DOCSLIB.ORG

Generation of Pulsed Quantum Light

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Generation of Pulsed Quantum Light GENERATION OF PULSED QUANTUM LIGHT A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Kevin Fischer August 2018 © 2018 by Kevin Andrew Fischer. All Rights Reserved. Re-distributed by Stanford University under license with the author. This dissertation is online at: http://purl.stanford.edu/xd125bf7704 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Jelena Vuckovic, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Shanhui Fan I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. David Miller Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract At the nanoscale, light can be made to strongly interact with matter, where quantum mechanical effects govern its behavior and the concept of a photon emerges|the branch of physics describing these phenomena is called quantum optics. Throughout the history of quantum optics, experiments and theory focused primarily on understanding the internal dynamics of the matter when interacting with the light field. For instance, in an ion trap quantum computer the motional states of the ions are of interest while the state of the light field is secondary. However, a new paradigm for information processing is becoming experimentally accessible where many quantum-optical devices are integrated in nanophotonic circuits. Then, the relevant information is encoded in the quantum states of the photon wavepackets as they fly around the nanophotonic chip. Hence, the converse problem is now important: the way the state of the photon field changes after interacting with the piece of matter. The effect of an individual device on a photon can now be formally described in a so-called scattering experiment. First, a photon wavepacket is prepared far away from the device. It travels freely towards the device and as it hits the interaction region forms a strongly entangled state of light and matter. Afterwards, the character of the interaction is imprinted on the outgoing wavepacket. This concept of a scattering experiment was originally envisioned in high-energy field theories with static Hamiltonians, and this thesis shows the concept adapted to nanophotonic devices driven by pulses of laser light (corresponding to time-dependent or energy nonconserving Hamiltonians). The formalism developed here will thus be of relevance to design and analysis of quantum information processing systems in which the information is encoded in the state of the photonic field, with the piece of matter implementing either a source of photons or implementing a unitary operation on the photonic state. In summary, for this dissertation I show experiments and theory that fully describe how the quantum state of a laser pulse changes when interacting with nano-sized pieces of matter. In partic- ular, this work covers both a general formalism for photon scattering as well as two standard physical iv systems as experimental examples that generate quantum light: the quantum two-level system and the Jaynes{Cummings system. v Acknowledgments I would like to dedicate this dissertation to my wonderful wife, Irena Fischer-Hwang. The PhD can sometimes seem surmountable, but with Irena as a partner in my life, I was able to face all its challenges. She constantly challenged me to be better and helped ground my life|without her none of this work would have been possible. Of course, no PhD is possible without a supportive adviser and colleagues. Prof. Jelena Vuˇckovi´c easily provided one of the best scientific environments to learn and grow, that any student could have possibly hoped for. I believe one of Jelena's most important qualities is the trust that she places in her students, providing critical guidance and direction but allowing us the proper space to learn and occasionally fail. In particular, I am grateful that Jelena sent me to conferences early and often, and even to give invited talks in her stead. She placed the trust in me that I could manage and handle some of the most complicated and expensive modifications to our lab. Most importantly, she trusted me with academic freedom to pursue the topics that were most interesting to me, helping to provide the context in framing their discussions. When finding my initial project, Dr. Kai M¨ullerserved as a secondary research advisor, with whom I have built one of the most successful working relationships in my career. Our collaboration began during our time at Stanford, but has lasted many impactful projects and publications into his time as a group leader at the Technical University of Munich. Kai is particularly calming in his ability to provide unbiased guidance for any difficult circumstance, technical or otherwise. In my overview in Ch. 1, I will acknowledge the very productive working relationships I have had with colleagues in the Vuckovic group, but in particular I'd like to mention Rahul Trivedi. Rahul constantly challenged me technically and would never take hand waving for granted. Working with Rahul closely on the photon scattering theory, I felt that my knowledge grew exponentially every day. Towards the end of my PhD career, I am grateful to the guidance of Tina Seelig and Fern vi Mandelbaum, as well as my Accel Innovation Scholars cohort. They have all helped provide a critical piece of my education, and helped me to effectively translate my skills onto life after the PhD. vii Contents Abstract iv Acknowledgments vi 1 Introduction 1 1.1 Cavity QED with a single quantum emitter . .3 1.2 Strong coupling with quantum dots . .3 1.3 The Jaynes{Cummings model . .4 1.4 Observing strong coupling . .5 1.5 Basics of nonclassical light generation . 