Circuit Quantum Electrodynamics - Yale School of Engineering ...

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CONTENTS 5 5.1.1 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1.2 Optical Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.1.3 Deposition and Liftoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.1.4 Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Cooper Pair Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2.1 Josephson Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2.2 Charging Energy and Voltage Division . . . . . . . . . . . . . . . . . . . . . . 130 5.2.3 Electron Beam Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.4 Veil of Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.3 Transmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.4 Printed Circuit Boards and Sample Holders . . . . . . . . . . . . . . . . . . . . . . . 137 6 Measurement Setup 141 6.1 Cryogenics and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.2 Pulse Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 6.3 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.3.1 Digital Homodyne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7 Characterization of CQED 154 7.1 Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7.1.1 Temperature Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.1.2 Magnetic Field Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.2 Cooper pair box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.2.1 Charge Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.2.2 Measured CPB properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.3 Transmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8 Cavity QED Experiments with Circuits 169 8.1 Resonant Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.1.1 Vacuum Rabi Mode Splitting with CPB . . . . . . . . . . . . . . . . . . . . . 171 8.1.2 Vacuum Rabi Mode Splitting With Transmon . . . . . . . . . . . . . . . . . . 173 8.2 Dispersive Weak Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
CONTENTS 6 8.2.1 AC Stark Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 8.2.2 Off-Resonant AC Stark Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 8.2.3 Sideband Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.3 Dispersive Strong Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 8.3.1 Photon Number Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 8.3.2 Anharmonic Strong Dispersive Limit . . . . . . . . . . . . . . . . . . . . . . . 197 9 Time Domain Measurements 200 9.1 Single Qubit Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.2 Single Shot Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 9.3 Single Photon Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 10 Future work 220 10.1 Evolution of Circuit QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 10.1.1 New Cavity and Qubit Designs . . . . . . . . . . . . . . . . . . . . . . . . . . 220 10.1.2 Scaling Circuit QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 10.1.3 Other quantum circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 10.1.4 Hybrid Circuit QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11 Conclusions 225 Appendices 226 A Operators and Commutation Relations 227 A.1 Harmonic Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A.2 Spin 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A.3 Jaynes-Cummings Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A.3.1 Interaction with Harmonic oscillator operators . . . . . . . . . . . . . . . . . 228 A.3.2 Interaction with Spin 1/2 Operators . . . . . . . . . . . . . . . . . . . . . . . 228 B Derivation of Dressed State Atom Picture 229 C Mathematica Notebooks 233 C.1 Cooper Pair Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Page 1 and 2: Abstract Circuit Quantum Electrodyn
Page 3 and 4: c○2007 by David Schuster. All rig
Page 5 and 6: friendship. All of my friends from
Page 7: CONTENTS 4 3.2.3 Split CPB . . . .
Page 11 and 12: List of Figures 1.1 Relaxation and
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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 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 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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