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 .