10 1.6 Overview . 11 2 Second-order quantum coherence 15 2.1 Hanbury{Brown and Twiss interferometer . 17 2.2 Connection to correlations of instantaneous fields . 21 2.3 Time-dependent quantum regression theorem . 23 3 Coherent drive in the Jaynes{Cummings system 25 3.1 Heisenberg picture . 27 3.2 Addition of coherent state drive . 29 3.3 Analytic analysis of homodyne interference . 31 3.4 Visualizing the homodyning in transmission spectra . 33 4 Cavity QED beyond the Jaynes{Cummings model 35 4.1 Dissipative structure . 36 4.2 Emitter-cavity detuning . 39 viii 4.3 Excitation pulse length . 42 4.4 Electron-phonon interaction . 44 4.5 Blinking of the quantum emitter . 47 4.5.1 Effects of blinking on transmission spectra . 48 4.5.2 Effects of blinking on nonclassical light generation . 50 4.6 Self-homodyne interference . 52 4.6.1 Effects of self-homodyne interference on emission spectra . 54 4.6.2 Effects of self-homodyne interference on nonclassical light generation . 56 4.7 Rabi oscillations on a cavity QED polariton . 60 5 Photon scattering formalism 61 5.1 Problem definition . 63 5.1.1 System Hamiltonian . 63 5.1.2 Bath Hamiltonian . 64 5.1.3 Waveguide-system coupling . 67 5.1.4 Interaction-picture Hamiltonian . 69 5.1.5 Scattering matrices . 70 5.2 Formalism . 71 5.2.1 Coarse-graining of time . 72 5.2.2 A general solution . 74 5.2.3 Extension to multiple output waveguides . 75 5.2.4 Connection to quantum trajectories and measurement theory . 77 6 Photon emission from a two-level system 79 6.1 Traditional theory of a single-photon source . 81 6.2 General theory of photon emission . 82 6.3 Short pulse regime . 86 6.3.1 Theory . 86 6.3.2 Experiment . 93 7 Conclusions and outlook 98 7.1 Homodyne interference . 98 7.2 Single-emitter cavity QED . 99 7.3 Photon scattering . 100 ix 7.4 Quantum two-level system . 100 7.5 Re-excitation in single-photon sources . 102 7.6 Indistinguishability . 102 x List of Tables 6.1 Counting statistics for a driven quantum two-level system . 91 xi List of Figures 1.1 AFM image of self-assembled InGaAs quantum dots . .2 1.2 Emission spectra from quantum dots . .2 1.3 Schematic of a strongly-coupled system based on a quantum dot embedded within a photonic crystal cavity . .4 1.4 Observation of strong coupling in either transmission or spontaneous emission spectra6 1.5 Cross-polarized reflectivity for observing strong coupling experimentally . .9 1.6 Principle of photon blockade and photon tunneling . 11 2.1 Schematic of the Hanbury{Brown and Twiss interferometer . 18 2.2 Hanbury{Brown and Twiss histogram of pulsed single-photon emission . 20 3.1 Input-output schematic of a Jaynes{Cummings system . 25 3.2 Difference between atom and cavity drive in the Jaynes{Cummings system . 26 3.3 Schematic of the Jaynes{Cummings system with homodyned output field . 31 3.4 Schematic of a Jaynes{Cummings drop filter . 33 3.5 Theoretical transmission spectra through a Jaynes{Cummings drop filter . 34 4.1 Climbing the Jaynes{Cummings ladder with dissipation . 38 4.2 Detuned photon blockade, experiment and theory . 41 4.3 Pulse-length dependence of photon blockade, experiment and theory . 43 4.4 Experimental effects of electron-phonon interaction on polariton lifetimes .
Load more

Recommended publications
  • Symposium of the Dodd-Walls Centre for Quantum Science and Technology
    Symposium of The Dodd-Walls Centre for Quantum Science and Technology 9-11 December 2008, Queenstown, New Zealand Monday, December 8 Welcome reception (6:00pm–7:00pm, Ben Lomond Restaurant) Cocktail hour and Cash bar Tuesday, December 9 Conference sign-in (8:00am-8:30am, Foyer) 8:30am–10:30am Ultra-cold atoms (Queenstown room) Prof. Crispin Gardiner, Presider 8:30am Opening remarks 8:45am TuA1 — From thermal to quasi-condensate to superfluid: Observation of a 2D Bose-gas Keynote Kristian Helmerson, Pierre Cladé, Changhyun Ryu, Anand Ramanathan, and William D. Phillips. Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8424, USA. We present evidence of the crossover to a superfluid state in an optically trapped, 2D, atomic Bose gas. In addition, we observe an intermediate, quasi-condensate state between the thermal and superfluid state. 9:30am TuA2 — Bragg spectroscopy of a strongly interacting Fermi gas Invited G. Veeravalli, E. Kuhnle, P. Dyke, and C. J. Vale. ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, 3122, Australia. The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic 6Li is stud- ied using Bragg spectroscopy. A smooth transition from molecular to atomic behaviour is observed and pair correlations are characterised. 10:00am TuA3 — General atom-optical quantum resonances Invited Simon A. Gardiner, K. J. Challis, T. P. Billam, P. L. Halkyard, and M. Saunders. Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom. Quantum resonances are an example of a dramatically quantum effect, and can manifest in a variety of differ- ent ways.
