 | Mendonça J.T. Physics of ultra-cold matter: atomic clouds, bose-einstein condensates and rydberg plasmas / J.T.Mendonça, H.Terças. - New York: Springer, 2013. - xx, 398 p. - (Springer Series on Atomic, Optical, and Plasma Physics; 70). - Incl. bibl. ref. - Ind.: p.395-398. - ISBN 978-1-4614-5412-0; ISSN 1615-5653
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1 Introduction ................................................. 1
1.1 Three Phases of Ultra-cold Matter ....................... 1
1.2 Historical Perspective .................................. 3
1.3 Book Overview ........................................... 4
References ................................................... 6
Part I Atomic Clouds
2 Laser Cooling ................................................ 9
2.1 Atom in the Laser Field ................................. 9
2.2 Laser Cooling Force .................................... 14
2.3 Doppler Limit .......................................... 17
2.4 Magnetic Traps ......................................... 18
2.4.1 Multipolar Field Configuration .................. 19
2.4.2 Helmholtz Configuration ......................... 20
2.4.3 Ioffe Configuration ............................. 20
2.4.4 Anti-Helmholtz Configuration .................... 21
2.5 Sisyphus Cooling ....................................... 23
2.6 Evaporative Cooling .................................... 25
2.7 Sympathetic Cooling .................................... 29
References .................................................. 33
3 Wave Kinetic Approach ....................................... 35
3.1 Wigner-Moyal Procedure ................................. 35
3.1.1 Quasi-distributions ............................. 36
3.1.2 Weyl Transformation ............................. 39
3.1.3 Wave Kinetic Equation ........................... 41
3.1.4 The Quasi-classical Limit ....................... 43
3.2 Center-of-Mass Equation ................................ 44
3.3 Wave Kinetic Description of the Laser-Atom
Interaction ............................................ 47
3.4 Two-Level Atom ......................................... 48
3.5 Links with Dynamics and Statistics ..................... 50
3.5.1 Quasi-classical Limit ........................... 50
3.5.2 Momentum Diffusion and the Doppler Limit ........ 51
3.6 Lambda Configuration ................................... 53
3.7 Two Coupled Radiative Transitions ...................... 55
3.8 Influence of a Blue-Detuned Pump ....................... 58
References .................................................. 60
4 Atomic Clouds ............................................... 63
4.1 Atom-Atom Collisions ................................... 64
4.2 Feshbach Resonances .................................... 69
4.3 Collective Forces ...................................... 74
4.4 Equilibrium Profiles ................................... 79
4.4.1 Qualitative Discussion .......................... 80
4.4.2 Quantitative Model .............................. 82
4.5 Coulomb Expansion ...................................... 84
References .................................................. 88
5 Waves and Oscillations in Clouds ............................ 89
5.1 Hybrid Sound ........................................... 89
5.1.1 Fluid Description ............................... 89
5.1.2 Kinetic Approach ................................ 91
5.2 Tonks-Dattner Modes .................................... 96
5.3 Large Scale Oscillations ............................... 99
5.3.1 The Centre-of-Mass Oscillation .................. 99
5.3.2 Normal Modes ................................... 100
5.4 Nonlinear Mode Coupling ............................... 103
5.5 Quasi-linear Diffusion ................................ 107
5.6 Phaser, the Phonon Laser .............................. 100
References ................................................. 114
6 Photons in the Ultra-cold Gas .............................. 115
6.1 Optical Properties .................................... 116
6.2 Modulational Instability .............................. 118
6.3 Photon Bubbles ........................................ 120
6.4 Roton Instability ..................................... 125
6.5 Density Fluctuations .................................. 131
6.6 Collective Laser Scattering ........................... 135
References ................................................. 138
Part II The Physics of Bose-Einstein Condensates
7 Bose Einstein Condensates .................................. 143
7.1 Uniform Gas ........................................... 144
7.2 Trapped Gas ........................................... 145
7.3 Atom Correlations ..................................... 149
7.4 Mean Field Approximation .............................. 153
7.5 Thomas-Fermi Approximation ............................ 155
7.6 Fluid and Kinetic Formulations ........................ 158
7.6.1 Quantum Fluid Equations ........................ 158
7.6.2 Wave Kinetic Equation .......................... 160
References ................................................. 161
8 Elementary Excitations in BECs ............................. 163
8.1 SoundWaves ............................................ 163
8.2 Global Oscillations ................................... 165
8.3 Kinetic Processes ..................................... 168
8.4 Landau Damping ........................................ 169
8.5 Dynamical Instabilities ............................... 171
8.6 Wakefields in Bose-Einstein Condensates ............... 174
References ................................................. 180
9 Solitons ................................................... 181
9.1 Effective One-Dimensional Gross-Pitaevskii Equation ... 182
9.2 One-Dimensional Dark and Grey Solitons ................ 184
9.2.1 Energy of the Soliton .......................... 187
9.3 The Inverse Scattering Transform ...................... 188
9.4 Interaction Between Two Dark Solitons ................. 189
9.5 Bright Solitons ....................................... 193
9.6 Dark Solitons in Harmonic Traps ....................... 194
9.7 The Soliton Gas ....................................... 197
9.8 Solitons in Two Dimensions ............................ 200
