me. To Kaerin, Alan, Angie, Tara, Erinn and Nonnie, for making (all!) the routine problems to go away and solve administrative and building-related jobs so efficiently. To Rob and Chris for quickly making parts of the lab to work properly. And to Sam for all the 4 years of IT hiccups solved. To Dave and Griffo: you are awesome and your job outstanding! I’ll keep nice memories for playing golf in the mechanic workshop... To Waleed for building such a fine microscope. Dive dive Pakistan! To Boris and Kai for their collaboration on making the high-bandwidth and high-power detector - you saved me so much time that I did not have! And to Ulrich for welcoming me on my PhD with a brand-new home-made squeezing oven. To QOLadies, Beibei, Aswa, Yasmine and Larnii, who cheered my always-surrounded-by-men days with the refreshment of bubble-tea. I will miss that. To my mentors, Andrew and Beibei, who were always so supportive, always so giving and sharing such good advices. And to the colleagues that supported me throughout my thesis: Steevo, Jacqui, Sally and Jacinda amongst others. To all my friends – from Brisbane and from all over the world, who independent of the time zone were always encouraging me and making my life more complete. Aos meus pais, Viviane, Raphael e Fabio,´ por estarem sempre dispon´ıveis do outro lado do mundo (ou desse!) para me auxiliarem com meus problemas, me guiarem em momentos dif´ıceis, ou apenas para um bate-papo as` 2 da manha.˜ To my husband Martin, whose support and invaluable help were the reason why I’m still standing. And to my daughter Sofia, who provided me with (what seems) infinite awaken nights and infinite energy loss, but in the end of the day is the fuel for me to carry on. Financial support

This research was supported by the Asian Office of Aerospace Research and Development scholarship (US Air Force Office of Scientific Research grant), UQI Tuition Fee Scholarship, the Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS), and EQUS Primary Carer Support Award.

Keywords

Physics, optics, quantum, squeezing, microscope, Raman, biophysics, medicine.

Fields of Research (FoR) Classification

FoR code: 0206, Quantum physics, 70% FoR code: 0903, Biomedical Engineering, 20% FoR code: 0299, Other Physical Sciences, 10%

Australian and New Zealand Standard Research Classifications (ANZSRC)

ANZSRC code: 020604, Quantum optics, 70% ANZSRC code: 090303, Biomedical Instrumentation, 20% ANZSRC code: 020699, Quantum physics not elsewhere classified, 10% For Martin and Sofia. Contents

Abstract ...... ii

List of figures xiv

List of tables xvi

List of abbreviations and symbols xvii

1 Introduction 1 1.1 Thesis structure ...... 2

2 Coherent Raman microscopy 5 2.1 Microscopy overview ...... 5 2.1.1 The microscope platform ...... 6 2.1.2 Nonlinear microscopy ...... 7 2.2 Stimulated Raman scattering (SRS) microscopy ...... 9 2.2.1 Coherent Raman scattering ...... 9 2.2.2 A special type of microscope ...... 10 2.2.3 Chemical bonds ...... 11 2.2.4 Stimulated Raman gain (SRG) or loss (SRL) ...... 11 2.2.5 State-of-the-art SRS ...... 14 2.3 SRS preparation ...... 14 2.3.1 Classical setup ...... 14 2.3.2 Choosing the light ...... 15 2.3.3 The EOM ...... 16 2.3.4 Sample preparation ...... 17 2.3.5 Spatial, temporal and polarisation alignments ...... 18 2.3.6 Filtering ...... 18 2.4 SRS detection and imaging ...... 19 2.4.1 Equipment used for detection ...... 19 2.4.2 SRG and Raman shift ...... 20 2.4.3 Shot-noise limited SRS ...... 22 xi xii CONTENTS

2.4.4 Microscope scan ...... 24 2.4.5 SRS imaging ...... 24 2.4.6 Photodamage ...... 24 2.5 Chapter summary and conclusions ...... 28

3 Quantum theory background 29 3.1 Describing the light ...... 29 3.1.1 Optical field ...... 29 3.1.2 Heisenberg’s uncertainty principle ...... 31 3.1.3 Coherent states ...... 32 3.1.4 The vacuum ...... 33 3.2 Squeezed states of light ...... 35 3.3 Quantum detection ...... 36 3.3.1 Linearisation of the optical field ...... 36 3.3.2 Single, or direct detection ...... 37 3.3.3 Balanced detections ...... 37 3.3.4 Visibility ...... 38 3.3.5 Quantum efficiency ...... 38 3.3.6 Application to equipment used in the detection ...... 38 3.3.7 Beam-splitter ...... 39 3.3.8 Direct detection for squeezing ...... 40 3.4 Chapter summary and conclusions ...... 42

4 Experimental techniques for quantum-enhanced microscopy 45 4.1 Introduction to quantum measurements ...... 45 4.1.1 General quantum enhanced measurements ...... 46 4.1.2 Quantum enhanced imaging systems ...... 47 4.2 Quantum light source for SRS microscopy ...... 47 4.2.1 The quantum ray ...... 47 4.2.2 The squeezer ...... 48 4.2.3 The nonlinear crystal and SHG ...... 49 4.2.4 Spatial, temporal and polarisation alignments ...... 50 4.2.5 Phase-locked loop ...... 51 4.3 The quantum-compatible microscope ...... 55 4.4 The detector ...... 55 4.5 Experiment efficiencies ...... 57 4.5.1 The Stokes light ...... 58 4.5.2 The pump light ...... 59 4.5.3 The squeezed states of light ...... 59 4.6 Characterisation of squeezed states of light ...... 60 CONTENTS xiii

4.6.1 De-amplification ...... 60 4.6.2 Squeezing ...... 60 4.7 Data processing with squeezed states of light ...... 62 4.8 Chapter summary and conclusions ...... 63

5 Quantum imaging 65 5.1 Experimental setup ...... 65 5.2 Signal-to-noise enhancement ...... 66 5.3 Overcoming photodamage limits with quantum light ...... 68 5.3.1 Measuring the signal and the noise ...... 68 5.3.2 Processing the signal-to-noise ratio ...... 68 5.4 Quantum enhanced imaging ...... 71 5.5 Chapter summary and conclusions ...... 72

6 Conclusions 73 6.1 Classic microscopy ...... 73 6.2 Quantum microscopy ...... 73 6.3 Outlook ...... 74

Bibliography 77

A Detailed experimental setup 83

B Microscope objectives 85 B.1 Nikon ...... 85 B.2 Leica Microsystems ...... 85

C Detectors 89

D The platform of the nonlinear crystal 93 List of figures

1.1 Thesis structure...... 3

2.1 The microscope platform ...... 6 2.2 Raman scattering ...... 10 2.3 Cross-section ...... 12 2.4 SRS modulation ...... 13 2.5 Simplified experimental setup ...... 15 2.6 Laser pulses ...... 16 2.7 Beam modulation ...... 17 2.8 SRS spectroscopy ...... 21 2.9 Power scaling ...... 21 2.10 Raman shift ...... 22 2.11 Stokes laser is shot-noise limited ...... 23 2.12 SRS imaging of yeast ...... 25 2.13 Bright field images of typical photodamage ...... 26 2.14 Quantifying photodamage ...... 27

3.1 Coherent state of light ...... 34 3.2 Vacuum state of light ...... 34 3.3 Squeezed state of light ...... 35 3.4 Schematic of a beam-splitter ...... 39 3.5 Single detection with squeezing ...... 40 3.6 Squeezing variance ...... 43

4.1 Platform for nonlinear crystal ...... 48 4.2 Second harmonic generation ...... 50 4.3 Phase-locked loop diagram ...... 52 4.4 Error monitor signal ...... 54 4.5 Detection noise ...... 56 4.6 Saturation from the detector ...... 57 4.7 Deamplification ...... 61 xiv LIST OF FIGURES xv

4.8 Squeezing ...... 62 4.9 Squeezing, shot-noise and electronic noise ...... 63

5.1 Simplified quantum experimental setup ...... 66 5.2 Quantum enhanced stimulated Raman spectroscopy ...... 67 5.3 Power scaling for squeezed SRS signal ...... 69 5.4 Non damage-inducing quantum stimulated Raman spectroscopy ...... 70 5.5 Quantum enhanced stimulated Raman microscopy ...... 71

A.1 Detailed experimental setup ...... 83

B.1 High transmission objective blueprint ...... 87

C.1 Photo of the purpose-built single detector ...... 89 C.2 Electronic circuit of the detector ...... 90 C.3 The balanced detector noise ...... 91

D.1 Platform for nonlinear crystal blueprint ...... 93 List of tables

2.1 Types of molecules ...... 11

xvi List of abbreviations and symbols

Abbreviations Description

AC Alternating Current (or high frequency) Att Attenuator BS Beam Splitter (non-polarizing) CARS Coherent Anti-Stokes Raman Scattering CR(m) Coherent Raman (microscopy) dB Decibel DC Direct Current (or low frequency) EOM Electro-Optic Modulator HPF High-pass filter HRS Hyper Raman Scattering Hz Hertz LED Light emitting diode LO Local Oscillator LPF Low-pass filter mod Modulation nl Nonlinear OPA Optical parametric amplifier OPO Optical parametric oscillator p Pump PBS Polarizing beam-splitter PDC Parametric down conversion PID Proportional integral differential servo PPKTP Periodically-poled K (potassium) Titanyl Phosphate px Pixel PZT Pb (lead) Zirconate Titanate RBW Resolution bandwidth rep Repetition rate RF Radio frequency RS Raman shift

xvii xviii LIST OF ABBREVIATIONS AND SYMBOLS

Abbreviations Description

S Stokes SA Spectrum analyser SEHRS Surface Enhanced Hyper Raman Scattering SERS Surface Enhanced Raman Scattering SFG Sum frequency generation SHG Second harmonic generation SNR Signal-to-noise ratio SRS Stimulated Raman Scattering VBW Video bandwidth

Symbols Description

α Coherent amplitude σ Cross-section q Electric charge ~p Electric dipole moment ~E Electric field

ε0 Electric permittivity g Gain (for squeezer) I Intensity ω Light frequency λ Light wavelength χ Nonlinear susceptibility Xˆ Quadrature operator Xˆ + Amplitude quadrature operator Xˆ − Phase quadrature operator aˆ Photon-annihilation operator aˆ† Photon-creation operator h Planck constant ~P Polarisation density

C8H8 Polystyrene ∆~x Position displacement Ω Resonant frequency (molecule) Sˆ Squeezing operator r Squeezing parameter ∆ Variation (standard deviation) Better far, Pursue a frivolous trade by serious means, Than a sublime art frivolously.

Aurora Leigh, Second Book, By Elizabeth Barrett Browning

Chapter 1

Introduction

Microscopes are fundamental tools used throughout history to allow our eyes to see beyond their natural limits. Although the use of lenses to magnify small objects have been known for thousands of years, it was only in the early 17th century that the first microscope was invented [2]. It consisted in two lenses put together with a variable distance between them to achieve even greater magnification of the object to be seen. It was, and is, extensively used in diagnostic medicine and in research to better understand and manipulate the microscopic world, hence the constant work on improving its resolution. All microscopes which use light to image the object in question are called optical microscopes. The simplest microscopes use sunlight, possibly redirected with a mirror, to illuminate the sample. It is slightly more convenient to use a halogen lamp or any bright light instead of the Sun, and we refer to all these as bright-field microscopes. The more intense the light, or the more power it contains, the higher the contrast and resolution of imaging. Therefore the most advanced optical microscopes we have available today use lasers, which are composed of coherent light. However, even Sun light is capable of burning objects - particularly animal skin, and so can lasers, causing what is called photodamage into the specimen. Hence, photodamage limits the improvement of resolution for biological measurements, and indeed state-of-the-art microscopes are severely limited by photodamage from the high intensity lasers they use [3–6]. One important type of microscopy that was developed in the past decades is the coherent Raman (CR) microscopy, after the foundings of Chandrasekhar Raman and Kariamanikkam Krishnan on nonlinear interactions of light and molecules in 1928 [7]. CR microscopy is a powerful tool widely used in many fields, especially in biomedical sciences [8–11], where it allows in-vivo1 imaging and can distinguish molecular constituents of the specimen without using any labelling on the sample. A special subcategory of CR microscopy, Stimulated Raman Scattering (SRS) microscopy, provides high contrast of imaging while superseding the limitations of other types of CR microscopy [12] and was chosen for the purpose of the current work.

1In-vivo refers to biological samples that are still alive when studied. 1 2 CHAPTER 1. INTRODUCTION

A major challenge for improving the signal detection in SRS microscopy, and therefore allowing faster imaging, is this trade-off between interaction strength scaling quadratically with intensity, and the incident power being limited by the need to avoid photodamage to the specimen, or even cell death. Given that the optical power is constrained, there are not many available options to improve signal-to-noise ratio apart from reducing the measurement noise. The noise in SRS microscopes has already been reduced as far as is possible in classical theory, i.e. to the shot-noise limit [3,13]. This limit, also known as quantum-noise limit, comes from the quantisation of light and cannot be reduced with classical approaches – further noise floor reduction can now only be achieved using quantum correlations of light. Many quantum optics techniques have been developed to overcome the limits imposed by quantum noise. Squeezed states of light, which exhibit a specific form of quantum correlation between photons, have shown promising performance [14]. They provide a relatively robust approach to reduce the noise level below the shot-noise limit, which has proved successful in highly controlled experiments such as gravitational wave interferometers [15, 16] and optical tweezers [17]. By adding squeezed states of light into the SRS microscope, we aim to improve the signal-to-noise ratio without increasing the incident power in the sample. Using laser powers in a range that is not harmful for biological specimen, while extracting higher signal-to-noise, provides new paths to increase the speed of imaging systems and improve imaging resolution. The goal of this Ph.D. thesis is to demonstrate the first biologically-relevant squeezing-enhanced SRS microscope and to show for the first time that quantum correlated light can be used to prevent photodamage in samples. This technique should open new doors for new discoveries in biophysics and medicine.

1.1 Thesis structure

The thesis structure is shown in Figure 1.1. The first chapter introduces the general goal of the thesis, explains what the thesis is about and the motivation behind the chosen project. It also enunciates the themes that will be discussed on each of the following chapters. Chapter 2 contains the classical microscopy theory that will be used later on in that chapter and in Chapter 5. It also describes our construction of a state-of-the-art SRS microscope, shows our results on classical microscopy using SRS, and our results on quantifying photodamage due to the intensity of the laser beams. Chapters 3 and 4 are related to the quantum part of the thesis. Chapter 3 introducing the theory of the quantum description of light, photon squeezing and detection of quantum light, which are relevant for the techniques used. Chapter 4 covers the implementation of these techniques and methods, starting with an overview of the literature for quantum measurements and imaging systems. It then describes the quantum light preparation, the microscope and detection systems for quantum measurements and the efficiencies of the experimental setup, finishing with the characterisation of the photon squeezing and how we perform the analysis with the quantum light. 1.1. THESIS STRUCTURE 3

Figure 1.1: Thesis structure.

Chapter 5 contains the final and comprehensive description of the quantum enhanced SRS mi- croscopy with its results and discussions. This chapter consolidates the achieved proof of principle, showing both signal-to-noise enhancement with quantum light and photodamage evasion. The thesis will be wrapped up in Chapter 6 with a summary of both classical and quantum-enhanced microscopy and finish with the outlook for future applications. There are supporting materials in the Appendices and they are cited in the relevant sections of the thesis. 4 CHAPTER 1. INTRODUCTION Chapter 2

Coherent Raman microscopy

As mentioned in Chapter 1, the 20th century saw the discovery and development of coherent Raman (CR) microscopy. It became a powerful tool for its label-free fingerprinting capabilities and is used in a range of applications, from biomedicine to exploration of life in other planets [18]. In this chapter I will introduce Raman microscopy by first contextualising it in the broader range of microscopes and nonlinear microscopes (Section 2.1). I will then define and describe the properties of CR microscopy and in particular those of a subcategory of CR, stimulated Raman scattering (SRS) microscopy (Section 2.2), which was the technique used for our results, providing also a view of its state-of-the-art. Section 2.3 contains descriptive information about the experimental setup with its equipment and operation mode. Section 2.4 focus on the detection system and the imaging itself, showing results on SRS spectroscopy and microscopy. I finalise with a summary of the chapter and a brief discussion on the limitations of CR microscopy (Section 2.5), which will be dealt with in the remaining chapters of this thesis. This chapter contains work published in Reference [1].

2.1 Microscopy overview

As described in Chapter 1, optical microscopy is a subcategory of microscopy that is particularly convenient for imaging biological specimen, because light can have a non-aggressive interaction with the sample (which is not true for other types of microscopy, such as electron microscopy [19]). In this section I will introduce a visualisation of a microscope with our purpose-built microscope platform and describe its parts to start a better understanding of how it will be applied. This platform follows a standard shape for microscopes, and was used for other experiments in addition to the ones described in this thesis. Following that, I will discuss a subcategory of optical microscopy called nonlinear microscopy, and a few of the techniques used for this type of measurement to contextualise the main subject of this thesis, which will be discussed in the next section (2.2). 5 6 CHAPTER 2. COHERENT RAMAN MICROSCOPY

2.1.1 The microscope platform

The platform for the purpose-built microscope (Figure 2.1) was adapted from a platform constructed by Dr. Muhammad Waleed during his Ph.D. studies at the University of Queensland under the supervision of Prof. Warwick Bowen, Dr. Michael Taylor and Dr. Lars Madsen. Its design was mainly inspired by atomic force microscopy and focused on stability and ease of dealing with samples [20]. The platform stability was fundamental for tracking instantaneous velocity in ballistical optical tweezers [21] and for the detection system of enhanced SRS, as will be described in Sections 4.3 and 4.5.

Figure 2.1: The microscope platform. (a) The light enters the microscope through a set of two irises to help with alignments. A dichroic mirror reflects the light upwards and an objective focus it into the sample. The sample stage is positioned via a 2-dimensional micro-precision stage (b) and nano-precision stage (c). After interaction with the sample, the light is collected with a condenser (d) and reflected through another dichroic mirror on top of the microscope which diverts the light to a mirror (e) that redirects the light back to the table level.

As can be seen in Figure 2.1, this particular platform is vertical and operates by transmission of the light through the sample (as opposed to reflection). Figure 2.1a indicates the entrance of the microscope, where the light beams are aligned into the microscope with the aid of two irises. The light is reflected upwards by a mirror (Thorlabs, BB1-E03), transmitted through a dichroic mirror1, and focused in the sample through an objective2 (Nikon, 65% transmission for 1064 nm, more details on

1No description of it is found on the setup or in [20]. 2This objective was used in the original setup being described here, as it was commercially available. It was later replaced by higher transmission objectives from Leica (see Section 4.3), which was used for all final results. 2.1. MICROSCOPY OVERVIEW 7

Appendix B). The objective focus is controlled using a Mad City Labs Nano-F200S focusing module, which gives a vertical degree of freedom for positioning of the focus. The sample stage is shown in Figure 2.1d, where a set of two coverslips clamped with two metal bars keep the sample in place. The stage displacement is performed by a horizontal 2-dimensional micro- and nano-precision stage (Figures 2.1b and c respectively, both Mad City Labs stages) which are controlled via computer software for positioning and raster scanning for imaging experiments. A condenser (or upper objective) collects the light transmitted through, and scattered from, the sample and sends it to a dichroic mirror which reflects the light to the mirror shown in Figure 2.1e, responsible to redirect the light to the optical table and for the detection system. A bright incoherent green or white light emitting diode (LED) is added on top of the platform via an optical fibre and through the top dichroic mirror. This light goes through the condenser, the sample, the objective and is finally reflected in the bottom dichroic mirror, going to a CCD camera (Allied Vision Manta). This enables bright-field imaging to be performed at the same time as our other measurements. While taking images, the sample stage has a drift due to the relaxation from its initial movement, which is higher at the beginning of the scan. We measured up to 5 µm drift (50% of the total image) over an 8 minute scan, corresponding to an average drift of 10.6 nm/s. This drift was corrected in the software by scanning one single line of the image and applying a feedback on the difference of the actual and nominal position from the position-output of the stage control. This correction was done before taking every image. After correction, all the data we took presented a drift smaller than 300 nm (3% of the total image) for the same scanning time, corresponding to an average drift of 0.6 nm/s. Many of them showed much lower drifts of around 100 nm, or 0.2 nm/s. This correction was essential for being able to scan the selected particle in its entirety. The remaining drift was fully corrected in the post-processing of the image, using the position-output of the stage control (for more details see Section 2.4.4).

