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Solid State Cavity Quantum Electrodynamics with Quantum Dots Coupled to Photonic Crystal Cavities

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Solid State Cavity Quantum Electrodynamics with Quantum Dots Coupled to Photonic Crystal Cavities SOLID STATE CAVITY QUANTUM ELECTRODYNAMICS WITH QUANTUM DOTS COUPLED TO PHOTONIC CRYSTAL CAVITIES 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 Arka Majumdar August 2012 c Copyright by Arka Majumdar 2012 All Rights Reserved 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. (Dr. Jelena Vuckovic) Principal 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. (Dr. David Miller) 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. (Dr. Hideo Mabuchi) Approved for the University Committee on Graduate Studies iii Acknowledgements Many people have made my five years as a graduate student fun and productive. First, I would like to thank my advisor, Professor Jelena Vuckovic, for her guidance and support. I also want to thank her for giving me so many opportunities to grow as an academic, sending me to conferences early and often, and giving me responsibili- ties with equipment purchases, teaching assistantships, mentoring new students etc. When I joined Stanford, I did not have much knowledge on quantum mechanics, and my background was mostly on RF electronics. I will always be thankful to Jelena for giving me an opportunity to work on a very different field than my expertise. I would also like to thank my co-advisor Professor David Miller, who was always available for any question I have. I would like to thank Professor Hideo Mabuchi for agreeing to be on my thesis reading committee. I learnt all the quantum optics from his lectures, as well as discussion with him outside the class-room. Finally I would like to thank Professor Mark Brongersma for agreeing to chair my thesis committee. My first ex- posure to nanophotonics came from the class I took from him and Professor Shanhui Fan. I have had great luck to work with some very talented and motivated people on experiments. In my early days of graduate school, I had the opportunity to work with Dr. Dirk Englund, Dr. Andrei Faraon and Dr. Ilya Fushman, three incredibly talented people. I learnt all the experimental techniques from them. I would also like to acknowledge all of my friends and colleagues in the Vuckovic group: Michal Bajcsy, Erik Kim, Armand Rundquist, Gary Shambat, Kelley Rivoire, Sonia Buckley, Jesse Lu, Jan Petykiewicz, Bryan Ellis, Maria Makarova, Mitsuru Toishi, Yiyang Gong, Alexander Papageorge and Ziliang Lin. In particular, I want to thank my close collaborators on the quantum dot project, Michal Bajcsy, Erik Kim and Armand Rundquist its been really great working and hanging out with these guys. I would also like to thank Krishna Balram, Peter McMohan and Kristiaan De Greeve, who helped me whenever I had questions about fabrications or optical setups. I want to thank the people of the Stanford Nanofabrication Facility. In particu- lar, I want to thank James Conway who trained me on the electron beam lithography iv system and whose deep knowledge of nanofabrication and maintenance of the equip- ment are remarkable. I also would like to Thank Tom Carver in Ginzton Microfab (now Stanford nano-characterization center) for helping me with metallization, and figuring out several recipes for electrical control. I would like to thank my parents for motivating me to pursue graduate school. I would also like to thank my wife Godhuli, for supporting me throughout the graduate school. Finally, I would like to thank the Almighty God. v Abstract Quantum dots (QDs) coupled to optical cavities constitute a scalable, robust, on-chip, semiconductor platform for probing fundamental cavity quantum electrodynamics. Very strong interaction between light and matter can be achieved in this system as a result of the field localization inside sub-cubic wavelength volumes leading to vacuum Rabi frequencies in the range of 10s of GHz. Such strong light-matter interaction pro- duces an optical nonlinearity that is present even at single-photon level and is tunable at a very fast time-scale. This enables one to go beyond fundamental cavity quantum electrodynamics (CQED) studies and to employ such effects for building practical in- formation processing devices. My PhD work has focused on both fundamental physics of the coupled QD-nanocavity system, as well as on several proof-of-principle devices for low-power optical information processing based on this platform. We have demonstrated the effects of photon blockade and photon-induced