References ................................................. 202
10 Quantum Field Theory of BECs ............................... 205
10.1 Bogoliubov Theory ..................................... 205
10.2 ВЕС Depletion ......................................... 209
10.3 Phonon Pair Creation .................................. 211
10.3.1 Time Refraction ................................ 211
10.3.2 Dynamical Casimir Effect ....................... 215
10.4 Acoustic Black Holes ................................. 217
10.4.1 Hawking Radiation .............................. 218
10.4.2 Effective Metric in a Condensate ............... 219
10.4.3 Acoustic Hawking (Unruh) Radiation ............. 220
References ................................................. 222
11 Superfluidity .............................................. 225
11.1 Phonon Kinetics ....................................... 225
11.2 Phonon Fluid Equations ................................ 228
11.3 Slow Perturbations in the Superfluid .................. 230
11.4 Superfluid Currents ................................... 232
11.5 Phonon Landau Damping ................................. 234
11.6 Roton Excitation ...................................... 235
11.6.1 Wave Kinetic Equation with Dipolar
Interactions .................................... 236
11.6.2 Dispersion Relation ............................. 237
11.6.3 Roton Instability ............................... 238
References ................................................. 240
12 Rotating BECs .............................................. 241
12.1 Quantum Vortices ...................................... 241
12.2 Vortex Nucleation ..................................... 244
12.3 Tkachenko Modes ....................................... 245
12.4 Rossby Waves .......................................... 246
12.5 Rossby-Tkatchenko Modes ............................... 252
12.6 Coupling with Photon OAM States ....................... 254
References ................................................. 256
13 Quantum Coherence .......................................... 257
13.1 Atom Interferometry ................................... 257
13.2 Time Interferometry ................................... 259
13.3 Decoherence Processes ................................. 262
13.4 Gravitational Decoherence ............................. 265
13.5 Josephson Tunneling of a Condensate ................... 269
References ................................................. 274
Part III The Physics of Ultracold Plasmas
14 Ultra-cold Plasmas ......................................... 277
14.1 Different Plasma Regimes .............................. 278
14.2 Basic Plasma Properties ............................... 280
14.3 Ionization Processes .................................. 283
14.4 Single Particle Motion ................................ 285
14.5 Adiabatic Invariants .................................. 289
14.6 Plasma Equations ...................................... 293
14.6.1 Klimontovitch Equation ......................... 294
14.6.2 Vlasov Equation ................................ 296
14.6.3 Kinetic Equations with Collisions .............. 298
14.7 Fluid Equations ....................................... 299
References ................................................. 302
15 Physics of Rydberg Plasmas ................................. 305
15.1 Plasma Expansion in the Collisional Regime ............ 306
15.1.1 Free Diffusion ................................. 306
15.1.2 Ambipolar Diffusion Regime ..................... 308
15.1.3 Recombination in Volume ........................ 309
15.2 Collisionless Plasma Expansion ........................ 310
15.3 Strongly Coupled Ions ................................. 313
15.3.1 Ion-Neutral Coupling ........................... 313
15.3.2 Ion-Ion Coupling ............................... 316
15.3.3 Phase Transitions .............................. 317
15.4 Disorder Induced Heating .............................. 321
15.5 Quasi-equilibrium States .............................. 323
15.6 Rydberg Atoms ......................................... 326
15.6.1 Basic Properties ............................... 326
15.6.2 Rydberg Blockade ............................... 329
15.7 Three-Body Recombination .............................. 334
References ................................................. 336
16 Waves in Rydberg Plasmas ................................... 339
16.1 Isotropic Plasmas ..................................... 340
16.2 Polaritons and Slow Light ............................. 343
16.3 Ponderomotive Force ................................... 349
16.4 Electron Drift Instability ............................ 351
16.5 Drift Waves at Plasma Gradients ....................... 353
16.6 Waves in Magnetized Cold Plasmas ...................... 355
16.6.1 General Dispersion Relation .................... 355
16.6.2 Parallel Propagation ........................... 358
16.6.3 Perpendicular Propagation ...................... 360
16.7 Waves in Expanding Plasmas ............................ 361
16.8 Waves in Strongly Coupled Plasmas ..................... 364
References ................................................. 366
17 Kinetic Theory of Waves .................................... 367
17.1 Kinetic Dispersion Relation ........................... 368
17.2 Electron Plasma Waves ................................. 371
17.3 Ion Acoustic Waves .................................... 373
17.4 Waves in Quantum Plasmas .............................. 374
17.5 Sound Waves in a Turbulent Plasma ..................... 378
17.5.1 Plasmon Kinetic Equation ....................... 378
17.5.2 Ion Oscillations ............................... 380
References ................................................. 381
18 Conclusions ................................................ 383
Appendix ................................................... 385
A.1 Atomic Structure ...................................... 385
A.2 Quantum Theory of Radiative Transitions ............... 389
Index
Appendix ...................................................... 385
A.1 Atomic Structure ......................................... 385
A.2 Quantum Theory of Radiative Transitions .................. 389
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