Quantum Many-Body Physics in Open Systems: Measurement and Strong Correlations

Supervisor’s Foreword......Page 7
Abstract......Page 9
Parts of this thesis have been published in the following journal articles:......Page 10
Acknowledgements......Page 12
Contents......Page 13
Notations and Abbreviations......Page 16
1 Motivation and Outline......Page 19
References......Page 25
2.1.1 Indirect Measurement Model......Page 31
2.1.2 Mathematical Characterization of Measurement Processes......Page 33
2.2.1 Repeated Indirect Measurements......Page 35
2.2.2 Quantum Jump Process......Page 38
2.2.3 Diffusive Limit......Page 42
2.2.4 Physical Example: Site-Resolved Measurement of Atoms......Page 43
References......Page 45
3.1.1 Motivation: Measurement Backaction on Strongly Correlated Systems......Page 47
3.1.2 Universal Low-Energy Behavior in One-Dimensional Quantum Systems......Page 50
3.2.1 Model......Page 57
3.2.2 Correlation Functions: Bifurcating Critical Exponents......Page 60
3.2.3 Realization in a 1D Ultracold Bose Gas  with a Two-Body Loss......Page 63
3.3.1 Model and Its Symmetry......Page 65
3.3.2 Perturbative Renormalization Group Analysis......Page 66
3.3.3 Numerical Demonstration in a Non-Hermitian Spin-Chain Model......Page 69
3.3.4 Nonperturbative Renormalization Group Analysis......Page 73
3.3.5 Realization in Ultracold Gases with a One-Body Loss......Page 77
3.3.6 Short Summary......Page 82
3.4.1 Model......Page 83
3.4.2 Measurement-Induced Shift of the Quantum Critical Point......Page 84
3.4.3 Realization with Ultracold Gases in an Optical Lattice......Page 87
3.5 Experimental Realizations in Ultracold Gases......Page 88
3.6 Conclusions and Outlook......Page 91
References......Page 98
4 Out-of-Equilibrium Quantum Dynamics......Page 104
4.1.1 Introduction......Page 105
4.1.2 General Idea: The Full-Counting Many-Particle Dynamics......Page 106
4.1.3 System: Atoms Subject to a Spatially Modulated Loss......Page 107
4.1.4 Nonequilibrium Dynamics of Correlations and Entanglement......Page 110
4.2.1 Introduction......Page 117
4.2.2 Statistical Ensemble Under Minimally Destructive Observation......Page 119
4.2.3 Numerical Simulations in Nonintegrable Open Many-Body Systems......Page 122
4.2.4 Application to Many-Body Lindblad Dynamics......Page 128
4.3.1 Introduction......Page 129
4.3.2 System: Atoms Under Spatial Observation......Page 130
4.3.3 Minimally Destructive Spatial Observation......Page 132
4.3.4 Many-Body Stochastic Schrödinger Equations......Page 133
4.3.5 Numerical Demonstrations......Page 136
4.4 Experimental Situations in Ultracold Gases......Page 138
4.5 Conclusions and Outlook......Page 140
References......Page 153
5.1 Introduction......Page 161
5.2 Disentangling Canonical Transformation......Page 165
5.2.1 Disentangling a Single Spin-1/2 Impurity  and an Environment......Page 166
5.2.2 Disentangling Two Spin-1/2 Impurities  and an Environment......Page 168
5.2.3 Disentangling the Single-Impurity Anderson Model......Page 171
5.3.1 Fermionic Gaussian States......Page 173
5.3.2 Variational Time Evolution of the Covariance Matrix......Page 174
5.3.3 General Expression of the Functional Derivative......Page 176
5.4.1 Kondo Problem......Page 178
5.4.2 Entanglement Structure of the Variational Ground State......Page 180
5.4.3 Benchmark Tests with the Matrix-Product States......Page 181
5.4.4 Benchmark Test with the Bethe Ansatz Solution......Page 186
5.4.5 Tests of Nonperturbative Scaling and Universal Behavior......Page 187
5.4.6 Spatiotemporal Dynamics after the Quench......Page 188
5.5.1 Model......Page 189
5.5.2 Spatiotemporal Dynamics of the Environment after the Quench......Page 190
5.5.3 Transport Properties......Page 192
5.6 Experimental Implementation in Ultracold Gases......Page 194
5.7.1 General Formalism......Page 196
5.7.2 Application to the Rydberg Central Spin Problem......Page 200
5.8 Conclusions and Outlook......Page 206
References......Page 212
6.1 Introduction: New Frontiers in Polaron Physics......Page 220
6.2 System: A Mobile Particle in a Synthetic Magnetic Environment......Page 222
6.3 Many-Body Interferometry Acting on the Environment......Page 225
6.4.1 Time-Dependent Variational Principle......Page 226
6.4.2 Quantum Dynamics of the Environment......Page 227
6.4.3 Many-Body Bound States......Page 229
6.5 Experimental Implementation in Ultracold Atomic Gases......Page 231
6.6 Conclusions and Outlook......Page 235
References......Page 236
7 Conclusions and Outlook......Page 240
Appendix  Curriculum Vitae......Page 242