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A Fiber Cavity Perpendicular to a Linear Ion Trap

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A Fiber Cavity Perpendicular to a Linear Ion Trap Quantum interface − A fiber cavity perpendicular to a linear ion trap DISSERTATION zur Erlangung des Grades DOCTOR OF PHILOSOPHY an der Fakultät für Mathematik, Informatik und Physik der Leopold-Franzens-Universität Innsbruck vorgelegt von KLEMENS SCHÜPPERT durchgeführt am Institut für Experimentalphysik unter der Leitung von o. Univ.-Prof. Dr. Rainer Blatt und Univ.-Prof. Dr. Tracy E. Northup 2020 Kurzfassung Quantennetzwerken werden vielseitige Answendungsmöglichkeiten für Quantenmesstechnik, -kommunikation, -simulation und -computer zugesprochen. Solche Netzwerke bestehen aus Quantenknoten, die über Quantenkanäle und klassische Kanäle verbunden sind. Die dafür not- wendigen Schnittstellen sind grundlegende Bausteine dieser Quantennetzwerke und verbinden die stationären Qubits, die in Knoten lokalisiert sind, mit fliegenden Qubits, die sich durch Quantenkanäle bewegen. Gefangene Ionen in optischen Hohlraumresonatoren sind ein vielver- sprechender Ansatz für Quantenschnittstellen, da Ionen nachweislich eine effiziente Initialisie- rung, kohärente Manipulation und Auslesung von Quantenzuständen ermöglichen und weiters die Hohlraumresonatoren die stationären Ionen effizient mit fliegenden Photonen verbinden. Wir beabsichtigen ein Ionenfallen-System mit einem Faserhohlraumresonator senkrecht zur Achse einer linearen Paul-Falle zu verwenden, um mehrere Ionen stark mit dem Lichtfeld des Hohlraumresonators zu koppeln. Aufgrund ihres kleinen Modenvolumens ermöglichen mikro- fabrizierte Faserhohlraumresonatoren das Regime der starken Kopplung zu erreichen, wodurch eine Quantenkommunikation mit hoher Güte und gleichzeitig hoher Effizienz durchgeführt wer- den kann. Diese Arbeit berichtet über die Entwicklung unseren Ionen-Faserhohlraumresonator Sy- stems. Wir stellten Faserspiegel her, die für Längen von 400–500 µm des Hohlraumresonators optimiert sind. Eine dreidimensionale lineare Ionenfalle wurde entworfen, um darin solch einen Faserhohlraumresonator zu integrieren. Nach dem Aufbau und der Charakterisierung des Sy- stems koppelten wir erfolgreich ein gefangenes Ion mit dem Lichtfeld des Hohlraumresonators. Ladungen auf den Fasern hinderten uns jedoch daran, diese Kopplung weiter zu optimieren. Nach kurzer Zeit waren wir nicht mehr in der Lage Ionen im Hohlraumresonator zu speichern. Ladungen auf den Fasern stören das Fallenpotential und wenn die Fasern verschoben wer- den, ändern sich die Gleichgewichtsposition und die säkularen Bewegungsfrequenzen des Ions. Wir haben diese beiden Parameter für verschiedene Positionen der Fasern gemessen und diese Messungen mit Simulationen verglichen, bei denen unbekannte Ladungsdichten auf den Fa- sern einstellbare Parameter waren. Unter Verwendung eines Modells, das auf zwei homogenen Oberflächenladungsflächen pro Faser basiert, wurden Werte im Bereich von -10 bis +50 e=µm2 bestimmt. Da die Ladungen auf unseren Fasern uns zwangen, einen gewissen Abstand zwischen Fasern und Ionen zu verwenden, wollten wir die Ionen-Photonen-Kopplung für eine bestimmte Län- ge des Hohlraumresonators optimieren. Durch einen verbesserten CO2-Laser-Ablationsprozess konnten wir den Hohlraumresonator bestehend aus unseren Faserspiegeln dem konzentrischen Regime annähern. Messungen in diesem Regime zeigten eine dreimal höhere erwartete Koope- rativität im Vergleich zu einem Hohlraumresonator im konfokalen Regime, der in Experimenten nach dem Stand der Technik üblich wäre. Dies bedeutet, dass die Ionen-Photonen-Kopplung im Vergleich zum Atomzerfall und dem Zerfall des Lichtfeldes im Hohlraumresonators verbessert wurde. iii iv Abstract Quantum networks promise versatile resources for quantum sensing, communication, simulati- on and computation. They are made out of quantum nodes connected via quantum and classical channels. Interfaces between stationary qubits localized in nodes and flying qubits traveling through quantum channels are fundamental building blocks for such quantum networks. Trap- ped ions in optical cavities are a promising approach for quantum interfaces, as ions have pro- ven to provide efficient initialization, coherent manipulation, and readout of quantum states and cavities interconnect the stationary ions with flying photons efficiently. To strongly couple mul- tiple ions with the light field of the cavity, we intend to use an ion-trap system with a fiber cavity perpendicular to the axis of a linear Paul trap. Due to their small mode volume, micro-fabricated fiber cavities enable access to the strong coupling regime, allowing quantum communication to be carried out with high fidelity and efficiency at the same time. This thesis reports on the development of our ion-cavity system. We fabricated fiber mirrors optimized for cavity lengths of 400–500 µm. A three dimensional linear ion trap was designed to host such a fiber cavity. After building and characterizing the ion-cavity system, we successfully coupled a trapped ion with the cavity light field. However, charges on the fibers prevent us to improve this coupling. Later, we