2.1.2 Nonlinear microscopy

Nonlinear optics

Interaction of light with matter generates an induced dipole. More specifically, applying an electromag- netic field to an atom will cause a temporal deformation of the electronic cloud. In a restoring potential, which is assumed when the field is not too strong, this produces a vibrating dipole. Considering a stationary particle, the magnetic part of the electromagnetic force is negligible and one can describe the light in terms of its electric field ~E(t). The resulting electric dipole moment is given by

~p(t) = q∆~x(t), (2.1) where q is the electric charge of the atom and ∆~x(t) the displacement from the atom’s equilibrium position. In this case, applying two electromagnetic fields with frequencies ω1 and ω2 will produce a vibrating dipole with frequencies ω1 and ω2. 8 CHAPTER 2. COHERENT RAMAN MICROSCOPY

Now considering N atoms experiencing the same electromagnetic field in vacuum. The sum of their dipole moments is the polarisation density, given by

~P(t) = N~p = ε0χ~E(t), (2.2) where ε0 is the electric permittivity in vacuum and χ the susceptibility of the medium (in this case the ensemble of N atoms). The last term of this equation is assuming low light intensities3, and in this case the induced polarisation is linearly proportional to the magnitude of the applied field. This linear behaviour occurs ubiquitously in our daily life, for example when sunlight reflects from a window. Nonlinear polarisation can be obtained with high optical intensities and this is easily achievable with the use of lasers. Under this strong field, the displacement of the particle’s centre of mass is large enough to explore anharmonicity of the potential, which induces other harmonic frequencies to appear.

In this case, applying two electromagnetic fields with frequencies ω1 and ω2 will produce a vibrating dipole with frequencies ω1, ω2 and harmonics. In terms of the polarisation, the susceptibility of this medium needs to take into account higher orders:

(1) (2) 2 (3) 3 ~P(t) = ε0[χ ~E(t) + χ ~E (t) + χ ~E (t) + ...]. (2.3)

The second order nonlinearity of the polarisation density allows different phenomena to arise, such as: second harmonic generation (SHG), sum and difference frequency generation, frequency doubling, optical rectification, parametric amplification and oscillation. From the third order nonlinearity of the polarisation density, the known phenomena include: third harmonic generation (THG), optical Kerr effect, self-phase modulation, cross-phase modulation, Kerr lensing, solitons, four-wave mixing, Brillouin scattering and Raman scattering.

Adding nonlinear optics into microscopes

Through the exploration of these effects obtained in nonlinear optics, a powerful subcategory of optical microscopes, the nonlinear microscopes, could be developed. These are particularly effective for in-vivo research, where nonlinear interactions with the molecules allows imaging without exogenous stains or labels, resulting in a non- or less-invasive technique. They are also effective on reducing scattering from the medium and for achieving sub-diffraction limited imaging. The most common nonlinear microscopes are the twophoton excited fluorescence (TPEF) mi- croscopy, which targets the electronic energy level of the medium; second harmonic generation (SHG) and third harmonic generation (THG) microscopy, which targets the nonlinear properties of the medium; and coherent Raman scattering (CRS) microscopy, which targets the vibrational and rotational energy levels of the medium.

3Nonlinearities are induced from fields of around 1 kV/cm, or 2.5 ×10−8 kW µm −2 [22]. 2.2. STIMULATED RAMAN SCATTERING (SRS) MICROSCOPY 9 2.2 Stimulated Raman scattering (SRS) microscopy

Section 2.1.2 described the nonlinear interactions of light and matter and how, from those, a range of techniques were developed to perform microscopic imaging, including coherent Raman scattering (CRS) microscopy. In this section I will describe the CRS broader technique in more detail and enunciate a few subcategories of CRS, in particular the stimulated Raman scattering (SRS) microscopy, understanding its relation to molecules’ chemical bonds and how the detection of this technique is possible, finishing with the current state-of-the-art of SRS microscopes. These concepts will pave the way for understanding the actual performance of experimental preparation of a SRS microscope, described in the next section (2.3).

2.2.1 Coherent Raman scattering

In 1928, Chandrasekhar V. Raman and Kariamanikkam S. Krishnan published for the first time a series of articles in Nature about a new type of secondary radiation, which was later known as Raman scattering [7]. They wrote in their first paper that the scattered light from molecules will contain the wavelength of the incident beam and “a modified scattered radiation of degraded frequency”. Each molecule has a number of resonant vibrational and rotational frequencies. For simplicity, let us target a particular frequency Ω. When a molecule is irradiated with an electromagnetic field of frequency ωp > Ω (p for pump), part of the energy at this frequency is used for excitation of the molecule and there will be a resulting radiation, with a frequency called Stokes frequency ωS, given by

ωS = ωp − Ω. (2.4)

This spontaneous generation of photons with frequency ωS is called spontaneous Raman scattering (see Figure 2.2a) and is a weak process. For a stronger effect, the Stokes field can be injected together with the pump field, generating a stimulated Raman scattering (SRS; Figure 2.2b). In this case, there is also the generation of a very weak anti-Stokes field ωaS = 2ωp − ωS (Figure 2.2c). For experimental convenience, light wavelengths λ = c/ω (given in nano-meters: nm) are more used than their frequencies, and therefore we use λS for the Stokes wavelength and λp for the pump wavelength. It is also convenient, for the microscopy community, to use the Raman shift RS = 1/λ −1 (given in reciprocal centimetre: cm ). In this case we use RSΩ = RSp - RSS for the molecular resonant Raman shift. Following Chandrasekhar and Kariamanikkam’s discovery, many types of nonlinear microscopes were developed. Coherent Raman scattering (CRS) microscopy is the umbrella term that can be subdivided into: stimulated Raman scattering (SRS), coherent anti-Stokes Raman scattering (CARS), surface-enhanced Raman scattering (SERS), hyper-Raman scattering (HRS) and deep ultra violet (DUV) Raman, with many variations within each technique. Here, we will focus on SRS microscopy, first applied in 2007 by Evelyn Ploetz et al. [23] and first applied in bio-imaging in 2008 by Christian Freudiger et al. [8]. 10 CHAPTER 2. COHERENT RAMAN MICROSCOPY

2.2.2 A special type of microscope

Stimulated Raman Scattering (SRS) microscopy uses a two-photon process where the light is down- shifted in frequency by being absorbed and subsequently inelastically scattered by the intrinsic molecular vibrations in the sample. It is a type of spectroscopy where the frequency shift of the scattered light, called the Raman shift, is used to acquire information about the structure and composition of the sample. Each element or molecule has a different response (see Section 2.2.3), allowing selective imaging of biological systems, also known as bio-molecule finger-printing. Raman microscopy is particularly useful because it is label-free (requiring no addition of dyes, beads or any implanted tracer), meaning that imaging contrast is achieved without modification of, or interference with, the specimen. In SRS, one of the two photons involved in the process comes from the pump beam and has frequency ωp, and the other comes from the probe beam, also called Stokes beam, and has frequency

ωS (see Figure 2.2b). The pump beam is used to excite the specimen from the ground level to a virtual level, while the Stokes beam will stimulate the emission of scattered photons from the virtual level to an intermediate excited level. When the difference between these frequencies is equal to the molecule’s characteristic frequency Ω, given by Equation 2.2.1, resonance is achieved and the pump beam is attenuated while the Stokes beam, amplified. These are referred to as Stimulated Raman Loss (SRL) and Stimulated Raman Gain (SRG) respectively (see Section 2.2.4). These intensity variations, ∆Ip and ∆IS respectively, are equal in magnitude with opposite sign, given by [12]

∆IS ∝ NσRamanIpIS

∆Ip ∝ −NσRamanIpIS , (2.5) where N is the number of molecules in the probe volume, Ip and IS are respectively the peak intensity of the pump and Stokes fields, and σRaman is the molecular Raman cross-section, which is the interaction

Figure 2.2: Raman scattering. The vibrational or rotational resonant frequency Ω of a molecule, between its ground n0 and excited ne energy levels, passing through a virtual energy level depicted with a dashed grey line, for different types of Raman interactions: (a) spontaneous Raman scattering where ωp is the frequency of the pumped field and ωS the Stokes frequency of the weak generated light; (b) stimulated Raman scattering with both pump and Stokes beams illuminating the molecule and a stronger light produced at the Stokes frequency; and (c) coherent anti-Stokes Raman scattering with both pump and Stokes beams illuminating the molecule and a weak anti-Stokes beam of frequency ωaS being produced. 2.2. STIMULATED RAMAN SCATTERING (SRS) MICROSCOPY 11 strength between the vibrational energy level and the incident light. Since the signal detected is proportional to the number of molecules, a quantitative chemical map is possible with SRS.

2.2.3 Chemical bonds

As mentioned in Section 2.2.2, Raman scattering relies on the intrinsic vibrational or rotational modes of the molecules, which can be categorized as symmetrical stretching, anti-symmetrical stretching, scissoring (or bending), rocking, wagging, or the twisting of a chemical bond in the molecule. Each molecule has a combination of different vibrational modes, some of which are easier to stimulate than others (see column Cross-section in Table 2.1). For example, the carbon-hydrogen (CH) bond is found in abundance in organic matter and its stretch mode has a Raman shift at 2917 cm−1 (equivalent to a frequency of ≈ 87 THz) and a very strong signal when on resonance, with a cross-section of 24.2×10−30 cm 2 sr −1.

Table 2.1: Types of molecules. Raman spectroscopy for a few biologically relevant molecules with their respective targeted bond, Raman shift and cross-section (numbers extracted from [24]).

Molecule type Bond Raman shift [cm−1] Cross-section [10−30 cm2 sr−1] O-H bend 456.3 0.0167 C-O stretch 883.1 0.967

N2 - 2331 1

O2 - 1556 1.41

C2 stretch 787.7 2.04 O-H stretch 3362 4.96 C-H stretch 2917 24.2 Cyclohexane C-H stretch 2730-3080 56.2

From Table 2.1, we can extract Figure 2.3, showing the cross-section for their respective chemical bonds on a linear scale. This emphasizes how strong is the CH signal compared to other bonds. For this reason, SRS usually targets the CH stretch bond (see Section 2.4.2 for our results), allowing physical structures containing CH bonds to be well imaged. In principle, SRS microscopy is much more powerful, enabling spatial mapping of many different chemical constituents in a sample. Enhancements in signal-to-noise ratio (SNR) at the level of a few percent are highly valuable, increasing the contrast and thereby also the speed at which the biological dynamics can be monitored (more on SNR on Chapter 5).

2.2.4 Stimulated Raman gain (SRG) or loss (SRL)

As mentioned in Section 2.2.3, one of the major limitations of multi-photon microscopes is the weakness of the interaction strengths. From Equation 2.5, the SRS signal is of the order ∆Ip/Ip ≈ 12 CHAPTER 2. COHERENT RAMAN MICROSCOPY ] 1

r 60 C6-H12 s

2 m c 0

3 40 0 1 [

n o i

t 20 NO2 c

e s - O-H s C O3

s H O-H 2 O2 N2 2 o r 0 C 0 1000 2000 3000 4000 Raman shift [cm 1]

Figure 2.3: Cross-section. Cross-section of a few biologically relevant chemical bonds and their respective Raman shift (numbers extracted from [24]).

−4 ∆IS/IS . 10 [12]. There are a few techniques to overcome this, such as enhancing the signal with an amplified laser system [23], which is not biologically compatible due to high peak powers damaging the sample, or using a high-frequency modulation transfer [8], which is explained below. While the presence of the Stokes beam introduces a change in the power of the pump (Section 2.2.2), which in principle allows chemical mapping, this DC intensity change is masked by low frequency noise. This noise comes from low frequency thermal and mechanical fluctuations and especially from laser noise. To avoid the low frequency noise when detecting SRS signals, the high-frequency modulation transfer technique is used. It consists of modulating either pump or Stokes beam with a frequency fmod (see Figure 2.4; for our modulation results see Section 2.3.3), splitting the main peak into two side bands, which shifts the SRS signal away from the laser noise at the laser repetition rate frep and therefore make it possible to detect the variations in the SRS signal. A modulation fmod > 1 MHz ensures that low frequency laser noise will not limit the detection. The modulation frequency must be higher than this lower limit and also an integer factor (>2) of the laser repetition rate, so that the two form a consistent periodic pattern. In our setup we use 20 MHz and 80 MHz respectively. Figure 2.4a shows the intensity of SRS light against frequency. In the left side, the input beams of frequencies ωp and ωS are represented, and they are chosen to be Ω apart to match the molecule resonating frequency. The output beams are shown in the right side, where the modulation results in a transfer of energy from the pump to the Stokes beam, causing stimulated Raman loss (SRL) in the intensity of ωp and stimulated Raman gain (SRG) in the intensity of ωS. 2.2. STIMULATED RAMAN SCATTERING (SRS) MICROSCOPY 13

Figure 2.4: Modulation of stimulated Raman scattering. (a) Spectrum intensity of input and output frequencies, with ωp the pump frequency, ωS the Stokes frequency and Ω the molecular resonant frequency. The frequency of modulation fmod applied (b) on the Stokes beam results in Stimulated Raman Loss (SRL) in the pump beam, and (c) on the pump beam results in Stimulated Raman Gain (SRG) in the Stokes beam (artwork based on [8, 12]). 14 CHAPTER 2. COHERENT RAMAN MICROSCOPY

Figures 2.4b&c show the intensity of SRS light against time. Figure 2.4b represents a modulation on the Stokes beam, and therefore the information that will be contained in the pump beam through SRL. Analogously, Figure 2.4c represents a modulation on the pump beam, and therefore the information will be contained in the Stokes beam through SRG. This technique allows signals as low as ∆I/I ≈ 10−8 to be measured [8].

2.2.5 State-of-the-art SRS

The current state-of-the-art in SRS microscope performance relates to both the noise from the light source, and the noise from the detection system. Christian Freudiger et al. [8] developed a technique to evade low frequency noise (more on Section 2.2.4, or Section 2.4.3 for our results). With high- frequency modulation transfer detection system (> 20 MHz), shot-noise limited signals can be reached. Yasuyuki Ozeki et al. showed this for the first time in 2010 [13].

2.3 SRS preparation

Having introduced the techniques used in SRS microscopy in the previous section (Section 2.2), we can now progress to the experimental realisation. In this section I present the experimental setup used to generate results in the remaining of the sections of this chapter, followed by a description of the laser used, the procedure for sample preparation, and finish with the techniques involved in aligning and filtering the light properly for detection, which will be discussed in more detail in Section 2.4.

2.3.1 Classical setup

Standard SRS is performed with the experimental setup shown in Figure 2.5. In the light sources panel, a laser (described in Section 2.3.2 below), with wavelength of 532 nm and repetition rate of 80 MHz, is used to pump an Optical Parametric Oscillator (OPO) to generate light of tunable wavelength λp. Its repetition rate is modulated at 20 MHz with an EOM (see Section 2.2.4). This pump beam is temporally and spatially overlapped with the 1064 nm Stokes beam on a dichroic beam-splitter (CVI, SWP-0-R1064-T700-900-PW1-1012-UV) with the use of delay lines (depicted with black arrows in the figure). In the microscope panel of Figure 2.5, both pump and Stokes beams interacts with the sample (see Section 2.1.1) and the pump beam is filtered and directed to an optical fibre coupler for alignment purposes (see Section 2.3.5). Also, a LED illuminates the sample and is detected through a CCD, allowing bright-field imaging. To detect and characterise the stimulated Raman scattering (detection panel), the Stokes laser is measured on a purpose-built resonant feedback photodetector and processed with a spectrum analyser (both described in Section 2.4.1 below). 2.3. SRS PREPARATION 15

Figure 2.5: Simplified experimental setup. (Red panel) Preparation of the pump beam (purple) via an Optical Parametric Oscillator (OPO) and 20 MHz modulation from an Electro-Optic Modulator (EOM), and Stokes beam (red). (Green panel) Stimulated Raman scattering is generated in samples at the microscope focus, with raster imaging performed by scanning the sample through the focus. A CCD camera and a light emitting diode (LED) allow simultaneous bright field microscopy. After filtering out the pump, the Stokes beam is detected and the signal processed using a spectrum analyser (blue panel).

2.3.2 Choosing the light

The Stokes laser is provided by a low noise solid-state pulsed laser (Coherent, Plecter Duo), with pulse −1 length of tpulse = 6 ps (equivalent to ωpulse =167 GHz and RSpulse =5.6 cm ), a pulse repetition rate of 80 MHz (see Figure 2.6), and a wavelength of λS = 1064 nm (for comparison, ωS = 282 THz and −1 RSS = 9398 cm ) with ≈ 1.5 W of output power. Prior to the laser output, part of the 1064 nm light is frequency-doubled to 532 nm, which has 3 to 4 W of output power. This frequency-doubled light is used to pump both the purpose-built squeezer (described in Section 4.2.1) and a commercial OPO (APE, Levante Emerald). The OPO generates a beam with power4 in the range of [500, 700] mW, which is wavelength-tunable over the range λp ∈ [750, 900] nm. This provides the capacity to probe −1 Raman shifts over the range RSΩ ∈ [1713, 3935] cm . The pulse duration of the laser source was chosen to be comparable to the decay time of molecular vibrations since this maximises the Raman interaction, with molecular decay times typically in the range of a few picoseconds [8]. In numbers, a typical Raman line (or the width of Raman spectral features) is around 10-15 cm−1, and 2-6 picosecond pulse duration corresponds roughly to 5-15 cm−1. Shorter pulses would not resolve Raman features (as the pulse is inversely proportional to the Raman shift), whereas longer pulses would not generate any extra signal and would suffer reduced signal due to their lower peak intensity. This particular pulse width range also facilitate the beam preparation along the experiment, since for the optics used here the dispersion of the pulse width is negligible in the picosecond range.

4All powers mentioned throughout this thesis refers to the average power P. Here, the peak power is

Ppeak ≈ P/(tpulse frep) = 21 W for an average power of 10 mW. 16 CHAPTER 2. COHERENT RAMAN MICROSCOPY

Figure 2.6: Laser pulses. Pump beam monitored in the oscilloscope, where τrep = 12.5 ns is the inverse of the repetition rate frep = 80 MHz. Data taken on a fast photodiode with a rise time of 1 ns (Thorlabs, DET10A).

The choice of 80 MHz repetition rate is mainly designed to minimise photodamage processes and allows for a high speed of imaging [12, 25, 26].

2.3.3 The EOM

In Section 2.2.4 we have discussed the importance of modulation for the SRS detection. Modulation can be achieved in many ways, e.g. mechanically, acoustically, or with an electric field. The modulation performed for this work used the latter, a resonant Electro-Optic Modulator (EOM; from APE, s/n: S05957), since they provide high modulation depth and can be used at MHz frequencies. It receives the 80 MHz repetition rate from the mode-locked laser (see Section 2.3.2 above) and phase- locks the amplitude modulation to a quarter of its frequency, releasing a ωm = 20.0083 MHz output (approximated as 20 MHz elsewhere henceforth; see Figure 2.7). The modulation depth shows the efficiency of the modulation. A 100% depth would give maximum SRG (see Section 2.2.4 above). Here, the modulation depth was maintained at around 80%. Another important parameter to be taken into account is the transmission efficiency of the EOM, which depends on external light alignment and its own electronic compounds. When the EOM driving radio frequency (RF) voltage source is off (i.e. not generating modulation), the light transmission is > 90%, dropping to 40–50% when RF is on. This transmission will limit the maximum pump power 2.3. SRS PREPARATION 17

Figure 2.7: Beam modulation. The pump beam modulated at τmod = 50 ns (equivalent to fmod = 20 MHz), where the modulation depth is 82% and τrep = 12.5 ns the same as in Figure 2.6. that can be used in the imaging process.

