Physics of Ultra-Cold Matter (eBook)

J.T. Mendonça, Instituto Superior Tecnico, Lisbon, Portugal, titomend@ist.utl.ptHugo Terças, Université Blaise Pascal, Aubière, France, htercas@gmail.com

Physics of Ultra-Cold Matter 3
Preface 5
Contents 7
List of Figures 13
List of Tables 21
Chapter 1: Introduction 23
1.1 Three Phases of Ultra-cold Matter 23
1.2 Historical Perspective 25
1.3 Book Overview 26
References 28
Part I Atomic Clouds 29
Chapter 2: Laser Cooling 30
2.1 Atom in the Laser Field 30
2.2 Laser Cooling Force 35
2.3 Doppler Limit 38
2.4 Magnetic Traps 39
2.4.1 Multipolar Field Configuration 40
2.4.2 Helmholtz Configuration 41
2.4.3 Ioffe Configuration 41
2.4.4 Anti-Helmholtz Configuration 42
2.5 Sisyphus Cooling 44
2.6 Evaporative Cooling 46
2.7 Sympathetic Cooling 50
References 54
Chapter 3: Wave Kinetic Approach 56
3.1 Wigner-Moyal Procedure 56
3.1.1 Quasi-distributions 57
3.1.2 Weyl Transformation 60
3.1.3 Wave Kinetic Equation 62
3.1.4 The Quasi-classical Limit 64
3.2 Center-of-Mass Equation 65
3.3 Wave Kinetic Description of the Laser-Atom Interaction 68
3.4 Two-Level Atom 69
3.5 Links with Dynamics and Statistics 71
3.5.1 Quasi-classical Limit 71
3.5.2 Momentum Diffusion and the Doppler Limit 72
3.6 Lambda Configuration 74
3.7 Two Coupled Radiative Transitions 76
3.8 Influence of a Blue-Detuned Pump 79
References 81
Chapter 4: Atomic Clouds 83
4.1 Atom-Atom Collisions 84
4.2 Feshbach Resonances 89
4.3 Collective Forces 94
4.4 Equilibrium Profiles 99
4.4.1 Qualitative Discussion 100
4.4.2 Quantitative Model 102
4.5 Coulomb Expansion 104
References 108
Chapter 5: Waves and Oscillations in Clouds 109
5.1 Hybrid Sound 109
5.1.1 Fluid Description 109
5.1.2 Kinetic Approach 111
5.2 Tonks-Dattner Modes 116
5.3 Large Scale Oscillations 119
5.3.1 The Centre-of-Mass Oscillation 119
5.3.2 Normal Modes 120
5.4 Nonlinear Mode Coupling 123
5.5 Quasi-linear Diffusion 127
5.6 Phaser, the Phonon Laser 130
References 134
Chapter 6: Photons in the Ultra-cold Gas 135
6.1 Optical Properties 136
6.2 Modulational Instability 138
6.3 Photon Bubbles 140
6.4 Roton Instability 145
6.5 Density Fluctuations 151
6.6 Collective Laser Scattering 155
References 158
Part II The Physics of Bose-Einstein Condensates 160
Chapter 7: Bose Einstein Condensates 161
7.1 Uniform Gas 162
7.2 Trapped Gas 163
7.3 Atom Correlations 167
7.4 Mean Field Approximation 171
7.5 Thomas-Fermi Approximation 173
7.6 Fluid and Kinetic Formulations 176
7.6.1 Quantum Fluid Equations 176
7.6.2 Wave Kinetic Equation 178
References 179
Chapter 8: Elementary Excitations in BECs 181
8.1 Sound Waves 181
8.2 Global Oscillations 183
8.3 Kinetic Processes 186
8.4 Landau Damping 187
8.5 Dynamical Instabilities 189
8.6 Wakefields in Bose-Einstein Condensates 192
References 198
Chapter 9: Solitons 199
9.1 Effective One-Dimensional Gross-Pitaevskii Equation 200
9.2 One-Dimensional Dark and Grey Solitons 202
9.2.1 Energy of the Soliton 205
9.3 The Inverse Scattering Transform 206
9.4 Interaction Between Two Dark Solitons 207
9.5 Bright Solitons 211
9.6 Dark Solitons in Harmonic Traps 212