    [Show full text]
  • Thermal Noise in Electro-Optic Devices at Cryogenic Temperatures
    Thermal Noise in Electro-Optic Devices at Cryogenic Temperatures Sonia Mobassem1;2, Nicholas J. Lambert1;2, Alfredo Rueda1;2;3, Johannes M. Fink3, Gerd Leuchs1;2;4;5, and Harald G. L. Schwefel1;2 1The Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand 2Department of Physics, University of Otago, New Zealand 3Institute of Science and Technology Austria, Klosterneuburg, Austria 4Max Planck Institute for the Science of Light, Erlangen, Germany 5Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia E-mail: [email protected] 21 August 2020 Abstract. The quantum bits (qubit) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion.
    [Show full text]
  • Hite (DVC Research)
    2nd Annual Dodd-Walls Symposium Dunedin 2008 Programme Monday 11th February 8.15-8.45: Conference hall available for putting up posters Session 1: Chair: John Harvey 8.45-9.00: Formal opening by Geoff White (DVC Research) 9.00-9.30: Crispin Gardiner: The Dodd Walls Centre: Vision and Strategy 9.30-10.00 Allister Ferguson: Optically pumped semiconductor disk lasers 10.00-10.20 Scott Parkins: Cavity QED with Microtoroidal Resonators. 10.20-10.40 Ashton Bradley: Spontaneous vortex formation in Bose-Einstein condensation 10:40 – 11.00 Morning tea Session 2: 11.00-12.00 Posters 12.00 – 1.00 Lunch Session 3: Chair: Crispin Gardiner 1.00-1.30 Hans Bachor: News from ACQAO: Entangling photons and Atoms 1.30-1.50 Cather Simpson: Diphosphenes. A new photonic switch? 1.50-2.10 Jevon Longdell Cavity QED with rare earths: what can you do with a weak oscillator 2.10-2.30 Lars Madsen Torsional control using laser induced alignment 2.30-2.50 Mikkel Anderson: An Atomic Interferometer 2.50 – 3.20 Afternoon tea 3.30 – 7.00 Excursion followed by Symposium Dinner (7pm, Etruscos). Tuesday 12th February Session 4: Chair: Andrew Wilson 8.30-9.00 Robert Clark: Current status and future prospects for QIP in Si:P MOS architectures incorporating single atom spintronics 9.00-9.20 Howard Carmichael: Quantum Optics in Auckland: Theory for Lasers, Atoms and Ions 9.20-9.40 Rainer Leonhardt: New lens design for Thz imaging 9.40-10.00 Stuart Murdoch: Fiber parametric oscillators and amplifiers 10.00 – 10.30 Morning tea Session 5: Chair: Howard Carmichael 10.30-11.00 Andrew
    [Show full text]
  • Symposium of the Dodd-Walls Centre for Quantum Science and Technology
    Symposium of The Dodd-Walls Centre for Quantum Science and Technology 9-11 December 2008, Queenstown, New Zealand Tuesday, December 9 8:15am–10:00am Ultra-cold atoms TBA, Presider 8:15am TuA1 — From thermal to quasi-condensate to superfluid: Observation of a 2D Bose-gas Keynote Kristian Helmerson, Pierre Cladé, Changhyun Ryu, Anand Ramanathan, and William D. Phillips. Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8424, USA. We present evidence of the crossover to a superfluid state in an optically trapped, 2D, atomic Bose gas. In addition, we observe an intermediate, quasi-condensate state between the thermal and superfluid state. 9:00am TuA2 — Bragg spectroscopy of a strongly interacting Fermi gas Invited G. Veeravalli, E. Kuhnle, P. Dyke, and C. J. Vale. ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, 3122, Australia. The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic 6Li is studied using Bragg spectroscopy. A smooth transition from molecular to atomic behaviour is observed and pair correlations are char- acterised. 9:30am TuA3 — General atom-optical quantum resonances Invited S. A. Gardiner, K. J. Challis, T. P. Billam, P. L. Halkyard, and M. Saunders. Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom. Quantum resonances are an example of a dramatically quantum effect, and can manifest in a variety of different ways. I will cover recent theoretical progress with a particular view to possible experimental implementations in an atom-optical context. Morning Tea (10:00am–10:30pm) 10:30am–12:10pm Ultra-cold atoms TBA, Presider 10:30am TuB1 — Birth of a superfluid: vortices and solitons in the formation of Bose-Einstein Invited condensates Matthew J.