2.3.4 Sample preparation

The Raman signal is tested using polystyrene microspheres, or beads. Polystyrene has a relatively simple spectrum with strong Raman bands with Raman shifts in the range of 600 to 3100 cm−1, overlapping with the range for our laser. The uniform composition and size of the beads allows the Raman spectrum (see Section 2.4), and the photodamage induced by the measurement (see Section 2.4.6), to be accurately and reproducibly measured. It also allows accurate benchmarking of the microscope performance. Here we work with both dry and wet samples. Wet samples are compatible with living organisms, so in those cases vacuum grease was spread around the edge of the microscope cover glasses (or coverslip; 1 ounce, 22x22 mm 100(20) µm thickness) as a sealant, the sample placed in the middle of it and a second coverslip pressed on top. The grease forms a seal around the edge while the cell solution fills the approximately 70 µm gap between the coverslips. Dry samples were used for the photodamage characterisation (see Section 2.4.6) for many reasons, such as stability of the sample, simplicity of the measurements that would have less exterior effects to take into account and lack of water evaporation, which changes the scattering of the beam with time. We also noticed that the absence of water reduces the power threshold for photodamage. In this case 18 CHAPTER 2. COHERENT RAMAN MICROSCOPY no vacuum grease was used and the sample would be left to dry for &4 hours. For synthetic samples, polystyrene (C8H8) spherical beads of 3.004(65) µm diameter (Polysciences, Inc.) were used. One drop containing 2.58% Solids-Latex was diluted in 1 mL of deionized water and from this solution, 15 µL is added onto a coverslip. For live cellular samples, dehydrated yeast cells (Saccharomyces cerevisiae) were sourced from a local supermarket, and hydrated in distilled water mixed with sugar (approximately 0.1% by weight) and salt (NaCl, approximately 0.1%) to provide sustenance and prevent osmotic shock. The cells were kept in this media for at least one hour to provide time to recover from dehydration. Cells were then transferred into sample chambers by pipetting 15 µL of the cell solution onto a coverslip. Once ready, the sample was left to rest for one hour before experiments to provide time for the cells to adhere to the surface, which is necessary for raster imaging. The health of the cell culture was verified separately by adding extra sugar and observing the production of carbon dioxide.

2.3.5 Spatial, temporal and polarisation alignments

In order to extract information about nonlinear interaction of the light with the sample, both pump and Stokes beam pulses need to be coinciding at the same time on the objective focus. These spatial and temporal alignments are perhaps the most demanding components of this phase of experimental assembly, since it consists of overlapping two 6 ps pulses (each 1.8 mm in length) in a space of 3.75 m, which is the space between pulses given by the laser’s repetition rate frep = 80 MHz. One technique used extensively throughout spatial alignments is the coupling of the light into an optical fibre. Because the light used here is predominantly Gaussian, the coupling efficiency is directly proportional to the overlap of the beams. This efficiency is measured with an optical power metre (Thorlabs, PM120VA) in the optical fibre output. The fibre coupling is made after the microscope, and mirrors prior to the fibre allow the Stokes beam to be coupled. Adjustments to the pump beam alignment are made with mirrors between the pump delay line and the dichroic beam-splitter prior to the microscope (see Section 2.3.1, and for more details Appendix A), ensuring spatial overlap in the sample. After the spatial overlap of the beams is optimised, temporal alignment is sought with the help of the delay lines (see Section 2.3.1) while monitoring the Stokes signal into the purpose-built resonant feedback photodetector. Having built the setup to within a precision of a few millimetres, the micrometre translation stages (Thorlabs PT1/M) from both delay lines provide the remaining millimetres for perfect temporal overlap. Once spatial and temporal alignments are done, polarisation alignment is performed with the use of a half-waveplate (Thorlabs, WPMH05M-780) for the pump beam prior to the microscope.

2.3.6 Filtering

Once the pump and Stokes beams are spatially overlapped, both beams will be directed to the purpose- built resonant feedback photodetector for detection. Because the detector is sensitive to a range of 2.4. SRS DETECTION AND IMAGING 19 wavelengths, and absorbing any trace of the pump beam will necessarily interfere with the SRS signal, all wavelengths apart from the Stokes must be filtered out. The filter used is a zero-order long pass filter (Thorlabs, FEL0950) transmitting ≈ 90.19% of 1064 nm and 1.4×10−3% for 800 nm. This filter is appropriate for SRS measurements, but the low transmission for 1064 nm is not ideal for quantum measurements, as will be explained in more detail in Chapter 4. Also part of the filtering system is a set of 3 dichroic mirrors (CVI, SWP-0-R1064-T700-900-PW1- 1012-UV), each reflecting > 99% at 1064 nm and transmitting > 80% at 700-900 nm, which allow the spatial alignment into the optical fibre (as seen in Section 2.3.5), as well as providing three degrees of freedom for the alignment into the detector.

2.4 SRS detection and imaging

The previous section (2.3) described the preparation of the main parts of the SRS microscope: the light, modulation, sample, alignments and filtering. With those tools in place, we can now proceed to the actual detection of SRS signal. In this section I present the equipment used in the detection system, show some results on Raman shift, shot-noise limited SRS spectroscopy and imaging, and finish with a quantification of photodamage in this context.

2.4.1 Equipment used for detection

When establishing a detection system, more than just the detector itself need to be accounted for. One standard method of SRS detection is to use a conventional large-area (e.g. 5x5 mm) photodiode to acquire the Stokes beam and extract the signal from the laser intensity in a lock-in amplifier [12]. State-of-the-art SRS microscopes require photodetectors that have high power handling to maximise the useable Stokes laser power and therefore signal-to-noise ratio, high bandwidth to maximise the achievable imaging frame rate, and low electronic noise [4]. To minimise electronic noise while still providing a high measurement bandwidth and power (further discussion for a broader application and photodetector characterisation in Section 4.4), we designed a resonant feedback photodetector in collaboration with Kai Barnscheidt and Boris Hage, who also built the photodiode. It is resonant at the SRS modulation frequency (fmod = 20 MHz; circuit shown in Appendix C) and made with a diode of 250 µm (Laser Components, G17X250S4i). It can handle up to 4 mW without saturation (see Figure 4.6), therefore for all applications throughout this thesis we use a safe 3 mW of Stokes beam power. A balanced detector (see Section 3.3.3) with the same two diodes was also built (see Appendix C) and can handle more than 30 mW without saturation, but for an initial direct proof of principle we chose to use the single photodiode. The detector outputs an alternate current (AC) and a direct current (DC) signal which both need to be read by a specific instrument before being processed on a computer. Here we use a 48 MHz low-pass filter (Mini-Circuits, BLP-50+) in the AC signal to be displayed in a spectrum analyser 20 CHAPTER 2. COHERENT RAMAN MICROSCOPY

(Agilent, N9010A 9k-3.6 GHz and N9320A 9k-3 GHz). With the spectrum analyser we can select the precise 20 MHz of the SRS modulation frequency to measure the noise levels and the SRG. There are three main settings in the spectrum analyser that are important to be understood for the results in this thesis: the resolution bandwidth (RBW), the video bandwidth (VBW) and the averaging. The RBW defines the frequency span of the bandpass filter that sweeps across the signal to be measured; a bigger frequency span contains less information and is faster to measure, whereas a shorter frequency span will contain more details, but in this case the time to acquire the data (sweep time) will be longer. The VBW defines the frequency span of the video filter, which will smooth the noise on the signal; analogous to the RBW, a bigger frequency span will have more noise and is faster to measure, whereas a shorter frequency span will be smoother in exchange for a longer sweep time. Therefore, to present a smoother trace, the VBW chosen was 10 Hz throughout the majority of the data. Typical SRS measurements were performed with RBW of 1 kHz, typical quantum measurements (see Chapter 5) were performed with RBW of 1 MHz, and for quantum-enhanced SRS measurements a trade-off of 3 kHz was used. The averaging defines the amount of times the spectrum analyser will sweep on the same data, used to reduce the measurement uncertainty; no averaging will give a noisier measurement (see Figure 2.8), whereas high averaging will give a neater measurement (see Figure 5.2). The DC signal is filtered with a 20 kHz low-pass filter (KR Electronics, 3201-20-BNC) and monitored with an oscilloscope (Agilent, DSOS104A). This signal was important to track the measured power throughout data collection, particularly for the experiments described in Chapter 4.

2.4.2 SRG and Raman shift

Using the detection system mentioned in the previous section (2.4.1) and a dry synthetic sample (as described in Section 2.3.4), SRG was measured as seen in Figure 2.8. This was taken without any averaging (which would smooth the traces as performed in Figure 5.2), and shows in light blue the shot-noise power at 3 mW in the Stokes beam with no pump; and in dark blue the same 3 mW power in the Stokes beam and 25 mW in the pump beam, which is set to λp = 803 nm (equivalent to RSΩ = 3055 cm−1). To first verify that SRS was being detected (Section 2.2), a power scaling of both Stokes and pump beams was made (see Figure 2.9). Note that the spectrum analyser itself displays power intensity in dBm, which implies in a quadratic scaling of the Raman signal with power. In order to be consistent with the literature, the measured power here is converted to amplitude, which then shows a linear scaling of the Raman signal with power. Figure 2.9 shows the linear dependence of the SRS signal for both Stokes and pump power. In these plots the blue dots are data and the dashed line are linear fits with angular coefficients of 0.69 mW−1 for the Stokes power scaling and of 0.11 mW−1 for the pump power scaling. From Equation 2.5, we can see that these coefficients are proportional to the number of molecules and the molecular Raman cross section, and therefore are expected to be the same if both beams are probing exactly the same amount of molecules. From the coefficients measured, we can infer that the beams used here did not 2.4. SRS DETECTION AND IMAGING 21

84

85

86

87 SRS signal [dBm] 88 Shot noise 89

20.005 20.006 20.007 20.008 20.009 20.010 20.011 Frequency [MHz]

Figure 2.8: Stimulated Raman Scattering spectroscopy. SRS measured in a 3 µm polystyrene bead, showing in dark blue the CH aromatic stretch resonance and in light blue the shot-noise (Stokes light with no pump). Results were taken without averaging, with 1 kHz spectrum analyser resolution bandwidth (RBW), 10 Hz video bandwidth (VBW), 3 mW of Stokes power and 25 mW of pump power.

overlapped perfectly. For this figure, the electronic noise was subtracted, so both fits go through the origin.

2.0 a b 2.0 ] 7 1.5

0 1.5 1 [

I /

I 1.0

1.0 G R S 0.5 0.5

0.0 0.0 0 1 2 3 0 5 10 15 20 Stokes power [mW] Pump power [mW]

Figure 2.9: Power scaling. Power scaling of (a) Stokes power and (b) pump power, detected with our custom-built resonant feedback photodetector. The signal is measured at the SRS modulation sideband frequency of 20.0083 MHz using a spectrum analyser with 1 kHz resolution bandwidth. Dashed grey line: linear fit. 22 CHAPTER 2. COHERENT RAMAN MICROSCOPY

A second step to check that SRS is being detected is to measure the Raman shift of the sample. To perform this measurement the spectrum analyser was set to zero span, where the data reading is fixed at one given frequency and the measurement is therefore sweeping over time. Figure 2.10 shows the Raman signal for this measurement at 20 MHz, when the pump wavelength in the OPO is swept from 800 nm (equivalent to 3102 cm−1) to 816 nm (equivalent to 2856 cm−1). The measurement time is dictated by the OPO sweep and matched on the spectrum analyser. We see one peak at 2916 cm−1 (purple) and a stronger one at 3050 cm−1 (green) and two smaller ones at around 3000 cm−1, which are the Raman signature for the polystyrene [27]. The inset shows the aromatic CH stretch bond (with green arrows showing a simplification of its resonant motion), and the antisymmetric CH2 strech bond (with purple arrows showing its resonant motion) [28–30].

Figure 2.10: Raman shift. Raman spectra measured in a 3 µm polystyrene bead, showing the CH2 antisymmetric stretch (purple) and CH aromatic stretch (green) resonances. Taken with 100 kHz spectrum analyser resolution bandwidth (RBW).

2.4.3 Shot-noise limited SRS

Many factors can prevent precision optics experiments from operating at the shot-noise floor; in particular technical laser noise and photodetector electronic noise. Both of these noise sources are especially problematic at low frequencies. As mentioned in Section 2.2.5, to evade low frequency noise we implement the technique devel- oped in Reference [8] wherein the pump laser is strongly amplitude modulated (see Section 2.2.4). 2.4. SRS DETECTION AND IMAGING 23

0.9

0.8 A = -0.00089P2 + 0.28P + 0.0024

0.7

0.6

0.5

0.4

0.3

Noise variance [a.u.] 0.2

0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Stokes power [mW]

Figure 2.11: Stokes laser is shot-noise limited. Power scaling of Stokes laser noise variance without squeezing, detected with our custom-built resonant feedback stimulated Raman photodetector. The variance is measured at the stimulated Raman modulation sideband frequency of 20 MHz using a spectrum analyser with 1 MHz resolution bandwidth. Dashed grey line: linear fit to the data points, with the equation for the fit given by A.

This modulates the stimulated Raman process, shifting the detected signal to sidebands around the modulation frequency, and away from the low frequency laser and electronic noise. As mentioned in Section 2.4.1, we custom-built a resonant feedback photodetector that would minimise the electronic noise. When detecting 3 mW of Stokes light we find that laser noise dominates electronic noise over a wide frequency band. To test whether the Stokes laser is shot-noise limited, we measured the power scaling of the Stokes light over 100 MHz bandwidth on a spectrum analyser. Figure 2.11 shows in blue the data at 20 MHz (for the full spectrum see Figure 4.5) and in grey the linear fit. This linear scaling is consistent with expectations for a shot-noise limited laser (see Section 4.4). If the laser were instead limited by technical noise, such as laser relaxation oscillation or spontaneous emission noise, quadratic scaling would be expected. This verifies that, over the 0–3 mW power range of the measurement, the Stokes laser is shot-noise limited. Therefore, the Stokes power reaching the detector is kept at 3 mW for all experiments, ensuring both shot-noise limited performance and large clearance (> 5 dBm, see the difference between the electronic noise (red curve) and shot-noise at 3 mW (dark blue curve) in Figure 4.5) from the electronic noise of the detector. 24 CHAPTER 2. COHERENT RAMAN MICROSCOPY

2.4.4 Microscope scan

As mentioned in Section 2.1.1, the microscope platform contains two stages that provide two degrees of freedom for horizontal displacements of the sample (one for micro- and one for nano-meter displacements), and one nanometre precision stage for the objective, providing one vertical degree of freedom. We operate those stages in the computer through modified versions of the LabView codes from the stages’ manufacturer (Mad City Labs), modifications made by Alex Terrasson. In the code we provide the origin position for the scan (allowing multiple scans of the same sample with accuracy, needed particularly for measurements described in Chapter 4), the dimensions of the image to be scanned (usually 10x10 µm), the steps to cover the image (usually 100 nm), the time to wait after each step (50 ms) and the time spent in each step (to synchronize with the data collection). The code generates a trigger signal that is sent to the spectrum analyser and it starts recording while the scan is performed. At the end of each step the spectrum analyser data is recorded and the delay allows the scan positions to be accurately measured with the software. At the end of each scan a text file is produced with the position of each step made by the scan (as mentioned in Section 2.1.1, the platform displacement causes small drifts that need to be compensated for), allowing precise overlap of scans for the same sample.

2.4.5 SRS imaging

After preparing the SRS pump and Stokes light (described in Sections 2.3.2 and 2.3.3) and a cellu- lar sample (described in Section 2.3.4), we generate images of yeast cells such as the example in Figure 2.12. In Figure 2.12 the cell nucleus is visible, as well as the faint outline of the cell membrane. A background Raman signal is visible in the buffer outside the cell, possibly due to sugar added to prevent cell burst. Here, the pump power is 6 mW, a level that was generally found to be safe for polystyrene (see Section 2.4.6) and that did not cause visible damage to cells either. The technique described here is not designed to better the current SRS techniques in terms of speed of detection, but to prove the principle of performing a quantum enhanced microscope that is suitable for current systems already in use. As mentioned in Section 2.1.1, the scan of a 100×100 pixel image would take around 8.3 minutes to complete. It means that the pixel dwell time – the time each pixel gets illuminated by the laser beam focus – is ≈ 50 ms /px, whereas current SRS techniques can achieve 1-100 µs.

2.4.6 Photodamage

Throughout Section 2.2 we discussed how improvements to the signal-to-noise ratio are limited by photodamage to the sample. In the process of imaging synthetic samples (see Section 2.3.4) with the Raman shift of 3055 cm−1, photodamage was indeed observed. We then opted to investigate how it affected the sample and what is the damage threshold for illuminating this sample. 2.4. SRS DETECTION AND IMAGING 25

Figure 2.12: SRS imaging of yeast. Image of a live yeast cell (Saccharomyces cerevisiae) in aqueous buffer at 2845 cm−1 Raman shift. Inset shows the cell image in bright-field microscopy. The pump power was set to 6 mW and Stokes power to 3 mW. Taken with 1 kHz spectrum analyser resolution bandwidth (RBW). Post-processing: Alex Terrasson.

Bright field images

When imaging a still sample, the Raman signal remains the same for a given low power. As seen in Sections 2.2.2 and 2.4.3, the signal intensity increases linearly with the power. However, once a certain power is reached, the signal becomes random, sometimes spiking briefly to then falling to almost zero, sometimes just dropping, and some times even dropping, spiking and dropping again. After many such measurements, I recorded the bright field image of the final state of the sample, shown in Figure 2.13. Several different damage modalities were observed, including deformation due to photo-absorptive heating, ablation due to the high peak intensity of the pump laser, and complete destruction or disintegration.

Quantification

To characterize the photodamage threshold, we systematically explored the shot-noise limited perfor- mance of the microscope by recording SRS signals from beads, while gradually increasing the pump power with a hand-turning neutral density filter wheel (Thorlabs, NDC-100C-4M). The Raman signal pattern for one particular bead is shown in Figure 2.14a. At low pump powers, the signal increases as expected (green shading). However, at high powers the signal diverges, typically 26 CHAPTER 2. COHERENT RAMAN MICROSCOPY

Figure 2.13: Bright field images of typical photodamage. Examples of the different photodamage modalities that were observed for 3 µm polystyrene beads. (a) Undamaged bead. (b) Slight deforma- tion. (c) Deformation of target bead and adjacent bead. (d) Ablation of two beads that were separately exposed. (e) Deformation. (f) Significant deformation. (g) Complete destruction. (h) Ablation. (i) Complete disintegration. In each image, the cross-hairs indicate the target bead(s). 2.4. SRS DETECTION AND IMAGING 27

a Peak intensity [kW m 2] 63 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

20 b

15 0

Pump power [mW] 10

65 5 Damage counts 0 70 1.0 c 75 0.8

0.6 80 No damage Damage 0.4 (>3 ) (>3 ) Raman signal [dBm] 85 0.2

Probability of damage 0.0 0 10 20 30 40 50 0 20 40 60 80 100 Time [s] Pump power [mW] a Peak intensity [kW m 2] 63 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

20 b

15 0

Pump power [mW] 10

65 5 Damage counts 0 70 1.0 c 75 0.8

0.6 80 No damage Damage 0.4 (>3 ) (>3 ) Raman signal [dBm] 85 0.2

Probability of damage 0.0 0 10 20 30 40 50 0 20 40 60 80 100 Time [s] Pump power [mW]

Figure 2.14: Quantifying photodamage. The Raman signal from a 3 µm polystyrene bead is probed as a function of pump power with a fixed 3 mW Stokes power. (a) Top: The pump power is gradually increased until photodamage is observed, in this example occurring at a power at the sample of 63 mW. It is then held fixed. Bottom: The Raman signal increases with power prior to photodamage (green) and drops at fixed pump intensity after the particle is damaged (red). Visual inspection (insets) confirms that photodamage has occurred. RBW: 1 kHz. (b-c) Characterization of the photodamage threshold for 110 particles. (b) Histogram of the pump power at which damage was observed, with Gaussian fit (dashed) of the histogram showing the mean photodamage threshold at 54.6 mW, corresponding to a peak intensity of 0.9 kW/ µm 2. (c) Cumulative distribution of the power at which photodamage occurs, with dotted line indicating the mean and each shading bar corresponding to +1σ from the mean. 28 CHAPTER 2. COHERENT RAMAN MICROSCOPY decreasing markedly and decaying over time (red shading). This is a signature of the onset of photodamage. We verify this by using bright field imaging which, for this example measurement, shows substantial deformation of the polystyrene bead due to absorptive heating, as well as deformation of an adjacent bead (Figure insets). The pump power measured for this particular damage was 63 mW. Photodamage modalities were observed to depend on both mean and peak intensity, which is an indication that the laser repetition rate and pulse length are well chosen to balance the different classes of photodamage [26]. To determine the photodamage statistics, we repeat the measurement on 110 beads, recording the threshold pump intensity at which the observed signal visibly diverges from damage-free expectations. Figure 2.14b plots the distribution, which can be approximated by a Gaussian with mean of 54.6 mW and standard deviation of 7.4 mW. The mean power corresponds to a peak pulse intensity of around 0.9 kW/ µm 2 consistent with known thresholds for laser ablation [31]. The probability of photodamage is highly sensitive to the optical intensity, as shown by the steep cumulative probability distribution in Figure 2.14c. For instance, when using a pump power of 30 mW none of the polystyrene beads exhibited photodamage, but at double that power, 60 mW, the majority were damaged.

