Circuit Quantum Electrodynamics - Yale School of Engineering ...

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List of Symbols and Abbreviations 17 (κ) Decay rate of photon out of the cavity (κγ) Decay of photons by decaying through the atom via non-radiative means � � κin/out Photon decay rate due to the input/output coupling (λL) The London penetration depth, describing the depth within which currents flow (µr) Relative magnetic permeability (σ ± ) Qubit excitation creation and annihilation operators (σx,y,z) Pauli matrices for a spin 1/2 particle used to measure x,y,z components of qubit (σn) Conductivity of the normal fluid (τn) Scattering time of the normal fluid (Drude model), which is a measure of the real part of the conductivity (χ) Cavity shift or Stark shift per photon, χ = g 2 /∆ for a two level atom (χij) Dispersive shift between cavity and qubit levels i and j (χeff) Effective dispersive shift due to interactions of all qubit levels with the cavity (ωa) Ground-excited state transition (angular) frequency (ωr) Cavity resonance (angular) frequency (ωs) Spectroscopy (angular) frequency
Chapter 1 Introduction Progress in science is often a result of exchanging principles and techniques between seemingly disparate disciplines. Often this interaction leads both fields in new directions. The subject of this dissertation, “circuit quantum electrodynamics” is an excellent example of such cross-pollination. In this work, techniques imported from atomic cavity quantum electrodynamics (QED), a field developed to study the quantum interaction of light and matter, are applied to superconducting circuits to realize the building blocks of a quantum computer. Amazingly, some circuits, though containing billions of atoms, can be accurately described as a single atom. Leveraging techniques from atomic physics, this metaphor is exploited to enhance the circuits’ fidelity and develop new ways of coupling them together. While circuits can behave much like “artificial” atoms, their properties are quite supernatural, allowing circuit QED to explore new regimes of cavity QED that are difficult to reach with ordinary atoms. The introduction will first discuss quantum computation, its importance, and the challenges associated with its realization. Next, some “simple” questions that arise in a quantum theory of light lead to a brief discussion of beautiful experiments in cavity QED. Finally, these ideas are brought together to describe an architecture for quantum computing employing a superconducting circuit version of cavity QED. 1.1 Quantum Computation Information is inherently a physical quantity, and the physics of information is the physics of all matter [Landauer1991]. The concept of the computer was developed in part as a concrete means to answer fundamental questions about information, such as “What questions can and cannot be answered?” The idea of a quantum computer arose out of studying the thermodynamics of compu- 18
Page 1 and 2: Abstract Circuit Quantum Electrodyn
Page 3 and 4: c○2007 by David Schuster. All rig
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Page 7 and 8: CONTENTS 4 3.2.3 Split CPB . . . .
Page 9 and 10: CONTENTS 6 8.2.1 AC Stark Effect .
Page 11 and 12: List of Figures 1.1 Relaxation and
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CHAPTER 3. CAVITY QED WITH SUPERCON
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Chapter 4 Decoherence in the Cooper
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CHAPTER 4. DECOHERENCE IN THE COOPE
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CHAPTER 5. DESIGN AND FABRICATION 1
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CHAPTER 6. MEASUREMENT SETUP 142 ω
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CHAPTER 6. MEASUREMENT SETUP 150 Q(
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Chapter 7 Characterization of CQED
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CHAPTER 7. CHARACTERIZATION OF CQED
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CHAPTER 8. CAVITY QED EXPERIMENTS W
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Chapter 9 Time Domain Measurements
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CHAPTER 9. TIME DOMAIN MEASUREMENTS
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Chapter 10 Future work The biggest
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CHAPTER 10. FUTURE WORK 222 possibl
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CHAPTER 10. FUTURE WORK 224 frequen
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CHAPTER 11. CONCLUSIONS 226 There i
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APPENDIX A. OPERATORS AND COMMUTATI
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APPENDIX B. DERIVATION OF DRESSED S
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APPENDIX B. DERIVATION OF DRESSED S
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Appendix D Recipes This Appendix wi
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APPENDIX D. RECIPES 236 PMMA develo
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APPENDIX D. RECIPES 238 Electron Be
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BIBLIOGRAPHY 240 [Bennett1984] C. H
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BIBLIOGRAPHY 242 [Clauser1974] John
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BIBLIOGRAPHY 244 frequency noise in
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BIBLIOGRAPHY 246 [Kuhn2002] Axel Ku
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BIBLIOGRAPHY 248 controlled by exte
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BIBLIOGRAPHY 250 [Rivest1978] R. L.
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BIBLIOGRAPHY 252 [Walls2006] D. F.
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