    [Show full text]
  • Theory of Microwave-Optical Conversion Using Rare-Earth Ion Dopants
    Theory of Microwave-Optical Conversion Using Rare-Earth Ion Dopants Peter S. Barnett and Jevon J. Longdell∗ Dodd-Walls Centre for Photonic and Quantum Technologies and the Department of Physics, University of Otago, Dunedin, New Zealand We develop a theoretical description of a device for coherent conversion of microwave to optical photons. For the device, dopant ions in a crystal are used as three-level systems, and interact with the fields inside overlapping microwave and optical cavities. We develop a model for the cavity fields interacting with an ensemble of ions, and model the ions using an open quantum systems approach, while accounting for the effect of inhomogeneous broadening. Numerical methods are developed to allow us to accurately simulate the device. We also further develop a simplified model, applicable in the case of small cavity fields which is relevant to quantum information applications. This simplified model is used to predict the maximum conversion efficiency of the device. We investigate the effect of various parameters, and predict that conversion efficiency of above 80% should be possible with currently existing experimental setups inside a dilution refrigerator. I. INTRODUCTION rare-earth ions, which are used as three level systems. This scheme was originally proposed in [13], and has Superconducting qubits are one of the main qubit de- been investigated theoretically and experimentally in signs for quantum computation, and have two states [14]. Similar proposals for conversion using crystals which are separated by a microwave frequency. This al- doped with three level systems have also been made lows them to be easily coupled and controlled with mi- [15, 16].
    [Show full text]
  • Rescue the Gardiner Book!
    ARTICLE IN PRESS Journal of Mathematical Psychology 50 (2006) 431–435 www.elsevier.com/locate/jmp Book review Rescue the Gardiner book! Crispin Gardiner, Physics Department, University of Otago, Dunedin, NEW ZEALAND ISBN 3-540-20882-8, 2004 (xvii+415pp., $84.82). Reviewed by Raoul P.P.P. Grasman, Eric-Jan Wagenmakers decision model (Diederich, 1997). Smith (2000) provides The book author, professor Crispin Gardiner, is currently an extensive introduction into the subject. honorary fellow at the physics department of Victoria University The book provides a detailed and systematic development of Wellington, New Zealand. He received his Ph.D. from Oxford University, England, and has since been working at various of techniques of mathematical analysis of stochastic institutes, including the University of Waikato, Hamilton, New processes, bringing together a wide range of exact, Zealand. Over the years, he has made many contributions to the approximate, and numerical methods for solving SDEs. study of Bose–Einstein condensation, quantum optics, and Compared to other volumes on stochastic processes and stochastic methods in physics and chemistry. His website can be SDEs (e.g. Arnold, 2003; Doob, 1953; Feller, 1971; found at http://www.physics.otago.ac.nz/people/ Klebaner, 1998; Øksendal, 2000), the book is written in a gardiner/index.html. informal, narrative and nonmathematical style. Neverthe- The reviewers, Raoul Grasman and Eric-Jan Wagenmakers, less, the book is not written for the mathematically timid. both received their Ph.D. at the University of Amsterdam. Their The first five chapters are certainly accessible for common research interests include sequential sampling models for advanced undergraduates of physics and mathematics.
    [Show full text]
  • Dynamics of Bose-Einstein Condensation
    DYNAMICS OF BOSE-EINSTEIN CONDENSATION MATTHEW JOHN DAVIS A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Oxford St John's College University of Oxford Hilary Term 2001 Dynamics of Bose-Einstein Condensation Matthew John Davis, St John's College. Thesis submitted for the degree of Doctor of Philosophy at the University of Oxford, Hilary Term 2001. Abstract This thesis is concerned with the dynamics of thermal Bose-Einstein conden- sates with two main areas of emphasis. We summarise the development of the quantum kinetic theory of C. W. Gar- diner, P. Zoller, and co-workers, and in particular its application to the problem of condensate growth. We extend an earlier model of the growth of a Bose-Einstein condensate to include the full dynamical effects of the thermal cloud by numerically solving a modified quantum Boltzmann equation. We find that the results can be easily interpreted by introducing an effective chemical potential for the thermal cloud. Our new results are compared with the earlier model and with the available experimental data. We find that in certain circumstances there is still a discrepancy between theory and experiment. Beginning with the second-quantised many-body Hamiltonian we develop an approximate formalism for calculating the dynamics of a partially condensed Bose gas. We divide the Hilbert space into a highly-occupied coherent region described by a Gross-Pitaevskii equation, and an incoherent region described by a kinetic equation. We discuss the interpretation of the terms in the equations, and their relevance to recent experiments in the field.
    [Show full text]