Thermodynamics and Synchronization in Open Quantum Systems (eBook)

Supervisors’ Foreword 6
Abstract 9
Acknowledgements 13
Contents 15
Acronyms 20
Part I Introduction to Open Quantum Systems and Quantum Thermodynamics 22
1 Basic Concepts 23
1.1 Quantum Mechanics 24
1.1.1 The Density Operator 25
1.1.2 Liouville–von Neumann Equation 27
1.1.3 Heisenberg and Interaction Pictures 28
1.1.4 The Microreversibility Principle 29
1.1.5 Composite Quantum Systems 31
1.1.6 Quantum Entropies 33
1.1.7 Distance Measures 36
1.2 Prototypical Systems 38
1.2.1 The Qubit System 39
1.2.2 Manipulation of Qubits by Classical Fields 42
1.2.3 The Harmonic Oscillator 43
1.2.4 Coherent States 46
1.2.5 Squeezed States 49
1.3 Quantum Measurement 53
1.3.1 Ideal Measurements 54
1.3.2 Generalized Measurements 56
1.3.3 Classes of Measurements 59
1.4 Classical and Quantum Correlations 64
1.4.1 Entanglement 64
1.4.2 Mutual Information 68
1.4.3 Quantum Discord 70
References 74
2 Open Quantum Systems Dynamics 79
2.1 Quantum Maps and Operations 80
2.1.1 Properties of CPTP Maps 83
2.1.2 Kraus Operator-Sum Representation 84
2.1.3 Environmental Models 85
2.1.4 Some Examples of CPTP Maps 87
2.2 Markovian Master Equations 89
2.2.1 The Lindblad Form 91
2.2.2 The Born–Markov Master Equation 92
2.3 Dissipative Qubits and Harmonic Oscillators 97
2.3.1 Qubit Relaxation in a Bosonic Environment 97
2.3.2 Bosonic Collisional Model 102
2.3.3 Quantum Brownian Motion 106
2.4 Open Many-Body Systems 111
2.4.1 Common Versus Independent Environmental Action 111
2.4.2 Coupled Dissipative Harmonic Oscillators 114
2.5 Quantum Trajectories 121
2.5.1 Continuous Measurements and Quantum Jumps 122
2.5.2 Stochastic Schrödinger Equation 125
2.5.3 Master Equation Unraveling 128
References 131
3 Quantum Thermodynamics 135
3.1 Principles of Thermodynamics 136
3.1.1 The First Law of Thermodynamics 138
3.1.2 The Second Law of Thermodynamics 140
3.1.3 Statistical Mechanics and Entropy 143
3.1.4 Helmholtz and Nonequilibrium Free Energy 145
3.1.5 The Third Law of Thermodynamics 147
3.1.6 Thermodynamics and Information 149
3.2 Fluctuation Theorems 151
3.2.1 Stochastic Thermodynamics 152
3.2.2 Classical Fluctuation Theorems 156
3.2.3 Quantum Fluctuation Theorems 161
3.3 Quantum Thermal Machines 168
3.3.1 Quantum Otto Cycle 169
3.3.2 Autonomous Thermal Machines 173
3.3.3 Quantum Effects in Thermal Machines 177
3.4 Other Topics in Quantum Thermodynamics 178
3.4.1 Equilibration and Thermalization 179
3.4.2 Resource Theories in Quantum Thermodynamics 182
References 186
Part II Quantum Synchronization Induced by Dissipation in Many-Body Systems 197
4 Transient Synchronization and Quantum Correlations 198
4.1 Synchronization Phenomena and Previous Works 199
4.2 Two Dissipative Harmonic Oscillators 200
4.3 Synchronization 203
4.4 Quantum Correlations 207
4.5 Dependence on Initial Conditions 209
4.6 Conclusions 211
References 217
5 Noiseless Subsystems and Synchronization 220
5.1 Prevention of Decoherence and Dissipation 221
5.2 Three Oscillators in a Common Environment 222
5.3 Noiseless Subsystems and Asymptotic Properties 224
5.3.1 Asymptotic Entanglement 228
5.3.2 Quantum Synchronization 233
5.4 Thermalization and Robustness of Quantum Correlations 235
5.4.1 Quantum Correlations 238