tun- neling, which confirm the quantum nature of the coupled dot-cavity system. Using these effects and the photon correlation measurements of light transmitted through the dot-cavity system, we identify the first and second order energy manifolds of the Jaynes-Cummings ladder describing the strong coupling between the quantum dot and the cavity field, and propose a new way to generate multi-Fock states with high purity. In addition, the interaction of the quantum dot with its semiconductor envi- ronment gives rise to novel phenomena unique to a solid state cavity QED system, namely phonon-mediated off-resonant dot-cavity coupling. We have employed this ef- fect to perform cavity-assisted resonant quantum dot spectroscopy, which allows us to resolve frequency features far below the limit of a conventional spectrometer. Finally, the applications of such a coupled dot-cavity system in optical information processing including ultrafast, low power all-optical switching and electro-optic modulation are explored. With the light-matter interactions controlled at the most fundamental level, the nano-photonic devices we implemented on this platform operate at extremely low control powers and could achieve switching speeds potentially exceeding 10 GHz. vi Contents 1 Introduction 1 1.1 Long distance quantum communication . 1 1.2 Optical interconnects . 3 1.3 Quantum dots and photonic crystal cavities . 4 1.4 Cavity quantum electrodynamics . 7 1.5 Outline of the thesis . 10 2 Theoretical study of the quantum dot-cavity QED system 12 2.1 Hamiltonian dynamics . 12 2.2 Master equation for lossy dynamics . 14 2.2.1 Quantum and semiclassical description . 15 2.3 Quantum trajectory . 16 2.4 Strong coupling . 17 2.5 Temporal dynamics of dot-cavity system . 18 2.5.1 Semiclassical equation of motion . 19 2.5.2 Dependence on the system parameters . 22 2.6 All-optical switching with quantum dot-cavity QED system . 24 2.6.1 Static response . 25 2.6.2 Dynamic response . 28 2.7 Theory of electro-optic modulation . 33 2.7.1 Frequency response . 36 2.7.2 Nonlinear distortion of signal . 38 2.7.3 Step response . 40 vii 2.7.4 Effect of dephasing on performance of the single QD modulator 44 3 Temporal dynamics and all optical switching with QD-CQED sys- tem: Experiment 45 3.1 Temporal Rabi Oscillation . 45 3.2 All-optical switch . 49 4 Fast electrical control of a single quantum dot-cavity system 57 4.1 Electro-optic modulation: lateral electrical control . 57 4.1.1 Switching power . 66 4.2 Vertical electrical control . 67 5 Photon blockade and photon assisted tunneling 70 5.1 Photon blockade . 71 5.1.1 Photon blockade in pulsed operation of the driving field . 71 5.1.2 Non-classical state generation via fast control of dipole frequency 77 5.2 Multi-Fock state generation . 81 5.2.1 Numerical simulation . 83 5.2.2 Experimental result . 87 5.2.3 Effect of dephasing on blockade and tunneling . 92 5.3 Sub-Poissonian light generation with a bimodal cavity . 92 5.3.1 Theory . 96 5.3.2 Proposed experiment and preliminary experimental data . 104 6 Cavity QED with a Single Quantum Dot in a Photonic Molecule 110 6.1 Introduction . 110 6.2 Theory . 111 6.3 Characterization of photonic molecule . 113 6.4 Strong coupling between a single QD and a photonic molecule . 113 6.5 Comparison with bimodal cavity . 118 viii 7 Phonon-mediated off-resonant interaction in a quantum dot-cavity system 120 7.1 Theory . 121 7.1.1 Theory with pure QD dephasing . 122 7.1.2 Theory with cavity enhanced phonon process . 123 7.1.3 Simulation results . 128 7.1.4 Experimental data . 133 7.2 Single photon source . 135 7.3 Resonant QD spectroscopy . 139 7.3.1 Probing exciton and biexciton . 139 7.3.2 Emission saturation and linewidth broadening . 142 7.3.3 QD dressing observed via off-resonant cavity . 150 7.4 Time resolved study of the off-resonant cavity emission . 165 7.5 Phonon assisted inter-dot coupling . 168 7.5.1 Theory . 168 7.5.2 Coupling between two quantum dots . 171 8 Spectral diffusion and its effect on CQED 179 8.1 Theory: QD linewidth broadening . 181 8.2 QD charging and modulation . 182 8.3 QD linewidth broadening . 186 9 Outlook 193 9.1 Coupled cavity array for quantum many body simulation . 193 9.2 Coherent control of phonons . 195 9.3 Spin-photon interface . 196 Bibliography 198 ix List of Tables 7.1 Details of the QD-cavity systems employed in the first experiment, when the cavity emission is observed by resonantly exciting the QD. Also shown are the fits for two different contributions to the QD linewidth, ∆!c and ∆!0, and the theoretical estimate for ∆!c (see Eq.
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