2.5 Chapter summary and conclusions

In this chapter we have seen the importance of coherent Raman microscopy for allowing the distinction of structure and composition of the sample, used from diagnostic medicine to finding life sources in exoplanets. I have described methods involving the preparation of a state-of-the-art experiment setup and characterized the stimulated Raman signal and imaging. It finished with the determination of a very clear photodamage threshold which limits coherent Raman microscopy. Optimisation of stimulated Raman microscopy has reached its limits in the classical regime. The lasers and detection systems used are operating at the shot-noise limit, which means that further improvements on this technology will depend on the increase of laser intensity for higher signal- to-noise ratio. However, we also characterized an upper limit to this increase of intensity due to photodamage, as here was measured in 3 µm polystyrene beads, at the mean power of 54.6 mW. Here we see the first contextualization of this project: aiming to improve the signal-to-noise ratio of SRS microscopes below the shot-noise limit. And not only aiming to show the proof of principle to create a quantum-enhanced microscope, but to provide a quantification of the enhancement while avoiding the photodamage threshold. Chapter 3

Quantum theory background

“–and it really was a kitten, after all.” Chapter XI: Waking, Through the looking-glass, by Lewis Carroll.

Chapter 2 discussed briefly how the performance of an optical system that is classically optimal can be further enhanced by using some quantum physics techniques. In this chapter I will provide the main background theory for the quantum optics techniques that we are going to use throughout the remainder of this thesis, in particular for those described in Chapter 4. I start by defining how the light is described in quantum mechanics by ladder operators and how their properties, applied on “number states”, will define the important coherent states of the light. Heisenberg’s uncertainty principle provides the base to understand not only the fundamental noise intrinsic to photons, but also a graphical way to understand coherent states of light. This is also favourable for understanding squeezed states of the light, which allow some key advantages for working with quantum light, as will be seen in Chapters 4 and 5. I will describe how direct and balanced detections work and provide a mathematical understanding of how to produce squeezing and how to perform quantum detection.

3.1 Describing the light

In this section we are going to see how the light is described mathematically, with the utilisation of ladder operators. I will define observables, number states and Heisenberg’s uncertainty principle. This will pave the way for understanding the important coherent states of the light and the so-called vacuum state of light.

3.1.1 Optical field

The wave-particle duality of light has been studied by many scientists throughout history, but it was only in the start of the 20th century that Max Planck theorised the quanta of light, which associated 29 30 CHAPTER 3. QUANTUM THEORY BACKGROUND for each light “packet” – what came to be called a photon – a precise energy E = hν, where h is the Planck’s constant and ν the frequency of the radiation. This was soon proved by Albert Einstein through the law of the photoelectric effect, giving him the Nobel Prize in 1921. In the quantum theory of light, it is convenient to create a representation of the photons. By associating the letter n to the number of photons of a system, hence n ∈ N0, we can talk about the number state |ni, which is the state of a light field that contains n photons in a given mode. With these concepts, let us define a helpful tool called the photon-number operator.

Definition 1 (Photon-number operator). The photon-number operator, or just number operator, nˆ, is defined by nˆ |ni = n|ni. (3.1)

We can clarify the structure of the definition above by enunciating the following:

Definition 2 (Observable or Hermitian operators). An observable Aˆ is an operator that describes a measurable quantity of a physical system. In the mathematical structure we represent the outcomes of measurement as projections of the state onto the eigenstates of Aˆ, with the corresponding measurement result A being an eigenvalue of A.ˆ Aˆ |ψi = A|ψi. (3.2)

Since measurements only yield real-valued results, we have a specific type of nomenclature for those operators, the Hermitian operators. Aˆ is a Hermitian operator if and only if A ∈ IR.

With this definition, we can see that the number states |ni in (3.1) are eigenstates of the number operatorn ˆ, and the number of photons n ∈ N0 ∈ IR implies that the number operator is Hermitian. Now let us start manipulating the optical field. We can define an operator aˆ† that creates a photon on the field √ aˆ† |ni = n + 1 |n + 1i, (3.3) and an operatora ˆ that destroys a photon in the field √ aˆ|ni = n |n − 1i. (3.4)

They are called, respectively, creation and annihilation operators, or the ladder operators. If we apply them both in succession, we have: √ aˆ†aˆ|ni = aˆ† n |n − 1i √ = n aˆ† |n − 1i √ √ = n n |ni = n|ni. (3.5)

Hence, we can write the photon-number operator as a function of the ladder operators:

nˆ = aˆ†aˆ. (3.6) 3.1. DESCRIBING THE LIGHT 31

This representation of the photon-number operator is extremely useful and will be used in derivations throughout the chapter. These definitions give us a method for representing modifications to the field in terms of the application of these operators. However, from a later concept described in Equation (3.18), we see that the ladder operators are not Hermitian and therefore do not correspond to observables. Two observables that we can, and do, measure in our experimental setup are the amplitude and phase quadratures1 of the field. The quadrature operators are a set of orthogonal values that describe a particular form of the system, and whose eigenstates form a complete basis set. The amplitude and phase quadratures are represented in the theory by the Hermitian operators Xˆ + and Xˆ −, respectively. The ladder operators can then be written in terms of these quadrature operators of the field. In terms of amplitude quadrature Xˆ + and the phase quadrature Xˆ −, we have: 1 aˆ ≡ Xˆ + + iXˆ −
2 1 aˆ† ≡ Xˆ + − iXˆ −
, (3.7) 2 which inversely can be written in terms of the optical field

Xˆ + = aˆ† + aˆ Xˆ − = iaˆ† − aˆ
. (3.8)

3.1.2 Heisenberg’s uncertainty principle

Consider three operators Aˆ, Bˆ and Cˆ (see Definition 2) satisfying the commutation relation defined as

[Aˆ,Bˆ] ≡ AˆBˆ − BˆAˆ = Cˆ. (3.9)

In classical mechanics the observables commute, which is equivalent to saying that the eigenvalues of the operator Cˆ in Equation (3.9) will just have the trivial solution C = 0. In quantum mechanics C will assume non-trivial solutions. In 1927, Werner Heisenberg described, for the first time, non-commuting observables in terms of an uncertainty principle for the position q and momentum p operators [32]. For this specific case, Equation (3.9) becomes h [pˆ,qˆ] = pˆqˆ − qˆpˆ = , (3.10) 2πi where h is Planck’s constant and i the imaginary number. This result comes from the quantisation of the light, and should be applied in the context of quantum mechanics. The fluctuations, or “uncertainty”, on some operator Aˆ are given by the standard deviation2

1 q ˆ 2 2 ˆ2 ˆ 2 ∆A = h(∆A) iψ = hA iψ − hAiψ . (3.11) 1There is no Hermitian operator corresponding to the true phase of the field. The phase quadrature operator is actually a potential phase operator for the limit of large hni. 2 ˆ ˆ ˆ hAiψ = hψ|A|ψi is the expectation value of the operator A in the state ψ. 32 CHAPTER 3. QUANTUM THEORY BACKGROUND

The uncertainty relation that follows from Equation (3.9), generalised by the product of the fluctuations of the observables Aˆ and Bˆ, is then [33] 1 ∆A∆B |hCi|. (3.12) > 2 This implies that the product of the measurement uncertainty of Equation (3.12) assumes a non- trivial and positive value, meaning that these observables cannot be simultaneously and perfectly determined for a quantum approach. Note that in classic mechanics, C=0 implies that any pair of observables can, in principle, be perfectly and simultaneously determined.

Considering n different fields aˆn, n ∈ N, the commutation relations for the creation and annihilation operators (Section 3.1.1) satisfy

† [aˆi,aˆ j] = δi, j † † [aˆi,aˆ j] = [aˆi ,aˆ j] = 0, (i, j) ∈ N. (3.13)

And from Equation (3.12) it follows that for an optical fielda ˆ, its uncertainty relation is 1 ∆a∆a† . (3.14) > 2 Remembering that the ladder operators are variables that cannot be measured, the above equation is not physically relevant. To obtain a physically measurable quantity we should use the field quadrature operators (Equation (3.8)). For the same field aˆ, it follows from Equation (3.9) that the quadrature operators Xˆ ± will have a non-commuting relation given by [Xˆ +,Xˆ −] = 2i. (3.15)

Analogously, their uncertainty relation is

+ − ∆X ∆X > 1. (3.16)

This shows that the amplitude and phase quadrature operators of the optical field have a minimum uncertainty that sets a limit of precision for simultaneous measurement of both observables, called the quantum limit. The more accurately we measure one, the less accurately we can observe the other. Or, crucially for quantum enhancement and this work, the less constrained one is, the more accurately we can measure the other.

3.1.3 Coherent states

Coherent states are defined as states formed by the superposition of the number states [34]:

2 ∞ n − |α| α |αi = e 2 ∑ √ |ni (3.17) n=0 n! where α ∈ C is the amplitude of the coherent state (in the phase-space, the distance between the origin and the center of the coherent state – see Figure 3.1) and |ni are number states, which form a complete 3.1. DESCRIBING THE LIGHT 33 set. They are particularly important because (i) they are the states that most resemble the classical electromagnetic wave properties and (ii) a single-mode laser generates coherent state light [35]. For those reasons, they are sometimes also referred to as “classical” states of light. By applying the annihilation operator aˆ on a coherent state (3.17) and using Equation (3.4), it follows that the coherent states are eigenstates ofa ˆ, with eigenvalues α:

aˆ|αi = α |αi. (3.18)

Which is not true for the creation operator aˆ†, for whom the coherent states are not eigenstates: ∗ hα|aˆ† = hα|α . Note that because α ∈ C the annihilation operator is not Hermitian (see Definition 2). From the definition of coherent states given above in Equation (3.17) and the number state (Section 3.1.1), we can see that the coherent state is normalised, as ∞ ∗n n 2 α α hα |αi = e−|α| ∑ = 1. n=0 n!

The expectation value of the creation operatora ˆ on a coherent state α is then

haˆiα = hα|aˆ|αi = hα|α |αi = αhα |αi = α · 1 = α, (3.19) which can be interpreted as the coherent amplitude of the fielda ˆ. The number of photons of a coherent state is given by the photon-number operator 3.6 applied on a coherent state. With this we obtain

† † ∗ ∗ ∗ 2 hnˆiα = haˆ aˆiα = hα|aˆ aˆ|αi = hα|α α |αi = α αhα |αi = α α = |α| , (3.20) which can be interpreted as the number of photons being proportional to the square of the coherent amplitude, which means it is proportional to the power3 of the field (see Section 3.3.2). Note that the coherent state is not an eigenstate of the photon-number operator, as nˆ |αi = aˆ†α |αi. This means that the photon-number of a coherent state has an uncertainty q q 2 2 2 2 4 ∆n = hnˆ iα − hnˆiα = α (1 + α ) − α = α, (3.21) where we used Equation (3.11) and the assumption that α is real. Figure 3.1 shows the representation of a coherent state in a phase-space diagram, where X+ and X− are the quadratures the field (Equation (3.8)). This state is defined by an amplitude α = |α|eiθ of the light field, where θ is the complex angle of α, and its fluctuations are ∆X+ = ∆X− = 1.

3.1.4 The vacuum

In classical optics, without photons there is no field. In quantum optics, there is a state corresponding to zero photons, n = 0, called the vacuum state. Fluctuations in the vacuum, also called vacuum noise, contribute to a value that cannot be ignored when dealing with quantum light. 3Strictly speaking, it is the energy that comes from the commutation relation as described above. The power would come from the commutation relation of time-domain operators [a(t),a†(t)], but in practice they are applied interchangeably. 34 CHAPTER 3. QUANTUM THEORY BACKGROUND

Figure 3.1: Coherent state of light. The phase space representation with axis being the quadrature operators X+ and X−. The coherent state is defined by an amplitude α and a phase θ of the light field and has a noise defined by ∆X+ and ∆X−.

Definition 3 (Vacuum and bright light). The coherent state that has zero amplitude is called vacuum state and is represented by |0i. Conversely, a bright light is a collection of photons.

From the definition above, and that of coherent states (3.17), we see that the vacuum state is the only coherent state that is also a number state. The vacuum field is represented in Figure 3.2. Note that differently from the coherent state, this field has neither amplitude nor phase, just noise in both amplitude and phase quadratures given by ∆X+ and ∆X−. Both these noise quadratures are equal, as with the coherent state, so ∆X+ = ∆X− = 1.

Figure 3.2: Vacuum state of light. The phase space representation with axis being the quadratures operators X+ and X−. The vacuum state is defined by fluctuations of the light field and has a noise defined by ∆X+ and ∆X−.

The shot-noise limit, or quantum-noise limit, refers to these fluctuations of the vacuum state. If we are restricted to using coherent states of light, our measurement accuracy is always limited by this vacuum noise level. The only way to reduce this noise beyond the quantum-noise limit is to operate in the quantum regime and perform, for example, photon squeezing. 3.2. SQUEEZED STATES OF LIGHT 35 3.2 Squeezed states of light

From Heisenberg’s uncertainty principle (Section 3.1.2), we have seen that the product of the fluctuation of two observables (∆A∆B) is always greater than or equal to a fixed constant. When a quantum state is such that this product takes on its minimum value, but ∆A and ∆B each have different values, it is said that the quadrature with reduced fluctuations has been squeezed, or that the state is squeezed. The light field can be squeezed in any pair of quadratures that do not commute. Figure 3.3 shows the representation of a coherent squeezed state (a vacuum squeezed state would be analogous, but with α = θ = 0). This state is defined, as with the coherent state, by the same amplitude α = |α|eiθ of the light field, which uncertainties are given by ∆X±.

Figure 3.3: Squeezed state of light. The phase space representation with axis being the quadrature operators X+ and X−. The squeezed state is defined by the reduced noise in either amplitude or phase of the light field, which are defined by ∆X+ and ∆X−.

The creation of squeezed states is represented mathematically by application of a nonlinear squeezing operator Sˆsqz to a coherent state. This operator is given by

1 (z∗aˆ2−zaˆ†2) Sˆsqz(z) ≡ e 2 , (3.22)

i2θ where z = re is the squeezing parameter, r ∈ IR>0 the squeezing amplitude, θ is the squeezing phase and aˆ and aˆ† are the ladder operators (3.7). With the quadratic dependence on the ladder operators, this operator acting on a state will create and annihilate photons in pairs. One of the techniques to obtain photon squeezing, which will be more broadly discussed in Section 4.2.3, is pumping a nonlinear crystal with a certain amount of power P. Using Equation (3.8), one can write the squeezing gain g of this process in terms of the variance of a given field quadrature, and as a function of the squeezing amplitude:

g = (∆Xˆ +)2 = e−r , (3.23) with the squeezing amplitude given by c √ r = ∗ P , (3.24) 2 36 CHAPTER 3. QUANTUM THEORY BACKGROUND where c is a constant4 and P is the pump power. This mathematical representation of a squeezed state of the light aims to give the reader a better understanding of the calculations that will be done to model the squeezing used throughout this thesis. For a more general description of squeezed states I suggest reading the PhD theses of Valerian´ Thiel [36], Warwick Bowen [37] and Ping Koy Lam [38].

3.3 Quantum detection

In this section I will approach some formalisms related to the detection of quantum light and define some of the functional forms used in Chapters 4 and 5. I start by introducing a helpful approximation used throughout the remaining of this chapter called linearisation of the optical field. This will allow us to obtain the expression for the photocurrent measured in terms of physical quantities for both direct and balanced detections. I introduce concepts such as the visibility and quantum efficiency, which provide tools for understanding some operational relations given in following chapters. I finalise by introducing the beam-splitter and its applications, and the development of direct detection functional forms for a squeezed beam of light, which is essential for our work in the following chapters.

3.3.1 Linearisation of the optical field

For many applications, the linearisation of the optical field is performed in order to obtain analytic solutions and real measurable values. This approximation is valid when the amplitude α of the optical field is much larger than its fluctuations, α  δaˆ, which is consistent with the usage of a bright beam of laser with low noise. The linearisation of the field consists firstly in describing the field operator in a first order approximation [38] aˆ ≈ α + δaˆ, (3.25) where the first term is the mean amplitude value of the field, whilst the last term represents its fluctuations, or noise. A second part of the linearisation method consists in neglecting second order terms in fluctuations. An important example can be seen in the photon-number operator, given by Equation (3.1), which becomes:

nˆ ≡ aˆ†aˆ ≈ (α∗ + δaˆ†)(α + δaˆ) = |α|2 + α∗δaˆ + αδaˆ† + δaˆ†δaˆ (3.26)

A first order approximation neglects the high order noise term given by the operator product δaˆ†δaˆ, so for α ∈ R we obtain nˆ ≈ α2 + αδXˆ +. (3.27)

4Not to be confused with the speed of light. 3.3. QUANTUM DETECTION 37

This gives the number of photons of the optical field in terms of its power and the fluctuations in the amplitude quadrature of the field, given by Equation (3.8). This approximation will be used throughout this chapter when dealing with the detection of the field.

3.3.2 Single, or direct detection

Single detection, or direct detection, is the use of one single photodiode detector to measure a signal comprised of one single incoming beam. Consider then a bright coherent beam of light being detected on a single diode. The photocurrent obtained though the photodiode is proportional to the number of photons that hit the photodiode [38] iˆ ∝ nˆ ≡ aˆ†aˆ (3.28) wheren ˆ is the photon-number operator (see Definition 1). Using the linearisation approximation of the optical field (Equation (3.27)), we obtain

iˆ≈ α2 + αδXˆ +, (3.29) which shows the measured photocurrent of the optical field in terms of its power (α2, see Equa- tion (3.20)), and the fluctuations in the amplitude quadrature of the field (δXˆ +, see Equation (3.8)), scaled by the coherent amplitude (α, see Equation (3.19)). The expected value of the fluctuations in amplitude quadrature of the field is said to be the shot-noise.

3.3.3 Balanced detections

Differently from direct detection (see Section 3.3.2), a balanced detection is a technique to detect the light when it interferes with either waves from the same source or the vacuum. There are a few types of balanced detection, such as self-homodyne detection, which relates to the interference with the vacuum, standard-homodyne detection, which relates to the interference with waves of identical frequency, and heterodyne detection, which has a frequency shift between the interferring beams [39]. This technique is broadly used in the quantum community because its configuration provides a way of achieving nearly unity detection efficiency [40]. The self-homodyne detection uses two identical detectors and a 50:50 beam-splitter (see Sec- tion 3.3.7). The signal beam, carrying the squeezed states of light, interferes in the beam-splitter with ˆ + the vacuum, with amplitude quadrature operator Xv . In post-processing we can subtract and sum the detected photo-currents, obtaining [38]:

2 + iˆsum ∝ α + αδXˆ ˆ ˆ + idiff ∝ αδXv . (3.30)

This implies that with a single measurement in self-homodyne detection we can retreive the same signal as a direct detection (with the sum) but with a calibration with respect to the vacuum fluctuations (with the difference). For more details on balanced detection I suggest reading the book of Gerry and Knight [41] and the PhD thesis of Ping Koy Lam [38]. 38 CHAPTER 3. QUANTUM THEORY BACKGROUND

Despite the high detection efficiency of this method, we decided not to use balanced detection in the first trials of our experiment. Direct detection was chosen to simplify the post-processing, which gets more complicated due to the purpose-built balanced detector having different gains on each photodiode. It also meant there was one less beam, the local-oscillator, to be set-up across the experiment, simplifying the experiment overall.

3.3.4 Visibility

When beams of light interfere, dark and bright fringes and can be seen. The visibility of these fringes, obtained when the overlap of both beams with the same intensity is close to optimum, is a very important aspect to consider in order to optimise this overlap and reduce losses.