5.4.2 Synchronous Thermalization 240
5.5 Conclusions 241
References 248
6 Dissipative Complex Quantum Networks 251
6.1 Dissipation Mechanisms and Synchronization 252
6.2 Collective Synchronization by Tuning One Oscillator 257
6.2.1 Common Dissipation Bath 257
6.2.2 Local Dissipation Bath 260
6.3 Synchronization of Clusters and Linear Motifs 261
6.4 Entangling Two Oscillators Through a Network 264
6.5 Conclusions 265
References 270
Part III Quantum Fluctuation Theorems and Entropy Production 273
7 Fluctuation Theorems for Quantum Maps 274
7.1 Fluctuation Theorems, Unital Maps and Beyond 275
7.2 Quantum Operations and Dual-Reverse Dynamics 276
7.2.1 Quantum Trajectories and Unconditional States 277
7.2.2 Dual-Reverse Dynamics 278
7.3 Fluctuation Theorems 279
7.3.1 Nonequilibrium Potential and Detailed Balance 279
7.3.2 Fluctuation Theorem for a Single CPTP Map 281
7.3.3 Fluctuation Theorem for Concatenated Maps 284
7.4 Applications 285
7.4.1 Boundary Terms 285
7.4.2 Unital Work Relations 287
7.4.3 Thermalization and Heat 288
7.4.4 Generalized Gibbs-Preserving Maps 290
7.4.5 Lindblad Master Equations 293
7.5 Conclusion 297
References 298
8 Entropy Production Fluctuations in Quantum Processes 302
8.1 Quantum Operations and Entropy Production 303
8.1.1 The Process 303
8.1.2 Reduced Dynamics 305
8.1.3 Average Entropy Production 306
8.2 Backward Process and Fluctuation Theorem 308
8.3 Adiabatic and Non-adiabatic Entropy Production 311
8.3.1 The Dual-Reverse Process 312
8.3.2 The Dual Process 314
8.3.3 Second-Law-Like Equalities and Inequalities 315
8.3.4 Multipartite Environments 317
8.4 Concatenation of CPTP Maps 318
8.5 Lindblad Master Equations 322
8.6 Conclusions 328
References 329
9 Simple Applications of the Entropy Production FT's 332
9.1 Autonomous Quantum Thermal Machines 333
9.1.1 Quantum Trajectories and Entropy Production 335
9.2 Periodically Driven Cavity Mode at Resonance 341
9.2.1 Failure of the FT for Adiabatic Entropy Production 343
9.2.2 Implications to the Second-Law-Like Inequalities 344
9.3 Squeezing in a Maxwell Fridge Toy Model 347
9.3.1 Thermal Reservoirs Case 349
9.3.2 Squeezed Thermal Reservoir Enhancements 352
9.4 Conclusions 357
References 358
Part IV Quantum Thermal Machines 360
10 Thermodynamic Power of the Squeezed Thermal Reservoir 361
10.1 Thermodynamics of the Squeezed Thermal Reservoir 362
10.2 Extracting Work from a Single Reservoir 365
10.3 Heat Engine with a Squeezed Thermal Reservoir 366
10.3.1 Optimal Otto Cycle 366
10.3.2 Regimes of Operation 369
10.4 Squeezing as a Source of Free Energy 372
10.5 Experimental Realization 374
10.6 Conclusions 375
References 379
11 Performance of Autonomous Quantum Thermal Machines 382
11.1 The Primitive Operation 383
11.2 Warm-Up: Three-Level Machine 386
11.3 Multi-level Machines 388
11.4 Single-Cycle Machines 390
11.4.1 Optimal Single-Cycle Machine 391
11.5 Multi-cycle Machines 394
11.6 Concatenated Three-Level Machines 396
11.7 Third Law 399
11.8 Statics Versus Dynamics for Single-Cycle Machines 400
11.9 Conclusions 401
References 412
Part V Conclusions 413
12 Summary and Outlook 414
12.1 Quantum Synchronization Induced by Dissipation in Many-Body Systems 414
12.2 Quantum Fluctuation Theorems and Entropy Production 417
12.3 Quantum Thermal Machines 420
References 422