Circuit Cavity QED with Macroscopic Solid-State Spin Ensembles (eBook)

Stefan Putz completed his Ph.D. at TU Wien in the field of solid state cavity QED. As postdoctoral research associate at Princeton University he continues his research on hybrid quantum systems and novel circuit QED architectures.

Supervisor’s Foreword 7
Abstract 9
Acknowledgements 11
Contents 13
Symbols 16
1 Introduction and Outline 18
1.1 Outline 19
References 20
2 Confined Electromagnetic Waves---Cavities 24
2.1 Electromagnetic Radiation 24
2.1.1 Mode Expansion in Free Space 24
2.1.2 Modes Inside a Cavity 25
2.2 Single Cavity Modes---Harmonic Oscillators 27
2.2.1 Canonical Variables of the Electromagnetic Field 27
2.2.2 Drive and Dissipation of a Classical Oscillator 28
2.2.3 Quantum Harmonic Oscillator 30
2.3 Electrical Oscillators---``From Classical to Quantum'' 32
2.3.1 Quantization of a LC Oscillator 32
2.3.2 Drive and Dissipation in a Classical LC Oscillator 34
2.3.3 Quantum Mechanical Description of a Real LC Cavity 37
References 40
3 Spins in the Cavity---Cavity QED 41
3.1 Single Spin in the Cavity 41
3.1.1 Cavity Spin Interaction 42
3.1.2 The Jaynes Cummings Model 44
3.1.3 Dressed States/Polariton Modes 46
3.2 Ensembles of Spins in the Cavity 49
3.2.1 Three Spins in the Cavity 49
3.2.2 N Spins in the Cavity 54
3.2.3 The Dicke Model 56
3.2.4 Low Excitation Limit 59
3.3 Coupling to Inhomogeneous Spectral Broadened Spin Ensembles 60
3.3.1 Equidistant Discretized Spin Ensembles 61
3.3.2 Non-equidistant Discretized Spin Ensembles 63
References 64
4 Experimental Implementation---Solid-State Hybrid Quantum System 66
4.1 Micro-Wave Cavities 66
4.1.1 Distributed Electrical Resonators 66
4.1.2 Lumped Electrical Resonators 70
4.2 Nitrogen Vacancy Center Spin Ensembles 72
4.2.1 Nitrogen Vacancy Center Level Structure 73
4.2.2 Thermal Polarization and Spin-Spin Interactions 74
4.3 Experimental Setup 76
4.4 Measurement Scheme 78
4.4.1 Up and Down Conversion 79
4.4.2 Signal Averaging 80
References 82
5 Collective Spin States Coupled to a Single Mode Cavity---Strong Coupling 85
5.1 Strong Coupling 85
5.1.1 ``Vacuum'' Rabi Splitting 86
5.1.2 Dispersive Measurements 88
5.2 Rabi Oscillations 90
5.2.1 Linear Rabi Oscillations 90
5.2.2 Non-linear Rabi Oscillations 92
5.3 Conclusion 93
References 94
6 Spin Ensembles and Decoherence in the Strong-Coupling Regime---Cavity Protection 96
6.1 Introduction 96
6.2 The Principle of Cavity Protection 97
6.3 Experimental Verification 100
6.4 Conclusion 104
References 104
7 Engineering of Long-Lived Collective DarkStates---Spectral Hole Burning 106
7.1 Introduction 106
7.1.1 The Principle of Spectral Hole Burning 107
7.1.2 Collective Spin Dark States 108
7.2 Experimental Implementation of Spectral Hole Burning 109
7.2.1 Spectral Hole Burning 109
7.2.2 Dark State Spectroscopy 110
7.2.3 Dark State Dynamics 112
7.3 Conclusion 114
References 114
8 Amplitude Bistability with Inhomogeneous Spin Broadening---Driven Tavis-Cummings 116
8.1 Introduction 116
8.2 The Principle of Bistability 117
8.3 Experiential Observation of Amplitude Bistability 120
8.4 Conclusion 122
References 123
9 Spin Echo Spectroscopy---Spin Refocusing 125
9.1 Introduction 125
9.2 Experimental Implementation 126
9.2.1 Car-Purcell-Meiboom-Gill Echo Train 126
9.2.2 Stimulated Spin Echo 127
9.3 Conclusion 129
References 129
10 Conclusion and Outlook 131
References 134
Appendix Curriculum Vitae 135