Definition 4 (Visibility). The visibility between two interferring beams is defined by the ratio of the signal amplitude and the mean intensity [42]

A (I − I )/2 Vis = = max min (3.31) I¯ (Imax + Imin)/2 where Imax is the maximum and Imin the minimum measured intensities of the interference pattern.

Note that if there is a non-zero offset in the output of the detector (the measurement when no light is incident on the detector), then in the equation above one should make the change Imax → Imax− offset and Imin → Imin− offset. This was used throughout the measurements performed on the squeezer (see Section 4.2.4). The definition above also connects to the overlap efficiency η of both beams via the relation [38]:

η = Vis2 (3.32)

3.3.5 Quantum efficiency

The quantum efficiency of a device is the ratio of the charge collected within the device to the number of photons hitting the device. If λ is the wavelength (as ν the photon frequency) of the light that has optical power P, and it hits a device that generates a photo-current ip, then the quantum efficiency ηq can be expressed as [42] ip/e ip hc ηq = = , (3.33) P/(hν) Pλ e where e is the elementary charge c the speed of light and h the Planck constant.

3.3.6 Application to equipment used in the detection

As well from the detector itself, there are two other pieces of equipment that make up the detection system: the oscilloscope and the spectrum analyser (see Section 2.4.1). The oscilloscope gives the DC values (i.e. zero frequency) of the detected photocurrent. From Equation (3.29), they correspond to the first term of the photocurrent given by the power α2. 3.3. QUANTUM DETECTION 39

The spectrum analyser gives the AC values (i.e. all frequencies but zero) of the detected photocur- rent. It shows the spectral power density of the signal, given by the sum of the power and variance of the field [37]. The shot noise given in Equation (3.29) is therefore measured on the spectrum analyser.

3.3.7 Beam-splitter

The beam-splitter (BS) is a device that separates an incoming beam of light into two parts. The simplest shapes of this device are the cube beam-splitter, which is a combination of two triangular glass prisms glued together forming a cube, or the plate beam-splitter, which is a mirror-shaped glass with a special coating on its surface. By defining a precise thickness for the glue and the coating needed, the beam-splitter can allow any split from half of the initial beam (a 50:50 beam-splitter), to almost no split (such as a 90:10 beam-splitter). Polarising beam-splitters (PBS) are also possible, with the horizontal and vertical polarisations of the light being split in the same way. Further discussion on design techniques for a beam-splitter can be found on the Springer Handbook of lasers and optics [42]. The beam-splitter is essential not only as an experimental device, but also as a tool to understand quantum properties of light-matter interaction. A very good discussion of classical beam-splitting and an initial derivation of the quantum mechanics of the beam-splitter is found in the book of Garry and Knight [41]. In a classical approach, a field a entering the beam-splitter will be split into: the reflected part of the field multiplied by the complex reflectance r of the beam-splitter (ra), and the transmitted part of the field multiplied by the complex transmittance t of the beam-splitter (ta). In a quantum approach, the argument above is not completely true – the fluctuations of the vacuum coming from the unused side of the beam-splitter will interfere with the output fields. This consideration is necessary to preserve the commutation relations (see Equation (3.13)). Figure 3.4 shows a simplified schematics of a beam-splitter, with the input field a, the vacuum states b and the output fields c and d.

Figure 3.4: Schematic of a beam-splitter. With an input field given by a, the output fields c and d are a combination of the reflection and transmission between the input field and the vacuum fluctuations given by b. Explanation in the text.

For the case of a lossless beam-splitter, which we will approximate to in our calculations, the transmittance and reflectance satisfy

|r|2 + |t|2 = 1. (3.34)

√ By relating the transmittance to the efficiency of the beam-splitter, we can write |t| = η and 40 CHAPTER 3. QUANTUM THEORY BACKGROUND √ |r| = 1 − η and hence the output fields c and d will be [42] √ √ c = η a + 1 − η b √ √ d = 1 − η a − η b. (3.35)

3.3.8 Direct detection for squeezing

From the results obtained in Section 3.3.2 we can now merge theory behind the direct detection process with the theory of squeezed states of light. The signal that goes through a squeezing process and is directly detected is depicted in Figure 3.5. Here we will omit the operators’ hats for simplicity.

Figure 3.5: Single detection with squeezing. The detected photocurrent can be calculated by the sum 0 of the input field X0 that has perfect overlap with the OPA pump, giving X2, and the part of the field that does not overlap X1, considering an overlap efficiency of ηv and the vacuum state Xv. The gain of the squeezer is given by g.

The field of the light to be squeezed and detected is given by the creation operator a (see Sec- tion 3.1.1). We are performing an amplitude squeezing of the field, so here we analyse only the changes in the amplitude quadrature X+ (hereafter just X for brevity) of the field. The input quadrature is shown in Figure 3.5 as X0. The squeezing of the optical field will be generated in the nonlinear crystal, with g = g(P) being the gain of the amplification and de-amplification of the optical field, which depends on the pump power P (not shown in the figure). The visibility of the overlap between the pump and the signal beams (see Section 3.3.4) can be modelled by a beam-splitter with efficiency

ηv. As seen in Section 3.3.7, the vacuum field quadrature needs to be considered and is shown as Xv. Propagating the fields through the beam-splitter and using Equation (3.35) we obtain √ √ X1 = 1 − ηv X0 − ηv Xv (3.36) √ √ X2 = ηv X0 + 1 − ηv Xv. (3.37)

The field X2 goes through the nonlinear crystal and is multiplied by the gain g

0 √ p  X2 = g ηv X0 + 1 − ηv Xv . (3.38) The coherent amplitude of the optical fields (see Equation (3.19)), can be simplified because the vacuum has no coherent amplitude (see Section 3.1.3), resulting in √ α1 = 1 − ηv α0 0 √ α2 = g ηv α0. (3.39)

Here we assume that the coherent amplitude is a real value, α ∈ IR. 3.3. QUANTUM DETECTION 41

De-amplification measurement

Let us now analyse the detected current, as from Equation (3.28). By taking its expected value and using the earlier result shown in Equation (3.20) we obtain

hii ∝ ha†ai = α2, (3.40) which shows that the measured current is proportional to the power of the field. 0 For a total current adding the contributions from both fields X1 and X2 (Equations (3.39)), Equa- tion (3.40) becomes

2 2 2 2 2 2 2 hiti = α1 + α2 = (1 − ηv)α0 + g ηvα0 = α0 (1 − ηv + g ηv). (3.41)

2 This equation shows the linear dependency of the total measured current on the input power α0 and on the visibility overlap ηv, and quadratic dependency on g. In the shot-noise limit, this equation can be interpreted as the shot-noise variance of the detected current

2 h(∆i) ishot−noise = hiti. (3.42)

Using the squeezing gain, g, given in Equation (3.23), we can write Equation (3.41) in a more convenient form √ hiti −c P 2 = ηve + 1 − ηv, (3.43) α0 which shows the ratio of mean detected current to input power. This ratio decays exponentially as a function of the amplitude of the pump power P. Classically, this equation shows the de-amplification of the field for a system with efficiency ηv when going through a nonlinear crystal. Because it relates to the power of the field, de-amplification is measured on an oscilloscope (see Section 3.3.6).

Squeezing measurement

The variance of the squeezing Vsqz is defined as the variance of the detected current in relation to the shot-noise variance of the current h(∆i)2i Vsqz = 2 . (3.44) h(∆i) ishot−noise To see how the mean detected current varies with the quadrature of the field, we linearise the optical field (see Section 3.3.1). The detected current, given by Equation (3.28) for each of the fields † † mentioned in the description of Figure 3.5, or i = a1a1 + a2a2 , becomes

2 + 2 + i = α1 + α1δX1 + α2 + α2δX2 . (3.45)

For the calculation of the squeezing we are interested in the variation ∆i of the current, so the 2 2 power terms α1 and α2 are neglected, obtaining

∆i = α1X1 + α2X2 2 2
= α0 (1 − ηv + g ηv)X0 + ηv(1 − ηv)(g − 1)Xv . (3.46) 42 CHAPTER 3. QUANTUM THEORY BACKGROUND

Here we expanded the amplitudes using Equations (3.39), X1 using Equation (3.36), and X2 using Equation (3.38). Because the expected variance of a coherent or vacuum quadrature field is unity (see Sections 3.1.3 2 2 and 3.1.4) we have that h∆X0 i = h∆Xv i = 1, so we can square Equation (3.46) and take its expected value obtaining

2 2 2 2 2 2
h∆i i = α0 (1 − ηv + g ηv) + ηv(1 − ηv)(g − 1) 2 4
= α0 1 − ηv + g ηv . (3.47)

Substituting Equations (3.47) and (3.42) into the expression for squeezing variance (Equation (3.44)), we obtain 4 1 − ηv + ηvg Vsqz = 2 . (3.48) 1 − ηv + ηvg By including the expression for the squeezing gain, g, given in Equation (3.23), and by incorporat- ing an efficiency ηt,d related to the transmission and detection of the detected signal, we obtain the measured squeezing variance √ −2c P t,d (1 − ηv + ηve ) V = ηt,d √ + (1 − ηt,d). (3.49) sqz −c P (1 − ηv + ηve ) As shown in Figure 3.6, this equation shows how the squeezing is affected by the pump power P. It shows that it, for lower powers, drops exponentially, reaching an optimum value of squeezing. At high powers, the variance will tend to unity, being dominated by the visibility inefficiencies of the squeezed beam. This influence of ηv can be seen in Figure 3.6b, where even for a good visibility efficiency of 0.95, a perfect efficiency for transmission would not improve much the maximum amount of squeezing compared with a 0.9 transmission efficiency. In the ideal case when ηt,d = ηv = 1, the variance tends to t,d zero – which means obtaining a perfect squeezing. Vsqz is the quantity that we measure on the spectrum analyser (see Section 3.3.6). This result will be directly used in Chapter 4 for the characterisation of the squeezing obtained.

3.4 Chapter summary and conclusions

In this chapter we have seen the necessary background for the quantum theory behind the concepts that will be used on the next chapters of this thesis. It is by no means a comprehensive quantum theory description, so the chapter aimed to focus on the necessary aspects of the physics used on this project. It provided a few basic concepts to describe the light, in particular those from the squeezed states of the light, finishing with a description of quantum detection: from the equipment used to the functional forms of the obtained measurement. We have seen, amongst a few important definitions and concepts, that the de-amplification signal of optical fields due to light-matter nonlinear interaction should drop exponentially with the amplitude of the squeezer pump field, being only limited by the overlap efficiency of the beams. We saw that the measured variance of squeezed states of light should also drop exponentially with the amplitude of the 3.4. CHAPTER SUMMARY AND CONCLUSIONS 43

t, d a Vsqz

1.0

0.8 0.7 0.8 0.6 0.9 0.95 0.4

0.2 0.999 v = 1 0.0 0 2 4 6 8 10 c P

t, d b Vsqz

1.0

t, d 0.8 0.7 0.8 0.6 0.9 0.95 0.999 0.4 1

0.2

0.0 0 2 4 6 8 10 c P

t,d Figure√ 3.6: Squeezing variance. Squeezing variance equation Vsqz against the squeezing amplitude c P , where c is a constant and P the pump power. (a) Showing dependence with the visibility effi- ciency ηv, assuming a transmission efficiency of 0.95. (b) Showing dependence with the transmission t,d and detection efficiency ηt,d, assuming a visibility efficiency of 0.95. The dashed grey line at Vsqz = 1 is the shot-noise value. 44 CHAPTER 3. QUANTUM THEORY BACKGROUND squeezer pump field, though these are limited by the efficiencies of transmission, detection and most importantly the efficiency of overlap between the pump and signal beams of light. With this background formed we should now be able to understand the mechanics of the experi- mental techniques developed and detailed in Chapter 4. Chapter 4

Experimental techniques for quantum-enhanced microscopy

In Chapter 2, we have seen how coherent Raman microscopes work and the techniques involved to perform data collection on them. In the last chapter (3), we have seen part of the quantum theory that describes how squeezed states of light can be generated and the theory applied here to detect them. In this chapter I will explain the techniques used to obtain the main results of this thesis (which will be shown in Chapter 5), around applying squeezed states of light into a coherent Raman microscope. I will start by motivating this work and giving an overview of quantum enhanced measurements (Sections 4.1 and 4.1.1) highlighting existing quantum enhanced imaging systems. I will then explain how the preparation of the quantum light source for our microscope was performed (Section 4.2), with a particular emphasis on alignments and the phase-lock. Section 4.3 will describe the necessary adjustments made on the microscope for quantum imaging, followed by Section 4.4 characterizing the detector for quantum measurements. Each of these parts of the experiment will contribute with their respective efficiencies (described in Section 4.5), which are essential for the final characterisation of the squeezed states (Section 4.6). Section 4.7 will describe the method used for the data processing with squeezed states. Finally, Section 4.8 will summarize the main aspects of the chapter.

4.1 Introduction to quantum measurements

Squeezed states of light were first measured by Slusher et al. in 1985 [43] using an atomic cloud and measuring 0.3 dB below the shot-noise level. This was a very exciting moment for the scientific community, since the notion of the squeezed states was first developed almost 60 years earlier by Earle Hesse Kennard, in 1927 [44]. From this time on, many ways of generating squeezing were explored: parametric down-conversion (PDC) [45], parametric up-conversion [46], optical fibres [47], semiconductor lasers [48]. In 2016, Henning Vahlbruch et al. [14] achieved the highest noise reduction below the shot-noise level demonstrated so far. They produced -15 dB of squeezing by using a continuous-wave laser 45 46 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY through a periodically poled potassium titanyl phosphate (PPKTP) nonlinear crystal (see Section 4.2.3) on a resonant optical parametric amplifier (OPA) configuration, a technique based on PDC and first developed by Slusher in 1987 [49]. A resonant OPA refers to the technique where the light bounces inside a mirrored cavity to generate higher photon squeezing1, to increase the nonlinearities between photons and crystals, which are intrinsecally very small. An alternative to this technique is to make a single-pass OPA with pulsed light, which contain higher powers locally in the beam pulse, therefore also obtaining higher squeezing [50]. Pulsed squeezing is still harder to produce, with the highest noise reduction below the shot-noise level of 5.8 dB shown by Chonghoon Kim and Prem Kumar in 1994 [51].

In this section we will go through some of the research on quantum measurements (Section 4.1.1), and in particular on quantum imaging systems (Section 4.1.2). This aims to provide the reader with an understanding of the field and show how it has developed so quickly in the past few years. It will also serve as comparison to contextualize our technique amongst the others and how it distinguishes from the ones applied before.

4.1.1 General quantum enhanced measurements

Since the first generation of squeezing in 1985, an increasing number of experiments are using this technique to improve detection performance. As things stand, quantum enhancements are not that substantial when compared with classical improvements on the system, but they provide a unique way of increasing signal-to-noise ratio that would be impossible for systems that are fully optimised classically. In addition, quantum correlations are very sensitive to loss of light on the system, due to inefficiencies of the crystals, mirrors and other optical devices used along the beam path – all these destroy the quantum correlations.

For this reason, one should improve the efficiency of the experiment as close as possible to its classical limit, before applying quantum correlated light. For instance, this was done by the Laser Interferometer Gravitational-Wave Observatory (LIGO) scientific collaboration in 2011 [52] and later in 2013 [15]. They produce squeezed states of light in a resonant OPA with a PPKTP crystal. This light is injected into their interferometer to improve detection performance for low frequency measurements, which are particularly important for the study of astrophysical gravitational wave sources, achieving up to 3.5 dB of noise-floor reduction. Other quantum enhanced measurements were performed on the fields of optomechanical magnetometry [53], positioning and clock synchronization [54], and teleportation [55], amongst others.

1Resonant cavities are also good mode-shape cleaners: after many rebouces of the light on the mirrors, the only light coming out will be an averaged mode, and therefore always the same while the imperfections of some differenlty scattered photons will be filtered out. 4.2. QUANTUM LIGHT SOURCE FOR SRS MICROSCOPY 47

4.1.2 Quantum enhanced imaging systems

With many imaging systems already operating at the shot-noise limit, quantum technologies are powerful tools that allow further improvement of those systems. Different techniques are being developed in order to exceed the limitations of optical imaging, such as continuous variables (which includes the photon squeezing that I am performing here), entangled imaging, noiseless amplification, amongst others – for a broader view on other systems I suggest reading Mikhail I. Kolobov’s book [56]. More specifically to the technique used in this work, in the past decade a variety of applications were performed applying quantum correlated light into imaging systems. From 2013 to 2015, experiments applying quantum light to improve sensitivity of biological measurements [17, 57], and to increase spatial resolution [58–60] started to pave the way for performing quantum-enhanced microscopy. Since the start of the work presented in this manuscript, in 2016, many other fine works have been developed in the same fashion [39, 61–67]. Two particularly relevant works were released in 2020 at a similar time as ours: that of Gil T. Garces et al. [68], which uses 120 fs pulsed light with 0.3 dB of noise-floor reduction for stimulated emission microscopy and that of R. B. Andrade et al. [69], which uses continuous-wave light with -3.5 dB of noise-floor reduction in a SRS. The main point that has not yet being shown, is the absolute quantum advantage of those systems – none of these previous experiments have reached the damage limits of conventional microscopy. In the following sections, I will describe our use of an single-pass OPA to produce the quantum source of squeezed states of light. The light is pulsed, which is ideal for biological measurements with CR microscopy. We developed a detection system that allows squeezed states of light to be detected at high powers and high bandwidth. In this regime, commercial detectors fail due to high noise overwhelming the quantum correlations, or have very low quantum efficiency and therefore not suitable to detect quantum light. Our technique provides quantum enhancement in biologically relevant CR microscopy.

4.2 Quantum light source for SRS microscopy

In this section I will describe our light source in the context of quantum measurements, going through the characteristics of the laser and the nonlinear crystal. I will then describe the necessary alignments to produce photon squeezing and the filters used, finishing with a description of the phase-lock – a fundamental part of the setup and allows changes in the phase angle of the squeezing, which is ultimately switching the squeezing on and off.

4.2.1 The quantum ray

The most relevant characteristic of our laser (introduced in Section 2.3.2) that enables quantum enhancement is its low-frequency noise. Noise at frequencies shorter than 1 MHz means that our measurements, made at the modulation frequency value of 20 MHz, are not laser noise-limited and 48 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY therefore it is possible to detect quantum enhancements. The low-frequency noise spectrum of the laser can be explicitly seen in Figure 4.5.

The laser pulse length tpulse = 6 ps is optimal for matching the Raman transition linewidth of the measurements we are performing (see Section 2.3.2). Also, at these pulse lengths the dispersion — or more precisely the group dispersion — of the light when propagating through air or any other material is negligible, which is not the case for shorter pulse lengths. Shorter pulse lengths would undergo a broadening of the pulse envelope in the time domain2.

4.2.2 The squeezer

The next component for generating a quantum light source is the nonlinear crystal and its operating system, referred to as the squeezer. We purpose-built an optical parametric amplifier (OPA) that produces bright amplitude-squeezed light in a single-pass configuration. Quantum correlations are generated between photons in the Stokes laser (with wavelength λS) by passing the beam through the squeezer and pumping it with λ532 = 532 nm light. The platform for the nonlinear crystal (shown in Figure 4.1) was built by Ulrich Hoff and Lars Madsen in 2016 (for the blueprint, see Appendix D). It consists of a monolithic base, for the crystal to be at beam height and with the least amount of vibration possible, copper plates that completely surround the crystal for good thermal conduction between the crystal and the thermo-electric element (Peltier; Marlow Industries Inc. model NL1013T), which is controlled by a Wavelength Electronics ◦ PTC2.5K-CH module [71], allowing a temperature change on the crystal with an uncertainty of . 1 .

Figure 4.1: Platform for nonlinear crystal. (a) The assembled platform on the optical table. (b) Its main parts: (white letters) (a) the base for the crystal to be at beam height, (b) copper plates to efficienlty transfer the temperature needed to the PPKTP crystal (c), (d) the thermo-electric operational cables coming from the controller and (e) the thermistor measuring the current temperature of the crystal for feedback to the controller.