were no longer able to store ions inside the cavity. Charges on fibers distort the trapping potential, and when the fibers are displaced, the ion’s equilibrium position and secular motional frequencies are altered. We measured the latter quan- tities for different positions of the fibers and compared these measurements to simulations in which unknown charge densities on the fibers were adjustable parameters. Using a model based on two homogeneous surface charge areas per fiber, values ranging from -10 to +50 e=µm2 were determined. As charges on our fibers restrict us to use a sufficient clearance between fibers and ions, we wanted to optimize the ion-photon coupling for a chosen cavity length. Due to an improved CO2-laser ablation process, we are able to approach the concentric regime with our fiber mirrors. Measurements in this regime showed a three times higher expected cooperativity compared to a cavity in the confocal regime, which is common in state-of-the-art experiments. This means that the ion-photon coupling would be enhanced compared to the atom and cavity decays. Contents 1 Introduction 1 2 Quantum interfaces based on optical cavities and ions 5 2.1 40Ca+ ions as stationary qubits . .5 2.1.1 Basics of linear ion traps . .5 2.1.2 Ions as qubits . .7 2.1.3 Ion cooling . 10 2.2 Interaction between ions and photons inside cavities . 12 2.2.1 Simplified model of ion-photon coupling inside a cavity . 12 2.2.2 Extension to a three-level system . 13 2.2.3 Physical implementation . 14 2.3 Comparison of different experimental setups . 16 2.3.1 Overview of experiments . 16 2.3.2 Substrate cavities versus fiber cavities . 19 2.4 Outstanding challenges of trapped ions coupled to fiber cavities . 22 3 Technology of our fiber cavities 23 3.1 Calculation of desired cavity characteristics . 23 3.1.1 Cavity geometry parameters . 23 3.1.2 Cavity QED parameters for asymmetric cavities . 25 3.1.3 Realistic model for fiber cavities . 26 3.2 Fiber mirror production . 31 3.2.1 Fiber treatment before CO2-laser ablation . 32 3.2.2 CO2-laser ablation . 35 3.2.3 Highly reflective coating . 39 3.2.4 Preparing photonic-crystal fibers for vacuum . 44 3.3 Characterization of fiber mirrors . 47 3.3.1 Experimental setup and measurement method . 47 3.3.2 Hybrid fiber-substrate cavity measurements . 49 3.3.3 Fiber cavity with a tilted fiber . 50 3.3.4 Bend losses of PC fiber . 52 v vi Contents 4 Linear ion trap with a perpendicular fiber cavity 55 4.1 Design of the cavity-trap system . 55 4.1.1 Idea and motivation . 56 4.1.2 Previous design . 56 4.1.3 Blueprints of the cavity-trap system . 58 4.1.4 Expected challenges . 59 4.2 Trap simulations with fibers . 60 4.2.1 Simulation method . 60 4.2.2 Study of radial potentials with fibers . 61 4.3 Assembly of the system . 63 4.4 Ion trap characterization . 65 4.4.1 Micromotion compensation . 65 4.4.2 Secular frequency measurements . 65 4.4.3 Further ion-trap characterization . 68 4.5 Characterization of the fiber cavity in vacuum . 69 4.5.1 Measurements of the fiber cavity integrated with the ion setup . 69 4.5.2 Locking the fiber cavity . 72 4.5.3 Drift of “double resonance” . 74 4.6 Charge manipulation . 76 4.6.1 Charging method . 76 4.6.2 Experimental implementation . 76 4.6.3 Observations after charging . 77 5 Coupling an ion to the fiber cavity 79 5.1 Experimental configuration . 79 5.2 Results . 81 5.2.1 Limited count rate . 82 5.2.2 Ion-cavity localization . 83 5.2.3 Charges on the fibers . 84 6 Characterization of charges 85 6.1 Experimental setup . 85 6.2 Measurement of ion position and trap frequencies . 86 6.3 Simulations of ion position and secular frequencies . 88 6.4 Patch potential . 90 6.5 Determining surface charge distribution of our fibers . 93 6.5.1 Positively charged fiber . 93 6.5.2 Almost neutral fiber . 95 6.6 Discussion . 96 6.6.1 Limits of the method . 96 6.6.2 Temporal stability of charges . 97 6.6.3 Possible applications . 98 Contents vii 7 Fiber cavities in the concentric regime 99 7.1 Finesse measurement . 99 7.2 Optical FFT simulations . 101 7.3 Expected cooperativity . 102 7.4 Limitations in the concentric regime . 106 8 Summary and outlook 107 Appendices 111 A Experimental configurations 111 A.1 Annealing oven . 111 A.2 Cavity lock feedback . 113 B Publications 115 List of abbreviations 117 List of Figures 118 List of Tables 119 Bibliography 121 Chapter 1 Introduction Today, we live in a fast-developing world impelled by the digital age. Our social life is con- nected closer and closer to the virtual world via the Internet, smartphones, social media, smart homes, and smart cities. Our industry is evolving to fully computerized factories enabled by the Internet of Things, cloud computing and artificial intelligence, so that every part of a pro- duction plant is connected and digitalized. Our academic and applied research is supported by supercomputers, big data, and, broadly speaking, information technology. This entire digital revolution is based on billions of modern computers, each one consisting of billions of transis- tors. One could claim that the transistor is the fundamental building block of today’s social, economic, and scientific progress.
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