9.7 The Soliton Gas 215
9.8 Solitons in Two Dimensions 218
References 220
Chapter 10: Quantum Field Theory of BECs 222
10.1 Bogoliubov Theory 222
10.2 BEC Depletion 226
10.3 Phonon Pair Creation 228
10.3.1 Time Refraction 228
10.3.2 Dynamical Casimir Effect 232
10.4 Acoustic Black Holes 234
10.4.1 Hawking Radiation 235
10.4.2 Effective Metric in a Condensate 236
10.4.3 Acoustic Hawking (Unruh) Radiation 237
References 239
Chapter 11: Superfluidity 241
11.1 Phonon Kinetics 241
11.2 Phonon Fluid Equations 244
11.3 Slow Perturbations in the Superfluid 246
11.4 Superfluid Currents 248
11.5 Phonon Landau Damping 250
11.6 Roton Excitation 251
11.6.1 Wave Kinetic Equation with Dipolar Interactions 252
11.6.2 Dispersion Relation 253
11.6.3 Roton Instability 254
References 256
Chapter 12: Rotating BECs 257
12.1 Quantum Vortices 257
12.2 Vortex Nucleation 260
12.3 Tkachenko Modes 261
12.4 Rossby Waves 262
12.5 Rossby-Tkatchenko Modes 268
12.6 Coupling with Photon OAM States 270
References 272
Chapter 13: Quantum Coherence 273
13.1 Atom Interferometry 273
13.2 Time Interferometry 275
13.3 Decoherence Processes 278
13.4 Gravitational Decoherence 281
13.5 Josephson Tunneling of a Condensate 285
References 290
Part III The Physics of Ultracold Plasmas 291
Chapter 14: Ultra-cold Plasmas 292
14.1 Different Plasma Regimes 293
14.2 Basic Plasma Properties 295
14.3 Ionization Processes 298
14.4 Single Particle Motion 300
14.5 Adiabatic Invariants 304
14.6 Plasma Equations 308
14.6.1 Klimontovitch Equation 309
14.6.2 Vlasov Equation 311
14.6.3 Kinetic Equations with Collisions 313
14.7 Fluid Equations 314
References 317
Chapter 15: Physics of Rydberg Plasmas 319
15.1 Plasma Expansion in the Collisional Regime 320
15.1.1 Free Diffusion 320
15.1.2 Ambipolar Diffusion Regime 322
15.1.3 Recombination in Volume 323
15.2 Collisionless Plasma Expansion 324
15.3 Strongly Coupled Ions 327
15.3.1 Ion-Neutral Coupling 327
15.3.2 Ion-Ion Coupling 330
15.3.3 Phase Transitions 331
15.4 Disorder Induced Heating 335
15.5 Quasi-equilibrium States 337
15.6 Rydberg Atoms 340
15.6.1 Basic Properties 340
15.6.2 Rydberg Blockade 343
15.7 Three-Body Recombination 348
References 350
Chapter 16: Waves in Rydberg Plasmas 352
16.1 Isotropic Plasmas 353
16.2 Polaritons and Slow Light 356
16.3 Ponderomotive Force 362
16.4 Electron Drift Instability 364
16.5 Drift Waves at Plasma Gradients 366
16.6 Waves in Magnetized Cold Plasmas 368
16.6.1 General Dispersion Relation 368
16.6.2 Parallel Propagation 371
16.6.3 Perpendicular Propagation 373
16.7 Waves in Expanding Plasmas 374
16.8 Waves in Strongly Coupled Plasmas 377
References 379
Chapter 17: Kinetic Theory of Waves 380
17.1 Kinetic Dispersion Relation 381
17.2 Electron Plasma Waves 384
17.3 Ion Acoustic Waves 386
17.4 Waves in Quantum Plasmas 387
17.5 Sound Waves in a Turbulent Plasma 391
17.5.1 Plasmon Kinetic Equation 391
17.5.2 Ion Oscillations 393
References 394
Chapter 18: Conclusions 396
Appendix 398
A.1 Atomic Structure 398
A.2 Quantum Theory of Radiative Transitions 402
Index 407