2For example, a pulse length of 22 fs will have, for a beam wavelength of 800 nm, a group dispersion of 36 fs 2 for each mm inside a material made of fused-silica [70]. 4.2. QUANTUM LIGHT SOURCE FOR SRS MICROSCOPY 49

The light is focused inside the crystal through a plano-convex lens (Thorlabs, LA1068-YAG), which was chosen for its low reflectance < 0.25% for both λ532 and λS. This lens has focal length of 75 mm, which was chosen on a trade-off between smaller focusing waists providing higher nonlinearity effects and bigger focusing waists providing a more homogeneous beam through the crystal, which is important for maintaining the photon squeezing. After interacting with the crystal, another lens of the same kind collimates the beam to be sent to the phase-lock (see Section 4.2.5 below) and to the microscope (see Chapter 5).

4.2.3 The nonlinear crystal and SHG

The interaction of light and a nonlinear crystal happens very fast. In theory, a short crystal would be optimal to obtain the desired nonlinearities, which are intrinsically small. One technique developed to enhance this nonlinear generation is to produce a longer crystal with a periodic domain structure, or a periodically poled cyrstal: each segment of the crystal has a precise length to match the wavelength of the light used. Each surface of those segments receives special coatings that, added to the orientation of the crystal structure will ensure positive built up of the nonlinearity throughout the crystal [72]. To generate this nonlinear interaction between photons and the crystal two relations must be satisfied [73]: the energy conservation relation 1 1 1 + = (4.1) λs λi λp and the quasi phase-matching condition

n(λ ,T) n(λ ,T) n(λ ,T) 1 p − s − i − = 0, (4.2) λp λs λi Γ(T) where λp, λs and λi are the wavelengths of the pump, signal and idler beams respectively, n(λp,T), n(λs,T) and n(λi,T) the refractive index of the pump, signal and idler beams respectively, T is the temperature and Γ(T) is the grating period of the crystal. Note that the quasi phase-matching condition depends on the temperature of the crystal, which needs to be carefully selected. The nonlinear crystal used in the present work is a periodically poled potassium titanyl phosphate (PPKTP) crystal (Raicol Crystals, s/n:7-112714933), with length of 7 mm and cross section of 1 mm ×2 mm. It was chosen because it generates about three times larger second-order nonlinearities when illuminated with a laser along its length (see Section 2.1.2), as opposed to a bulk KTP crystal [74]. For the purpose of generating second harmonic generation (SHG, see Section 2.1.2), the pump beam is what in the remaining of this thesis is called the Stokes light, at the wavelength of λS = 1064 nm.

The crystal will convert two photons of λS into one of λSHG = 532 nm. To optimise the quasi phase-matching condition for SHG production, both the polarisation of the pump beam and the temperature of the crystal are changed (see Section 4.2.2 above for the temperature control) while tracking the power of λ532 with an optical power meter (Thorlabs, PM130D). The highest SHG power produced for a fixed pump power corresponds to a temperature of ≈ 32◦C on 50 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY the crystal3. At this temperature, we measure the power scaling of SHG for different powers of the 1064 nm light (Figure 4.2).

12 A = 0.00194 P2 + 0.01 P + -0.025

10

8

6

4 SHG power [mW]

2

0 0 10 20 30 40 50 60 70 80 Stokes power [mW]

Figure 4.2: Second harmonic generation. Power of the second harmonic generation produced (λ532 = 532 nm) on the nonlinear PPKTP crystal, while varying the Stokes power λS = 1064 nm. The quadratic fit is shown in grey, with the equation for the fit given by A, where P is the Stokes power. The error on the values is 1% and the errorbars are smaller than the size of the dots.

In this figure we can see the quadratic scaling of the field, which agrees with Equation 2.1.2, as (2) (2) 2 the electric field is proportional to the second order polarisation: ESHG ∝ P = χ (ES) . For the remaining of the experiments described in this thesis, this optimal SHG was fixed and used for the photon squeezing production.

4.2.4 Spatial, temporal and polarisation alignments

In Section 2.3.5 we discussed alignments of the pump and Stokes beams for the nonlinear interaction of both lights with the sample. Fine spatial, temporal and polarisation alignments are also needed to generate nonlinearities to engineer quantum correlation processes. For this part of the setup, however, the light pumping the OPA has wavelength of λ532 = 532 nm, which needs to be synchronized with the Stokes light inside the nonlinear crystal.

Because the Stokes beam also generates light at the wavelength λSHG = 532 nm through SHG (see

Section 4.2.3 above), both λ532 and λSHG can interfere (see Section 3.3.4). By measuring the visibility 3This optimal temperature varies slightly when the spatial, temporal and polarisation alignments change, so this optimal value was obtained after many iteration in the optimisation of all those values. 4.2. QUANTUM LIGHT SOURCE FOR SRS MICROSCOPY 51 of this overlap from both beams of light (see a simplified schematics on the red panel in Figure 4.3) we can optimise their spatial, temporal and polarisation overlap. The Stokes light coming from the

OPA needs to be filtered out for the visibility measurement to be performed. Hence, λS is reflected using a high energy harmonic separator (CVI, BSR-15-1025), which reflects > 99.5% at 1064 nm and transmits > 90% at 532 nm. The transmitted light at 532 nm from both beams is aligned into an optical fibre. The first step is to maximize the SHG (see Section 4.2.3), which sets a polarisation for the Stokes

field. The beams of wavelengths λ532 and λSHG are then aligned using a similar technique to that described in Section 2.3.5, but in this case the light collected through the optical fibre is detected on a DET10A Thorlabs detector — to spatially overlap the beams — and monitored on an oscilloscope (Agilent, DSOX3054A). As the oscilloscope provides an effective way to measure the power on each beam (see Section 3.3.6), it is used to set equal power on each beam, so the interference pattern can be maximised (see Section 3.3.4). We then modulate the phase of either beam with a piezo-electric ceramic4 (piezo; Piezomechanik, HPSt 150/14-10/12) driven at low frequencies by a function generator (BK Precision, 4011A). The synchronization of the temporal position of the pulses is achieved through delay lines in both beam paths, both using micrometre translation stages (Thorlabs, PT1/M). When synchronization is close to optimum, an interference pattern from both beams can be seen on the oscilloscope and be used to optimize their overlap. The polarisation on the λ532 field is changed to match that of the Stokes field. It is iteratively optimised with the other alignment parameters to reach the global maximum of the overlap. The good overlap of the beams is one of the key features necessary to obtain quantum correlations, therefore the interference’s visibility (see Section 3.3.4) is carefully improved prior to every measure- ment. The visibility was kept at a value Vis ≈ 0.92. From Equation (3.32), we obtain the efficiency related to this visibility:

2 ηvis = Vis ≈ 0.846. (4.3)

4.2.5 Phase-locked loop

Once the beams are well overlapped and SHG is maximised, we can set the phase-locked loop. It is a feedback system to keep the phase of the output beam constant, and in our case, also to control the relative phase between the Stokes beam, of wavelength λS, and the pump for the OPA, of wavelength

λ532. A block diagram of the phase-locked loop is shown in Figure 4.3. The red shade indicates components that are on the optical table. The remaining components are off the table and depicts our

4Commonly called PZT due to the most used materials for this ceramic: lead zirconate titanate. It converts electrical signal, or a voltage, into mechanic expansion and compression. Attached to a mirror, it provides a phase shift on the light reflected off the mirror. 52 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

Figure 4.3: Phase-locked loop diagram. The elements on the optical table are highlighted in the red panel, with φS the phase introduced on the Stokes beam through the piezo and φ532 the phase introduced on the beam of wavelength λ532 through another piezo. Both beams interact with the crystal on the squeezer. In the output, λ532 is detected for the phase-locked loop, which is all off the optical table. It sends the AC detected signal to a mixer, which receives a 104.7 kHz signal from a function generator (part of this signal is used to modulate φ532). Its output feeds the PID, which is also supplied with a 12 Hz from another function generator. The output of the PID locks the phase φS. LPF1 is a 100 kHz low-pass filter, Amp1 a low-noise amplifier, LPF2 a 20 kHz low-pass filter, Att a collection of attenuators (10+2+1 dB) and Amp2 a voltage amplifier.

phase-locked loop. Both input beams, of wavelengths λS and λ532, have a piezo attached to one of the mirrors on the beam path to modulate their respective phase, φS and φ532. Those two beams interact with the PPKTP crystal in the squeezer. The Stokes beam proceeds to the output, while a small amount of both 532 nm wavelength beams, the pump for the OPA and the SHG beam, are collected on a switchable gain detector (Thorlabs, PDA36A-EC) through a filter blocking any remaining Stokes light (Thorlabs, FES1000). The visibility of their interference (as seen in Section 4.2.4 above) can also be optimised with this signal. For the phase-locked loop, a bias-tee (Tektronix, PSPL5547) separates the detected DC signal which is used for monitoring the signal on an oscilloscope, from the AC signal which is used for the 4.2. QUANTUM LIGHT SOURCE FOR SRS MICROSCOPY 53 loop. After passing the AC signal through a 100 kHz low-pass filter (LPF1; KR Electronics, KR2928) and a low-noise amplifier (Amp1; Mini-Circuits, ZFL-500LN+), the signal is sent to a frequency mixer (Mini-Circuits, ZAD-3+). The signal from a function generator (RIGOL, DG1022) is split in a power-splitter (Mini-Circuits, ZSC-2-1+). The frequency selected, 104.7 kHz, is one of the frequencies that makes the piezo resonate. Part of this signal goes to a succession of attenuators (Att; Mini-Circuits, HAT-2+, HAT-1, HAT-10) and to a coaxial amplifier (or voltage amplifier, Amp2; Mini-Circuits,

ZHL-32A) before modulating φ532. The other part is sent to the frequency mixer. The output signal of the frequency mixer is filtered with a 20 kHz low-pass filter (KR Electronics, KR2484) and sent to the input (labelled “error”) of a proportional integral derivative controller (PID; New Focus, LB1005), which is the main component of the feedback loop. The PID can fix the loop to a constructive or destructive phase between λS and λ532, depending on the input selection. This causes amplification or de-amplification of λS, which also results in amplification or de-amplification of the amplitude fluctuations, leading to bright amplitude anti-squeezing or squeezing of light states, respectively [75]. Channel C1 from the PID receives a 12 Hz signal from a function generator (BK Precision, 4011A), which is used on the sweep function of the PID. The sweep function is used to both synchronize the signal and error, and to improve the error output quality (minimizing white noise and precision of the output channel). Channel C2 is the error monitor signal sent to the oscilloscope to be monitored. The

PID output drives the modulated φS. The PID also has four controls (input offset, P-I corner, gain and LF gain limit) to optimise the phase-lock, which in our case are used to optimise the de-amplification of the beam. A power meter is used to detect the Stokes beam propagating after the nonlinear crystal. After locking the phase to de-amplification, which means the lock is in a deep of the sinusoidal phase, the power of the Stokes beam will drop. The optimisation of this de-amplification is achieved by decreasing the power as much as possible with the PID four controls, while keeping both the error monitor signal and the detected DC signal from the Stokes beam constant and smooth. After this optimisation, the Stokes beam power is increased to the same power it had prior to de-amplification (to compare photon squeezing levels with shot noise at the same power) and is sent to the purpose-built detector to measure the de-amplification and squeezed states of light. Figure 4.4 shows an example of what is seen in the oscilloscope when the sweep function of the PID is activated. For both Figure 4.4(a&b), the blue curve shows the detected Stokes beam in the output of the squeezer, being amplified and de-amplified by the OPA pump beam, and the red curve shows the error monitor signal. In Figure 4.4(a) the error monitor is saturated, as can be seen by its squared shape. This figure was taken for a setup which (i) did not use a power-splitter after the RIGOL function generator, but instead set two channels of the function generator to feed independently the frequency mixer and φ532 and (ii) did not use the filter LPF1 and amplifier Amp1 prior to the frequency mixer. Figure 4.4(b) is taken with the setup described above, which shows the error monitor not being saturated, but with an increased noise. We were able to reduce this noise by swapping a few cables for new ones, and setting a better connection between electronic components. For the remainder of the 54 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

a SHG 0.3 Error monitor 0.2 DetC

0.1

0.0

0.1 OSC value [V] 0.2

0.3

0.100 0.075 0.050 0.025 0.000 0.025 0.050 0.075 0.100 Time [s] b SHG Error monitor 0.2 DetC

0.1

0.0

0.1 OSC value [V]

0.2

0.3

0.100 0.075 0.050 0.025 0.000 0.025 0.050 0.075 0.100 Time [s]

Figure 4.4: Error monitor signal. Shown for a sweep fuction of the PID activated, with input powers of 3 mW for the Stokes beam and 150 mW for the OPA pump beam, blue curve is the detected Stokes beam after the squeezer and the red curve the error monitor signal. (a) shows a previous setup with saturating error monitor. (b) shows the setup described in the main text, without saturation. 4.3. THE QUANTUM-COMPATIBLE MICROSCOPE 55 thesis, the photon squeezing was produced with similar error monitor signal as shown in Figure 4.4(b), but with reduced noise.

4.3 The quantum-compatible microscope

After generating quantum-correlated photons in the Stokes light (Section 4.2), it is important to avoid complete destruction of this correlation and to keep it as high as possible. The stability of the microscope platform mentioned in Section 2.1.1 helps to minimize those losses, as vibrations will introduce noise. Also for this reason, monolithic posts were used, and kept as short as possible (mirrors closer to the optical table will reduce those vibrations, as will thicker mirror mounts with more stiff springs). The whole system was designed for the Stokes light to be reflected from the optics wherever possible, rather than transmitted, since the latter would increase losses due to dispersion inside the optics. All optics were very carefully selected to have the highest reflectivity for the Stokes light, especially the objectives. Light is both focused and collected in the microscope using two matching water- immersion objectives (Leica Microsystems, HC-PL-APO63x/1.20W, more details on Appendix B). These objectives have a custom anti-reflection coating at 1064 nm applied to the lenses, which ensures a high Stokes transmission of > 92%. To ensure this high transmission is maintained in both dry and aqueous media we under-fill the objectives with the incoming beams, resulting in an effective numerical aperture of 0.9.

4.4 The detector

In the previous sections (4.2 and 4.3) we saw how to generate the quantum light and how to protect it from losses. In this section we will talk about the last important step prior to analysing quantum measurements (Section 4.6), which is the detector itself. In Section 2.4.1 I described the purpose-built detector and its main features. Here we are going to characterise its importance for a quantum measurement. It was designed in collaboration with Kai Barnscheidt and Boris Hage, who also built it (see Figure C for its photo and circuit). The characterisation of the detector is performed by measuring the power scaling of the Stokes light (see Figure 4.5 in different shades of blue). The detected signal is sent to the spectrum analyser without using its internal pre-amplifier, which is on by default. The grey curve of Figure 4.5 shows the electronic noise of the spectrum analyser over 100 MHz bandwidth. We see that it dominates the noise at frequencies . 1 MHz, due to the choice of 1 MHz for the resolution bandwidth of the measurement. The detector’s electronic noise is shown in red. Also in the same figure we can see the feature of a resonant detector at 20 MHz, which is the modulation frequency fmod for the Raman detection (see Section 2.2.4). At this frequency, the peaks of the power scaling (in blue) follow a linear progression (see bottom left panel), which means that the Stokes laser and detection system is quantum-noise limited (as discussed in Section 2.4.3; also see 56 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

a

40 3.0 mW 1.5 mW 0.75 mW 50 0.37 mW Electronic noise SA noise 60

70

Stokes intensity [dBm] 80

0 20 40 60 80 100 Frequency [MHz]

b 20 MHz peaks c 80 MHz peaks

2 2 1.0 A = -0.0P + 0.29P + 0.11 80 A = 7.01P + 2.16P + -0.22

0.8 60 0.6 40 0.4

20

Noise variance [a.u.] 0.2

0.0 0 0 1 2 3 0 1 2 3 Stokes power [mW] Stokes power [mW]

Figure 4.5: Detection noise. (a) Noise from the Stokes light, in different shades of blue, for 0 to 3 mW for a range of 0 to 100 MHz with the spectrum analyser’s internal pre-amplifier off. The red curve is the detector’s electronic noise and the grey curve the spectrum analyser’s (SA) electronic noise. (b) The peak amplitude at 20 MHz for each power. (c) The peak amplitude at 80 MHz for each power. For both (b&c) we have that: the red diamond is the electronic noise, the dashed grey line is the fit to the data points, with the equation for the fit given by A. No averaging, RBW: 1 MHz, VBW: 300 Hz. 4.5. EXPERIMENT EFFICIENCIES 57

Section 3.1). Similar analysis was made at the frequency corresponding to the laser repetition rate frep of 80 MHz, finding a quadratic scaling and therefore being classical-noise limited. When detecting 3 mW of Stokes light at 20 MHz, we find that the laser noise dominates the electronic noise by ≈ 10 dB. A good clearance is found over a frequency band of & 10 MHz. This shows that our purpose-built photodetector has high bandwidth, allowing high-speed microscopy imaging, and low electronic noise for the frequency needed, necessary for quantum-enhancements. To verify at which power the detector saturates with the Stokes light, a power scaling from 0 to 6 mW was performed in the same fashion as the one described above. Figure 4.6 shows that there is saturation after 4 mW, so to avoid this the maximum power used in experiments was 3 mW.

Figure 4.6: Saturation from the detector. Power scaling of Stokes light at 20 MHz showing saturation after 4 mW. The red diamond shows the detector’s electronic noise. The dashed grey line is the linear fit to the first five data points, with the equation for the fit given by A along the fit. The solid grey curve is the quadratic fit to all data points, with the equation for the fit given by A on top of the figure. The negative quadratic parameter indicates saturation; the linear fit shows the maximum saturation value.

4.5 Experiment efficiencies

In the previous sections (4.2 to 4.4) we have seen the description and characterisation of our experi- mental system composed of the quantum light-source, the microscope and the detector. For each of these steps we can associate an efficiency η, which will contribute to the preservation of the quantum correlations. In this section I will describe the efficiencies related to the Stokes light (4.5.1), to the pump light (4.5.2) and to the detector, merging them into one total efficiency describing the possible levels of squeezing (4.5.3). 58 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

4.5.1 The Stokes light

To obtain the efficiency in the squeezer, we measure the beam power just before the PPKTP crystal and compare it to the power measured after the crystal (nominal transmission > 99%, SHG ≈ 99.5%), one lens (Thorlabs, LA1608-YAG, ≈ 99%), one mirror (Thorlabs, BB1-E03, > 99%) and two harmonic separators (CVI, BSR-15-1025, > 99.5%). We measure an average efficiency of 95±1% in power transmission. Note that even with only Stokes light being injected into the crystal, there is generation of 532 nm photons through SHG and therefore this light is present at a measurement straight after the crystal. To avoid this contamination, the power measurement for the Stokes beam is made after the harmonic separators. For the Stokes power used, the SHG conversion is about 1% of the total power. Taken this into account on the total efficiency calculation, the measured average efficiency is then

ηsqzer = 96±1% in total power transmission, which is compatible with the nominal component values described above. The path from the squeezer to the microscope platform (path1) contains six mirrors (Thorlabs, BB1-E03) and one dichroic beam-splitter (CVI, SWP-0-R1064-T700-900-PW1-1012-UV, > 99%). The efficiency measured through this path is ηpath1 = 99±1%. The microscope platform is composed of 1 mirror (Thorlabs, BB1-E03), one dichroic mirror transmitting 1064 nm and reflecting 532 nm (no specifications5, ≈ 96.5%), two objectives coated for 1064 nm (Leica, HC PL APO, > 92%), two microscope coverslips (calculated efficiency ≈ 95%, considering a Schott D263 glass coverslip and a water-glass and glass-air interface6) and one dichroic mirror reflecting 1064 nm and transmitting 532 nm (no specifications7). The efficiency measured was

ηmic = 75±1%. The path from the microscope platform to the detector (path2) contains two mirrors (Thorlabs, BB1-E03), one half-wave-plate (Thorlabs, WPMH05M-1064, ≈ 99.5%) and three dichroic beam- splitters (CVI, SWP-0-R1064-T700-900-PW1-1012-UV, > 99%). The efficiency measured was ηpath2 = 98±2%. The need to use one extra filter for SRS measurements (Thorlabs, FEL0950, see Section 2.3.6) implies that quantum measurements for Raman microscopy were also affected by an efficiency of ηfilter = 89±2%. The efficiency for the transmitted Stokes light prior to detection has therefore a measured total efficiency of

ηtr = ηsqzerηpath1ηmicηpath2 = 70 ± 2% (4.4) and accounting for the filter

ηtr+filter = ηsqzerηpath1ηmicηpath2ηfilter = 62 ± 2%. (4.5)

We also have two other configurations that are worth mentioning. The first configuration was used on the early stages of the experiment, achieved by placing the detector prior to the microscope and

5No description of it is found on the setup or in [20]. 6Note that this value will differ for the experiments made on water, as the water-glass interface has a reflectance 10 times smaller than the air-glass interface. 7See footnote 5. 4.5. EXPERIMENT EFFICIENCIES 59 measuring an efficiency of ηtr,simple = 88±1%. The second configuration, used towards the end of the project, allows quick diversion of the beam around the microscope in order to measure the squeezing levels and avoid the higher inefficiencies of the microscope. This shortcut path consists of two flipped mirrors cutting through path1 into path2 with only one mirror in between, and has the efficiency of

ηtr,shortcut = 93±1%.

