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Lateral Quantum Dots for Quantum Information Processing

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Lateral Quantum Dots for Quantum Information Processing University of California Los Angeles Lateral Quantum Dots for Quantum Information Processing A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Matthew Gregory House 2012 c Copyright by Matthew Gregory House 2012 Abstract of the Dissertation Lateral Quantum Dots for Quantum Information Processing by Matthew Gregory House Doctor of Philosophy in Physics University of California, Los Angeles, 2012 Professor Hong Wen Jiang, Chair The possibility of building a computer that takes advantage of the most subtle nature of quantum physics has been driving a lot of research in atomic and solid state physics for some time. It is still not clear what physical system or systems can be used for this purpose. One possibility that has been attracting significant attention from researchers is to use the spin state of an electron confined in a semiconductor quantum dot. The electron spin is magnetic in nature, so it naturally is well isolated from electrical fluctuations that can a loss of quantum coherence. It can also be manipulated electrically, by taking advantage of the exchange interaction. In this work we describe several experiments we have done to study the electron spin properties of lateral quantum dots. We have developed lateral quantum dot devices based on the silicon metal-oxide-semiconductor transistor, and studied the physics of electrons confined in these quantum dots. We measured the electron spin excited state lifetime, which was found to be as long as 30 ms at the lowest magnetic fields that we could measure. We fabricated and characterized a silicon double quantum dot. Using this double quantum dot design, we fabricated devices which combined a silicon double quantum dot with a superconducting microwave resonator. The microwave resonator was found to be sensitive to two-dimensional electrons in the transistor channel, which we measured and characterized. ii We developed a new method for extracting information from random telegraph signals, which are produced when we observe thermal fluctuations of electrons in quantum dots. The new statistical method, based on the hidden Markov model, allows us to detect spin-dependent effects in such fluctuations even though we are not able to directly observe the electron spin. We use this analysis technique on data from two experiments involving gallium arsenide quantum dots and use it to measure spin-dependent tunneling rates. Our results advance the understanding of electron spin physics in lateral quantum dots, in silicon and in gallium arsenide. iii The dissertation of Matthew Gregory House is approved. Kang Wang Karoly Holczer Stuart Brown Hong Wen Jiang, Committee Chair University of California, Los Angeles 2012 iv For my parents John and Susan v Table of Contents 1 Introduction :::::::::::::::::::::::::::::::::::::: 1 1.1 Background . 1 1.2 Quantum information processing . 4 1.3 Quantum dots . 7 1.4 Quantum dots as qubits . 8 1.4.1 Charge qubit . 8 1.4.2 Spin qubit . 9 1.4.3 Singlet-triplet qubit . 10 1.4.4 Valley qubit . 11 1.5 Silicon quantum dots . 11 1.6 Random telegraph signal analysis . 13 1.7 Dissertation outline . 14 2 Quantum dots in silicon MOSFET structures ::::::::::::::::: 15 2.1 Lateral quantum dots . 15 2.2 Silicon MOSFET quantum dot device design . 16 2.3 Silicon MOSFET quantum dot device fabrication . 18 2.3.1 Aluminum depletion gates . 22 2.4 Semiconductor physics relevant to quantum dots . 23 2.4.1 Physical parameters . 24 2.4.2 Nuclear spins . 25 2.4.3 Conduction band valley . 27 vi 2.4.4 Disorder . 28 2.5 Conclusion . 29 3 Characterization of a silicon MOSFET double quantum dot :::::::: 30 3.1 Introduction . 30 3.2 Device description . 31 3.3 Transport stability diagrams . 33 3.3.1 Two-gate Coulomb blockade diagram . 34 3.3.2 Coulomb diamond stability diagram . 34 3.3.3 Charge traps . 36 3.4 Charge sensing stability diagrams . 36 3.4.1 Charge sensing setup . 36 3.4.2 Honeycomb diagrams . 38 3.4.3 Few-electron regime . 39 3.5 Interpretation of double quantum dot stability diagrams . 40 3.5.1 Determining gate coupling strength . 40 3.5.2 Bias triangles . 43 3.6 Inter-dot transition tuning . 45 3.7 Long term stability . 45 3.8 Conclusions . 47 4 Measurement of the spin relaxation time of single electrons in a silicon MOS quantum dot ::::::::::::::::::::::::::::::::::: 49 4.1 Background . 49 4.2 Spin relaxation theory . 50 vii 4.3 Device description . 51 4.4 Experimental methods . 53 4.4.1 Pulse spectroscopy . 53 4.4.2 Excited state relaxation time measurement technique . 56 4.4.3 Rate equation model . 59 4.5 Discussion . 61 4.5.1 N = 1 $ N = 2 transition . 61 4.5.2 N = 0 $ N = 1 transition . 61 4.5.3 Comparison to similar experiments . 62 4.5.4 Conclusions . 63 5 Coupling a double quantum dot charge qubit to a microwave resonator 65 5.1 Background . 65 5.2 Introduction and motivation . 66 5.2.1 Cavity quantum electrodynamics . 66 5.2.2 Solid state CQED . 68 5.2.3 CQED theory . 70 5.3 Experimental details . 73 5.3.1 Experiment design . 73 5.3.2 Device layout . 76 5.3.3 Microwave electronics at UC Berkeley . 77 5.3.4 Microwave electronics at UCLA . 79 5.4 Resonator circuit models . 80 5.4.1 RLC model . 80 5.4.2 Transmission line model - quarter wave resonator . 81 viii 5.4.3 Capacitively coupled quarter wave resonator . 83 5.5 Experimental results . 85 5.5.1 Electrical detection of microwave signal . 85 5.5.2 Reflected microwave signal . 88 5.5.3 Modulated reflection amplitude measurements . 93 5.6 Conclusions . 98 5.6.1 Findings . 98 5.6.2 Outlook . 99 6 Data analysis for real-time observations of electron tunneling events :: 101 6.1 Introduction . 102 6.1.1 Analysis problem . 102 6.1.2 Random telegraph signals . 103 6.2 Hidden Markov models . 106 6.2.1 Background . 106 6.2.2 Discrete time HMM . 107 6.2.3 Continuous time HMM . 108 6.2.4 HMMs for two RTS models . 110 6.2.5 Likelihood function . 111 6.2.6 Model selection . 112 6.2.7 Confidence intervals for HMM-estimated parameters . 115 6.3 Example analysis . 116 6.4 Application to simulated data . 118 6.4.1 Various noise levels simulated . 119 6.4.2 Hidden state detection . 121 ix 6.5 Zhang, et al. experiment . 122 6.5.1 Experiment description . 122 6.5.2 HMM analysis . 123 6.5.3 Tests for additional states . 125 6.6 Li, et al. experiment . 126 6.6.1 Experiment description . 126 6.6.2 Tunnel rate physics . 128 6.6.3 Results at B=0 T . 129 6.6.4 Spin state detection . 131 6.6.5 Spin-dependence of tunnel rates . 134 6.6.6 Testing for other possible state configurations . 139 6.7 New directions in RTS analysis . ..
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