4.5.2 The pump light

600 mW of pump light is generated from the OPO using an input of about 2 W of 532 nm wavelength light. It is reflected from six mirrors (Thorlabs, BB1-E03, > 99%) before the beam passes through either a beam-dump8 or neutral density filters, to select the power of the pump beam to go into the microscope. A beam-dump is very effective for a specific wavelength, but when multiple wavelengths are used – as in the Raman microscope to target different molecular resonances, neutral density filters are optimal. This light proceeds to the EOM (APE, s/n: S05957), one half-wave plate (Thorlabs, WPMH05M- 780, ≈ 99.5%), three mirrors (Thorlabs, BB1-E03, > 99%) and one dichroic beam-splitter (CVI, SWP-0-R1064-T700-900-PW1-1012-UV, > 80%). The average efficiency in this part of the setup was measured to be ηEOM ≈ 43%, with most of the inefficiencies coming from the EOM. On the microscope platform, the optics are the same as listed for the Stokes beam above (Section 4.5.1), though the transmissions are different. The averaged measured transmission through the sample, before the top objective was of ≈ 26.6%. Considering one Schott D263 glass coverslip (air-glass-air coverslip transmission of ≈ 92%, and water-glass-air coverslip transmission of ≈ 95%), the efficiency from the start of the microscope platform to the sample is calculated to be ηsample ≈ 29% and the objective transmission to be ηobj ≈ 32%.

4.5.3 The squeezed states of light

As mentioned in Section 4.1.1, quantum correlated light is highly susceptible to loss of photons in the system, and therefore knowing the overall efficiency of the setup provides information on the maximum obtainable squeezing value. This efficiency will be referred to as ηsqz and can be calculated by taking the product of the visibility efficiency ηvis (Equation (4.3)), the transmission efficiency ηtr

(Equation (4.4); either ηtr+filter, ηtr,simple, or ηtr,shortcut can also be used depending on the chosen setup) and the detection efficiency ηdet.

The efficiency of the detector ηdet can be calculated through the equation for quantum efficiency

(Equation (3.33)). Using P = 3 mW, λ = 1064 nm and ip = 93 mV/(50Ω), we obtain

 93 × 10−3/50  hc η ≈ ≈ 72%. (4.6) det 3 × 10−3 × 1064 × 10−9 e

8Composed of one half-wave plate and one polarising beam-splitter. 60 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

In this case, and using ηtr as the transmission efficiency, the total efficiency for the squeezed states of light is

ηsqz = ηvisηtrηdet ≈ 0.846 × 0.62 × 0.72 = 38%, (4.7) which means that there is around a 62% inefficiency degrading the squeezing we obtain for SRS spectroscopy and imaging. Note that using ηtr,simple as the transmission efficiency, we have an increased 0 total efficiency of ηsqz = 54%, which is relevant for Chapter 5.

4.6 Characterisation of squeezed states of light

In Section 4.5 we have seen a detailed list of the efficiency for each component of the experimental setup and how it relates to the squeezed state of the light. In this section I will show the experimental results for the de-amplification of light (Section 4.6.1) and its corresponding squeezing of the states of light (Section 4.6.2) and how they are linked with the efficiency values described above.

4.6.1 De-amplification

As mentioned in Section 4.2.2, we inject light of wavelengths λS and λ532 into the crystal. By controlling the relative phase between those fields (Section 4.2.5) it is possible to either amplify or de-amplify the Stokes light. Figure 4.7 shows the de-amplification of the Stokes light with 3 mW of power, for a power scaling from 0-70 mW of the λ532 light, measured on the oscilloscope. The fit to Figure 4.7 is given in Equation (3.43), and fits well to the data. We can see that the extracted efficiency of the overlap between the beams is ηv = 0.85±0.022 and the coefficient defining the squeezing parameter c = 0.14±0.0056 (see Equation (3.24)). Comparing ηv with Equation (4.3), we see good agreement between the measured values.

In the hypothetical case that there is no overlap between the beams, ηv would be zero and the in output Stokes power the same as the input P1064 = P1064, i.e. equal to 1. Analogously, if we had a perfect overlap between the beams, or ηv = 1, the light is de-amplified exponentially tending towards zero for high powers of the 532 nm light.

4.6.2 Squeezing

As explained in Section 4.2.5, the de-amplification of the amplitude fluctuations results in amplitude- squeezed state of light, which we detect in the spectrum analyser. Figure 4.8 shows the squeezing variance of the Stokes light with 3 mW of power, for a power scaling from 0-70 mW of the λ532 light, measured at the detector resonant frequency of 20 MHz. Note that the squeezing, being measured in reference to the shot-noise, needs to have the same power as the shot-noise. At every new power of

λ532 the phase-lock is turned on, the de-amplification is optimised (Section 4.2.5), and the power of the Stokes beam is increased back to 3 mW in the detector for the comparison with the shot-noise. The DC signal is measured on the oscilloscope and has the same value as the shot-noise, since their powers are the same. The AC signal, measured on the spectrum analyser, shows the squeezing levels. 4.6. CHARACTERISATION OF SQUEEZED STATES OF LIGHT 61

1.0

0.9 P1064 c P in = v e + (1 v) P1064 0.8

v = 0.85±0.022

0.7 c = 0.14±0.0056

0.6

0.5 De-amplification 1064 nm [snu] 0.4

0 10 20 30 40 50 60 70 Power 532 nm [mW]

Figure 4.7: Deamplification. Measurement of the de-amplification of the Stokes light when it goes through the nonlinear crystal, for a power scaling of 532 nm light of 0-70 mW. The data (in blue) was normalised to the measured shot-noise value and shown in shot-noise units (snu). Data taken on the oscilloscope.

The fit to Figure 4.8 is given by Equation (3.49). A three parameter fit to this data alone would not tightly constrain the values (i.e. ηt,d = 0.49±0.86,ηv = 0.92±0.46 and c = 0.20±0.29). However, ηv and c are also constrained by the fit to de-amplification data (Section 4.6.1) which, having only these two free parameters, constrains them quite precisely (ηv = 0.85±0.022 and c = 0.14±0.0056). Fixing these values for the squeezing variance fit then allows us to extract an accurate value for the remaining parameter, the efficiency of transmission and detection, ηt,d = 0.65±0.011. Note that the configuration used for this data collection is the one for which the transmission efficiency is ηtr,simple (Section 4.5.1). This transmission efficiency multiplied by the calibrated detection efficiency given by Equation (4.5.3), gives us ηtr,simple × ηdet = 64%, which is consistent with the values obtained for ηt,d.

We see from this fit that if the visibility were perfect, or ηv = 1, the shape of the squeezing variance would be the same as the de-amplification shown in Figure 4.7, with the asymptote given by ηdet. However, at high powers the variance starts being dominated by the visibility inefficiencies of the squeezed beam (see Section 3.3.8 for further discussion). The highest squeezing value is around 50 mW of power for the OPA pump, and therefore it will be the power used throughout the squeezing measurements henceforth. Having measured a power scaling for the squeezing characterisation, we can now see how the 62 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY

1.00

(1 + e 2c P ) v v 0.95 V = t, d + (1 t, d) c P (1 v + ve )

0.90 Fit: t, d = 0.65±0.011

Fix: v = 0.85, c = 0.14 0.85

0.80 Squeezing variance [snu] 0.75

0.70 0 10 20 30 40 50 60 70 Power 532 nm [mW]

Figure 4.8: Squeezing. Measurement of the squeezing variance of the Stokes light when it goes through the nonlinear crystal, for a power scaling of 532 nm light from 0-70 mW. Measurements were taken on a spectrum analyser at the centre frequency of 20 MHz, RBW: 1 MHz, VBW:10 Hz. squeezing behaves over the frequency bandwidth of the detector. Figure 4.9 shows 3 mW of power for the λ1064 light while injecting 50 mW of power for the λ532 light into the crystal. This measurement was made on the spectrum analyser in the range of 3-55 MHz. From Figure 4.9 we note that the electronic noise from the detector has a peak at 20 MHz, this being because the detector is resonant at this frequency. The shot-noise and squeezing traces are around 10 dB higher than the electronic noise, which allows a clear measurement for the squeezing. During the experiment, however, an electronic noise pick-up would appear at 20 MHz when the EOM is active. Through grounding and removal of the electronic cables that were acting as antennae, we kept the pick-up noise at a maximum of around 1 dB from the electronic noise level. The noise-floor reduction achieved with the squeezed states of light was up to -1.5 dB. Note this value is for illustration only; small changes on the setup can easily change this value. Figure 4.9 shows the typical squeezing value achieved in our experiment, which is around -1.15 dB.

4.7 Data processing with squeezed states of light

With both squeezing and SRS running satisfactorily, merging them was a matter of small adjustments in taking and processing the data. As explained in Section 4.6, with this setup configuration the squeezing can only be really measured when it has the same amount of power as the shot-noise. 4.8. CHAPTER SUMMARY AND CONCLUSIONS 63

0 Shot-noise 10 Squeezing

Electronic noise

1 10 Intensity [a.u.]

2 10

10 20 30 40 50 Frequency [MHz]

Figure 4.9: Squeezing, shot-noise and electronic noise. Spectrum of the squeezed light detected in the range 1-55 MHz without any normalisation. The detector is resonant at 20 MHz, and electronic noise pickup from the EOM is seen. The maximum value of squeezing reached is -1.15 dB. RBW: 1 MHz, VBW: 10 Hz, Average: 35x.

Therefore, a one-dimensional plot (as Figure 4.9) only needs one measurement of the shot-noise and one measurement of the squeezing level at the same power. In order to validate this for a two-dimensional plot (as for Figure 5.5), for all quantum images we have taken two consecutive scans: one for the shot-noise (which varies in power when the light is scattered through the sample), and one for the quantum light. As mentioned in Section 2.4.4, the precise position of each step is recorded so that the comparison of both shot-noise and quantum light can be made. As the position is not perfectly matched for two consecutive runs, we interpolate the values for the shot-noise at the positions corresponding to the squeezing data, providing a reliable comparison.

4.8 Chapter summary and conclusions

In this chapter we have seen the experimental methods and techniques used in this project to generate the quantum light and to merge it into an optical microscope. I have given a brief overview of the current quantum measurements, shown how the laser and detector used are compatible with quantum measurements, and described the squeezer: how to operate it to obtain the quantum light and shown its characterisation. I have provided the tools to understand the changes made in the microscope to allow 64 CHAPTER 4. EXPERIMENTAL TECHNIQUES FOR QUANTUM-ENHANCED MICROSCOPY quantum measurements and detailed the efficiencies of the whole setup, which are closely linked with the squeezing levels obtained. Finally, I have characterised the squeezed states of the Stokes light and described how we perform the quantum measurements and imaging with this light. We have made a resonant detector and shown that it provides shot-noise limited measurements without saturation to values up to 4 mW. The visibility achieved for the overlap between the Stokes light and the 532 nm light was kept around 92%. The transmission efficiencies for the setup were calculated to be 62±2% for measurements performing SRS. This value improves to 93±1% when only squeezing measurements are needed, by using a shortened optical path. The detection efficiency was measured to be around 72%. All three measured efficiencies were consistent with the values extracted from the squeezing characterisation. We have achieved a reliably reproducible value of -1.15 dB for the squeezing on this setup. With this chapter we consolidate and apply some of the concepts seen in Chapter 3 and develop the tools used for the results shown in Chapter 5. Chapter 5

Quantum imaging

In this chapter I present the major outcome of this thesis. By applying some aspects of quantum physics (Chapter 3) to the stimulated Raman scattering microscope (Chapter 2), with methods detailed in Chapter 4, we were able to develop a quantum-enhanced microscope, overcoming the photodamage limits of light microscopy. This achieves a recognised milestone in quantum technology, as specified in both the current UK and EU Quantum Technologies Roadmaps [76, 77]. After a brief overview of the experimental setup (Section 5.1), I will describe the experiments that were done and show our main results. These include increasing the signal-to-noise ratio of a SRS microscope (Section 5.2), overcoming photodamage limits with quantum light (Section 5.3), and performing quantum enhanced imaging with SRS microscopy (Section 5.4). The chapter finishes in Section 5.5 with conclusions on the main experiments. This chapter contains work published in Reference [1].

5.1 Experimental setup

The experimental setup for this part of the project has undergone a few critical changes from the features first described in Section 2.3.1. In Figure 5.1, in the light sources panel, we show the same 80 MHz laser pumping the same OPO with a 532 nm light which is converted to a tunable wavelength light for the SRS pump beam, modulated with an EOM to a frequency of 20 MHz. Here the squeezer (for more details see Section 4.2) was added to the Stokes field, which has the same wavelength as before, λS = 1064 nm. It is composed by a set of 2 lenses focusing the light into a nonlinear PPKTP crystal (see Sections 2.1.2 and 4.2.1), generating quantum-correlated Stokes light, which will be temporally and spatially overlapped with the pump beam on a dichroic beam-splitter. On the microscope platform, Figure 5.1 at the microscope panel, the objectives were upgraded to the >92% transmission objectives (for more details see Section 4.3) in order to minimize degradation of quantum correlations. Both pump and quantum-correlated Stokes beams will interact with the sample, the pump will be filtered out through a dichroic beam-splitter (CVI, SWP-0-R1064-T700-900- PW1-1012-UV) and used for alignment purposes using an optical fibre (see Section 2.3.5). Bright 65 66 CHAPTER 5. QUANTUM IMAGING

Figure 5.1: Simplified quantum experimental setup. (Red panel) Preparation of the pump beam (purple) via an Optical Parametric Oscillator (OPO) and 20 MHz modulation from an Electro-Optic Modulator (EOM), and Stokes beam (red) which is amplitude squeezed in a periodically poled KTiOPO4 crystal pumped with 532 nm light. (Green panel) Stimulated Raman scattering is generated in samples at the microscope focus through high-transmission objectives, with raster imaging performed by scanning the sample through the focus. A CCD camera and a light emitting diode (LED) allow simultaneous bright field microscopy. After filtering out the pump, the Stokes beam is detected and the signal processed using a spectrum analyser (blue panel).

field imaging, with a LED shining through the microscope platform and detected with a CCD camera, remained unchanged. The detection system at the detection panel also remained unchanged, with the quantum-correlated Stokes light being detected in our purpose-built photo-detector and the signal acquired in a spectrum analyser. A full optical table setup can be seen in Appendix A.1.

5.2 Signal-to-noise enhancement

To increase the signal-to-noise ratio (SNR) of stimulated Raman microscopy, we introduce quantum correlations in the Stokes photons. The quantum correlations are generated using a purpose-built optical parametric amplifier that produces bright amplitude squeezed light (see Section 4.2.1). This allows the measured noise-floor to be reduced beneath the shot-noise limit. Figure 5.2a shows in blue the resulting reduction in noise variance as a function of frequency, normalised to the reference light, or shot-noise. This normalisation is refered to as shot-noise units (snu; for more information see Section 4.6). The reduction achieved was of -1.06 dB (≈ 22%) at 20 MHz, the frequency of the stimulated Raman modulation sidebands. This measurement was made via the shortcut path (Section 4.5) which skips the microscope platform and goes directly to the detector. The bandwidth of quantum-enhancement is & 50 MHz, suitable for high-speed imaging [4]. The phase-locked loop was turned off and the OPA pump light was blocked to obtain the shot-noise curve. To demonstrate quantum-enhanced performance we inject the squeezed Stokes laser into the SRS 5.2. SIGNAL-TO-NOISE ENHANCEMENT 67

Figure 5.2: Quantum enhanced stimulated Raman spectroscopy. (a) Spectrum of squeezed light detected in the range 1-55 MHz normalised to the shot-noise (snu: shot-noise units). The maximum squeezing is near the 20 MHz Raman modulation (vertical dashed line), of -1.06 dB (≈ 22%). RBW: 1 MHz, VBW: 10 Hz, Average: 35x. (b) Stimulated Raman signal of a 3 µm polystyrene bead with 3 mW of pump light at the sample, with squeezed light reducing the total measurement noise by -0.6 dB (≈ 13%) below shot-noise and thereby improving the SNR by 15%. RBW: 3 kHz, VBW: 10 Hz, average: 100x.

microscope while probing the CH aromatic stretch bond (3055 cm−1) of a 3 µm polystyrene bead. We then measure the power spectrum of the detected photo-current. A typical spectrum is shown in Figure 5.2b. The peak in the spectrum is the stimulated Raman signal. Once again, the phase-locked loop was turned off and the OPA pump light was blocked to obtain the shot-noise curve. The signal-to-noise ratio is defined as the ratio of the height of the stimulated Raman peak to the power spectrum noise-floor: (i) with the quantum-correlated light (SNRQuantum) and (ii) without the quantum-correlated light (SNRShot−noise). Losses of around 35% in transmission (through the microscope, pump filters, sample coverslips and polystyrene bead) degrade the quantum correlations (see Section 4.5). Nevertheless, the noise floor is still reduced by -0.6 dB (≈ 13%) at the frequency of the Raman peak, consistent with expectations given the additional loss. 68 CHAPTER 5. QUANTUM IMAGING 5.3 Overcoming photodamage limits with quantum light

In the last section (5.2), we defined the signal-to-noise ratio (SNR) with and without quantum-correlated light. Now we analyse the enhancement of the SNR for stimulated Raman microscopy beyond the constraint due to photodamage. The final result of this section, shown in Section 5.3.2, is a complex analysis from a long set of measurements, described and shown in Section 5.3.1.

5.3.1 Measuring the signal and the noise

In this set of measurements we track the Raman signal of one single particle, as shown in Figure 5.2b, increasing the power of the pump beam until evident damage is seen in the Raman signal (i.e. the signal increase ceases to be proportional to the power increase). Note that this damage threshold in the power is not the same for every particle as seen in Section 2.4.6. One example is shown in Figure 5.3. In this figure, the signal (in dBm) is collected through the detector on a spectrum analyser and plotted against the frequency, centred at the EOM modulation frequency fmod. The first panel on the top left shows the electronic noise (EN), with an electronic noise pickup of 1 dB (generated by the EOM, as seen in Section 4.6). The shot-noise (SN), or the Stokes light with neither squeezing nor SRS signal, is shown on the second panel in light blue and its average represented by the dashed cyan line. All the remaining panels of Figure 5.3 show the same shot-noise in light blue, the squeezed SRS signal in dark blue and a Gaussian fit for the latter represented by a dashed cyan line. For the flat-bottom region of the Gaussian fit a linear fit was made, shown here by the dotted cyan line. The linear fit was chosen instead of an average value for the squeezing, in order to extract the exact value of the squeezing at the same frequency of the SRS signal peak (as seen in Figure 5.2, the signal is on a slight slope). The pump power is indicated on the top left corner of each panel, and was taken with a power-meter before each measurement. The coloured numbers refer to the SNRShot−noise in light blue and SNRQuantum in cyan. To calculate the SNRShot−noise, the SRS peak was divided by the average of the shot-noise curve for each plot. Similarly for the SNRQuantum, the SRS peak was divided by the squeezing linear fit (dotted cyan line) at the same frequency as the peak.

5.3.2 Processing the signal-to-noise ratio

In this part we carry out the SNR analysis with the same data as Section 5.3.1, targeting one single particle. Extracting the peaks from Figure 5.3 up to 40 mW, we can see the trend of the signal-to-noise ratio. This trend is shown in Figure 5.4, where the SNRShot−noise is represented by the orange dots Shot−noise and fitted by the bottom dashed blue line, whereas SNRmax is the intersection of this fit with the maximum power that appears to induce no damage. Similarly, SNRQuantum is represented by the blue Quantum dots and fitted by the the top dashed blue line, whereas SNRmax is the intersection of this fit with the maximum power that appears to induce no damage. We find that the SNR initially increases quadratically with Raman pump power, as expected for stimulated Raman scattering [8] (see Section 2.4.2). However, the manifestation of photodamage 5.3. OVERCOMING PHOTODAMAGE LIMITS WITH QUANTUM LIGHT 69

95.5 84.0 EN 0mW (SN) 84.0 2mW 4mW 82 84.2 0.26 96.0

84.5 3.23 3.79 0.86 84.4 96.5 84 85.0 84.6 20.008 20.008 77.5 75 6mW 8mW 10mW 12mW 75 80.0 75 80 6.12 8.74 9.30 6.71 80 10.84 12.48 11.39 82.5 80 13.05

85.0 85 85 85 20.008 20.008 20.008 20.008 70 14mW 70 16mW 18mW 20mW 70 70 75 75 15.27 13.87 16.44 17.48 15.81 17.97 16.97 80 14.41 80 80 80

85 85

] 20.008 20.008 20.008 20.008 m B

d 22mW 24mW 26mW 28mW [

l 70 70 70 70 a n g i 18.23 18.88 19.50 19.83 18.73 19.35 20.29 20.01 S 80 80 80 80

20.008 20.008 20.008 20.008

30mW 35mW 40mW 45mW 70 70 70 70 18.49 21.14 20.24 21.39 18.98 21.62 20.70 21.86 80 80 80 80

20.008 20.008 20.008 20.008 60 50mW 60 55mW 60mW

70 70 70 23.11 24.76 21.49 23.59 25.30 21.96 80 80 80

20.008 20.008 20.008 Frequency [MHz]

Figure 5.3: Power scaling for squeezed SRS signal. Top left plot: electronic noise (EN). Second plot: shot-noise (SN) in light blue and its average in cyan dashed line. All remaining plots show shot-noise in light blue, squeezed SRS signal in dark blue with a Gaussian fit in dashed cyan line and a dotted line showing the minimum of the Gaussian fit. The values of SNRQuantum are given in cyan, SNRShot−noise in light blue, and the pump powers indicated in black on the top left corner of each plot. The errorbars are shown in cyan dotted lines, but are smaller than the thickness of the lines. RBW: 3 kHz, VBW: 10 Hz, average: 25x. 70 CHAPTER 5. QUANTUM IMAGING

Figure 5.4: Non damage-inducing quantum stimulated Raman spectroscopy. SNR for one 3 µm polystyrene particle with increasing pump power. The SNR increases quadratically as expected until 26 mW (green), indicating the particle is undamaged, then rises more slowly, suggestive of some disruption within the particle, and finally drops (red) when the power reaches the threshold for visible damage. Dashed lines are fits to the undamaged SNR, with the blue shading highlighting the increase in quantum enhanced SNR over the shot-noise limit. RBW: 3 kHz, VBW: 10 Hz, average: 25x.

prevents this scaling from continuing indefinitely. When using shot-noise limited light there is a Shot−noise strict maximum in damage-free SNR, which for the example of Figure 5.4 is SNRmax = 91 from a measurement with 3 kHz resolution bandwidth. Quantum correlations enhance the sensitivity, Quantum providing damage-free imaging up to SNRmax = 102, an 11% improvement. This proof of principle is not an attempt to improve by orders-of-magnitude the current state-of- the-art SRS microscopes. These results present the first realization of a quantum-enhanced Raman microscope that overcomes photodamage. As biological specimens are generally more sensitive to photodamage than polystyrene, and are affected by photochemical intrusion in a variety of ways at intensities lower than those that cause visible damage [26,75,78], the SNR enhancement observed in our work is directly relevant to biological imaging applications. 5.4. QUANTUM ENHANCED IMAGING 71 5.4 Quantum enhanced imaging

To demonstrate quantum-enhanced imaging, we record the power of the stimulated Raman signal as the microscope sample stage is raster-scanned over samples of both dry polystyrene beads and living Saccharomyces cerevisiae yeast cells in aqueous solution (see Section 2.3.4). Figure 5.5a shows a typical quantum-enhanced image of a collection of 3 µm polystyrene beads, with signal-to-noise ratio enhanced by -0.9 dB (≈ 19%) compared to the shot-noise limit (as explained in Section 4.7). This SNR was calculated over the whole background of the figure. Figure 5.5b shows the equivalent image for a single yeast cell, in this case recorded at a Raman −1 shift of 2841 cm to target the CH2 bonds that are most prevalent in lipids. Here, the microscope benefits fully from the water-immersion objectives with high numerical aperture, which demonstrated sub-micron spatial resolution (see inset, Figure 5.5b). Compared to the bright field microscope image in the inset of Figure 5.5b, the Raman image provides significantly more information about the interior structure of the cell. The cell membrane is visible by its faint outline, with a stronger signal possibly originating from the cell nucleus and a smaller signal generated from intracellular structures.

Figure 5.5: Quantum enhanced stimulated Raman microscopy. (a) Image of 3 µm polystyrene beads at a Raman shift of 3055 cm−1 obtained with 6 mW of pump power at the sample. The background (coloured green) has no Raman signal, and is limited by measurement noise which is 0.9 dB below the shot-noise, providing an ≈ 19% increase in SNR. (b) Image of a live yeast cell Saccharomyces cerevisiae in aqueous buffer at the Raman shift of 2845 cm−1. A region of intracellular cytosol produced no detectable Raman signal, and here we see noise 0.6 dB below the shot-noise, indicating that the SNR is increased by 13%. Top inset, cell image in bright-field microscopy. Bottom inset, zoom over the bottom region of the cell. The cell nucleus and membrane are resolvable while being less than a micron apart. Here, the pump power was set to 6 mW, a level that was generally found to be safe for polystyrene (see Figures 2.13(b) and (c)) and that did not cause visible damage to cells. For both (a) and (b), RBW: 1 kHz, VBW: 10 Hz, no average. Post-processing: Alex Terrasson.

In the yeast cell image, background Raman scattering is visible outside the cell which could originate from traces of organic material in the aqueous media. Sugar has a Raman signature in the range 2850–3050 cm−1 [79], and indeed the background signal was extinguished after we waited for one hour before starting the imaging, in which time the yeast cells had processed the added sugar (see Section 2.3.4). 72 CHAPTER 5. QUANTUM IMAGING

However, within the cell there are regions of cytosol1 in which no Raman scattering is measurable, such that the signal is limited by measurement noise. This allows us to confirm that within the cell the use of squeezed light reduces the noise floor by -0.6 dB (≈ 13%) below shot-noise, thereby improving image contrast. This is particularly useful in sub-cellular imaging since many features have far-sub-wavelength dimensions and produce a correspondingly small Raman signal. For instance, the cell membrane is typically 10 nm thick. In our measurements it generates a Raman signal that ranges in magnitude from 11% below the shot-noise floor to a factor of three above it. Indeed, approximately 11% of the visible membrane generated a signal beneath the shot-noise floor and therefore would not have been observable in a shot-noise limited measurement.

5.5 Chapter summary and conclusions

In this chapter we have seen the major achievement of my work. By merging two distinct techniques, Raman scattering microscopy and squeezing of light, we were able to demonstrate the feasibility of a quantum-enhanced microscope. We started by seeing how the experimental setup can be organised for this purpose. We have provided a quantitative measurement of the quantum enhancement obtained and used it to overcome the photodamage limit described in Section 2.4.6. Finally, we have demonstrated that quantum-enhanced imaging is indeed possible, and demonstrated for the first time that quantum-correlated illumination could allow microscopes to operate safely beyond the limits introduced by photodamage, achieving both sensitivity and contrast that would otherwise not be possible. We achieved -1.06 dB of noise-floor reduction using a system composed of a low-noise laser and a high-power and low-noise purpose-built photodetector. We also showed a -0.6 dB reduction when the system includes the noise coming from the sample and extra optics for the microscope system. This was enough to increase the signal-to-noise ratio by 13% to avoid photodamage and to image features that would be otherwise invisible. With this chapter, we conclude the project by demonstrating improvement of the signal-to-noise ratio below the shot-noise limit and using it to avoid photodamage to samples.

1The aqueous media of a cell’s cytoplasm. Chapter 6

Conclusions

This thesis describes the work performed to demonstrate, for the first time, a biologically-relevant squeezing-enhanced stimulated Raman scattering microscope. In the process of achieving this goal, we also showed that photodamage can be avoided with using quantum light. Imaging of both synthetic and biological samples were made, with quantum enhancements improving the signal-to-noise ratio of the images. These results, with increasing publications around the subject on the last few years, are part of milestones set on quantum technologies road-maps for both the United Kingdom and European Union. This interdisciplinary work has advanced both the field of biophysics and quantum physics, and opens a new door for exploring quantum improvements in microscopy.

6.1 Classic microscopy

Stimulated Raman scattering (SRS) microscopy has been recognised as a valuable technique to image biological samples without labelling interventions. In Chapter 2 I gave a detailed description of how the SRS microscope works, and the techniques involved in building a state-of-the-art microscope, which I built from the scratch. I explained how to use a SRS microscope to image samples of both polystyrene beads and yeast (Saccharomyces cerevisiae) cells. I have also shown that enhancements in the signal- to-noise ratio are limited due to photodamage in the sample. I characterised this photodamage and found a mean power of 54.6 mW for photodamage on polystyrene beads. The implications of this result are physical boundaries for enhancements on the performance of those nonlinear microscopes, which can be explored and changed with the utilisation of quantum techniques.

6.2 Quantum microscopy

From the motivations given in the previous section, we explored the quantum properties of the light with the view to enhancing the signal-to-noise ratio of imaging systems, in particular of the stimulated Raman scattering microscope. In Chapter 3 we have seen the description of light from a quantum mechanics perspective and introduced squeezed states of light. With these, we developed the theory 73 74 CHAPTER 6. CONCLUSIONS behind the quantum detection used throughout the thesis, mainly for describing the functional forms for the detected de-amplification and squeezing variance. They both decrease exponentially with the amplitude of the pump field from the squeezer, and are strongly limited by the overlap efficiency of the beams. The concepts established in Chapter 3 were fundamental for understanding the methods and techniques developed in Chapter 4. In Chapter 4 I have shown how we perform the quantum imaging system used in Chapter 5, and how it differs from the works on the literature. From a quantum- measurement compatible perspective, I have described and characterised the laser, the microscope and the purpose-built direct detector, which can take up to 4 mW of power without saturating. A balanced detector that can take up to at least 30 mW of power without saturation was also built for future experiments - I helped designing and creating both detectors in collaboration with Kai Barnscheidt and Boris Hage. I built and characterised the squeezer, and shown here how it works. The squeezer overlap visibility of both incoming beams was kept at around 92%. Having provided a detailed description of the transmission efficiencies of the experiment, I obtained a 93% efficiency for the transmission measurements of the squeezing-reference path, a 62% efficiency for the transmission through the microscope imaging system, and a detection quantum-efficiency of around 72%. These results were validated by the characterisation of the de-amplification and the squeezing variance. The average squeezing levels obtained for the 6 ps pulsed laser under those efficiencies was -1.15 dB of noise floor reduction, which provided sufficient enhancement to perform quantum-enhanced SRS microscopy. In Chapter 5 I presented my main result: the implementation of quantum-correlated photons, or squeezed states of the light, in a SRS microscope. I demonstrate for the first time that quantum- correlated light can allow microscopes to operate safely beyond the limits introduced by photodamage, achieving both sensitivity and contrast that would otherwise not be possible. We use the microscope to demonstrate imaging of molecular bonds within a living cell with quantum-enhanced contrast for the first time, and do this with sub-micron resolution. We achieve -0.6 dB of noise floor reduction for those images, which is an improvement of 13% on the signal-to-noise ratio, revealing features that would otherwise be fundamentally inaccessible. Though this improvement itself is not dramatic from a classical perspective, it is the first time it has been done, and thus provides a vital proof of principle, opening the door to the greater enhancements that quantum optics can provide for biophysics and medicine.

6.3 Outlook

From the day that our first piece of equipment was installed on the optical table, to the first results being taken, the unique setup took four years to build. As I write, further data and more precise images are being taken with the same setup, as we become more and more acquainted with refined techniques for imaging. As was discussed in Chapter 2, different ways of preparing samples makes a big difference for the imaging quality; one of several areas where further improvement is possible. Another improvement is the quality of the quantum-correlated light mode. The main inefficiencies 6.3. OUTLOOK 75 of the quantum-correlated light come from the microscope, so further improvements could be achieved by thoroughly scanning the mode shape of the beam and its power around the objectives and sample, so as to maximize the transmission of the beam. Another important development is in the classical optimization of SRS microscopes, which could be possible by changing the configuration of the conventional direct-detection system. Each of the microscope’s two beams, the Stokes and the pump, carries uncorrelated shot-noise, which costs a factor of 2 in signal-to-noise ratio. By setting a local oscillator beam (which has already been redirected from the Stokes beam after its delay line – see Appendix A) for a balanced homodyne detection with the use of the purpose-built balanced detector (discussed in Chapter 3), should provide a very good step that would be of significant relevance on its own. The main attribute for our microscope’s low-acquisition time, as discussed in Section 2.4.5, is the usage of the sample stages to perform the scan. Although very precise, those stages cannot move as fast as to compete with real-time imaging. Implementing a galvanometer scanner, which are mirrors fixed in rotary motors, could greatly increase the acquisition time of images. Another technique, that could be alternative or complementary to the one above, would be to design an algorithm to perform data compression. At first, the image could be divided in blocks and a quick scan through it all would pickup some features of the sample. Then the light can spend time proportionally on the blocks that have more information. By targeting only places that contains information, it should make the imaging faster than conventional procedures. In conclusion, this apparatus has only just been finished and therefore has a lot more to provide in the next years. A few implementations that it is ready to perform would be the demonstration of quantum-enhanced imaging in optogenetics, cellular structures, such as cell surface to study the membrane tension, action potentials, and other biological systems [80–82]. Performing multi-spectral imaging would provide more information in a single image, and should be easily accomplished without changes in the setup. Analysing signalling in neural networks should also be possible, and using zebra-fish in our quantum-enhanced microscope would potentially bring new information about how the brain works. We consider this project a major step forward, breaking a long-standing fundamental barrier in optical microscopy and providing a path to future advances. 76 CHAPTER 6. CONCLUSIONS Bibliography

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Detailed experimental setup

Figure A.1 shows the full optical table setup.

Figure A.1: Detailed experimental setup. Detector 1 was used for beam alignments, detector 2 for phase-lock, detector 3 to monitor the 20 MHz modulation, detector 4 for the daily spatial alignment of the pump and Stokes beam (mirror in B3 can be flipped for Stokes to be detected) and detector 5 is the purpose-built detector discussed in the main text and in Appendix C.

Regions [(C1-C3),(H1-H3)], [(L6),(L15)] and [(I16-I18),(L16-L18)] were used for another experi- ment that led to publication [21]. 83

Appendix B

Microscope objectives

Below I describe the two sets of objectives used during the thesis, followed by the blueprint of the high-transmission Leica objectives.

B.1 Nikon

CFI Plan Fluor, magnification 100x, oil immersion, numerical aperture: 1.3, working distance: 0.16 mm, physical depth of focus: 0.25 µm, actual field of view: 0.25 mm diameter, weight: 250 g, remarks: spring-loaded, with stopper, 70% transmission for 800 (x2 objectives = 50%), 65% transmission for 1064 (x2 objectives = 42%).

B.2 Leica Microsystems

HC PL APO, magnification 63x, water immersion, numerical aperture: 1.2, free working distance: 0.3 mm, parfocal distance: 45.06, focal length tube lens: 200 mm, weight: 200 g, 85 86 APPENDIX B. MICROSCOPE OBJECTIVES

1064 nm transmission: > 92% (x2 objectives = 84%). 800 nm transmission: ∼42% (estimated from measurement; x2 objectives ≈ 18%). B.2. LEICA MICROSYSTEMS 87

Figure B.1: High transmission objective blueprint. Fabrication and artwork: Leica Microsystems GMBH.

Appendix C

Detectors

The detector used is shown in Figure C.1 and its electronic circuit in Figure C.2. The characterisation of the balanced detector is shown in Figure C.3.

Figure C.1: Photo of the purpose-built single detector. The label C distinguishes this detector from the A-B homodyne detector and the D single detector which were also made for characterisation and comparison of the measurements. The knobs to the left are the AC output, which was used to send the signal for post-processing in the spectrum analyser, the DC output, which was used to send the signal for post-processing in the oscilloscope. The third knob is the input operational power.

89 90 APPENDIX C. DETECTORS

5

+5V 4.7µH

49,9 1k +5V 10p 49,9 1n 49,9 715 5k - -V - D ~250 + + 49,9 1k 1µH OPA690 68p LMH6624 V -Out -5V AC

20.5k 100p

-

+ OP27 49,9

VDC-Out

FigureThe green C.2: Part Electronic is used circuit to reduce of the detector the diode used. capacitance. The photodiode Ideally used both was aresistors IG17X250S4i, would serial be numberidentical Z5587. but the (Green current panel) for circuit the transistor used to reduce is limited the diode and capacitance. going far below Artwork: 1 k KaiΩ would Barnscheidt. de- stroy it. The other resistor essentially limits the current as the voltage drop lowers the bias voltage. For 10 m A the bias voltage would be lowered by 2.5 V. Usually this is used in our low power CW-detectors as only a few hundred µW are inci- dent. In case of your balanced didoes this circuit doesn’t exist. And for very high optical powers it is not suitable but it reduces the electronic dark noise a fair bit in the MHz frequency range.

The DC-Ouput Voltage per mW of optical is essentially given by the 50 Ω Resistor in the feedback loop. There will be ≈ 1 Ω extra due to the inductor (actually 468 mΩ is written in the data sheet of the inductor that I think should be in the detector) and a re- duction by the parallel 5 kΩ. The offset of -0.3V from the Transistor should be constant after the detector has warmed up. Measuring the slope of the Output voltage here depending on the input power should e yield good results for the quantum efficiency: ΔU = ΔP ⋅ Rλ ⋅ R = η ⋅ ΔP ⋅ R ⋅ . hv Usually a well calibrated optical power is the problem as for 1064nm usually a calibra- tion error of ±5% or more of the optical power meter is limiting. 91

Noise from home-made detector AB

28.8 mW 40 14.4 mW 7.2 mW 3.6 mW 50 1.8 mW 0.9 mW Electronic noise SA noise 60 Amplitude [dB]

70

0 20 40 60 80 100 Frequency [MHz]

20 MHz peaks 80 MHz peaks 0.8 6 A = 0.0P2 + 0.19P + 0.38 A = 0.001P2 + -0.01P + 0.07

0.6 4 0.4

Amplitue [a.u.] 2 0.2

0 0.0 0 10 20 30 0 10 20 30 Power [mW] Power [mW]

Figure C.3: Power scaling of Stokes light, with the spectrum analyser’s internal preamplifier on, for the purpose-built balanced detector with two diodes (Laser Components, IG17X250S4i).

Appendix D

The platform of the nonlinear crystal 5

4 3 2 1

PARTS LIST ITEM QTY PART NUMBER DESCRIPTION A 1 Pedestal Material: Aluminium G 1 Peltier Not part of project F 1 Crystal enclosure, bottom Material: Copper D D D 2 End cap Material: POM H 1 Crystal (1x2x7 mm) Not part of project E 1 Crystal enclosure ,top Material: Copper B 1 Bracket Material: POM C 2 End face Material: Aluminium B

E C C D D

F F

G

C

B B

C

A

DRAWN QQOL - Warwick P. Bowen Ulrich Hoff 27/01/16 CHECKED Contact: Ulrich Hoff, [email protected] / 0451 559 591 Exploded view of the squeezer with identification of all constituent parts. TITLE A QA A MFG Pulsed squeezer (assembly, exploded view)

APPROVED SIZE DWG NO REV C Pulsed squeezer SCALE SHEET 1 OF 1 4 3 2 1 Figure 1.1: Figure D.1: Platform for nonlinear crystal blueprint. Fabrication and artwork: Ulrich Hoff.

93

A lumine mota.