Latest Posts

Bose-Einstein condensation in dilute gases - Pethick C.J., Smith H.

Contents


1 Introduction 1
1.1 Bose–Einstein condensation in atomic clouds 4
1.2 Superfluid 4He 6
1.3 Other condensates 8
1.4 Overview 10
Problems 13
References 14
2 The non-interacting Bose gas 16
2.1 The Bose distribution 16
2.1.1 Densityof states 18
2.2 Transition temperature and condensate fraction 21
2.2.1 Condensate fraction 23
2.3 Densityprofile and velocitydistribution 24
2.3.1 The semi-classical distribution 27
2.4 Thermodynamic quantities 29
2.4.1 Condensed phase 30
2.4.2 Normal phase 32
2.4.3 Specific heat close to Tc 32
2.5 Effect of finite particle number 35
2.6 Lower-dimensional systems 36
Problems 37
References 38
3 Atomic properties 40
3.1 Atomic structure 40
3.2 The Zeeman effect 44

3.3 Response to an electric field 49
3.4 Energyscales 55
Problems 57
References 57
4T rapping and cooling of atoms 58
4.1 Magnetic traps 59
4.1.1 The quadrupole trap 60
4.1.2 The TOP trap 62
4.1.3 Magnetic bottles and the Ioffe–Pritchard trap 64
4.2 Influence of laser light on an atom 67
4.2.1 Forces on an atom in a laser field 71
4.2.2 Optical traps 73
4.3 Laser cooling: the Doppler process 74
4.4 The magneto-optical trap 78
4.5 Sisyphus cooling 81
4.6 Evaporative cooling 90
4.7 Spin-polarized hydrogen 96
Problems 99
References 100
5 Interactions between atoms 102
5.1 Interatomic potentials and the van der Waals interaction 103
5.2 Basic scatteringtheory107
5.2.1 Effective interactions and the scattering length 111
5.3 Scattering length for a model potential 114
5.4 Scattering between different internal states 120
5.4.1 Inelastic processes 125
5.4.2 Elastic scattering and Feshbach resonances 131
5.5 Determination of scattering lengths 139
5.5.1 Scattering lengths for alkali atoms and hydrogen 142
Problems 144
References 144
6 Theory of the condensed state 146
6.1 The Gross–Pitaevskii equation 146
6.2 The ground state for trapped bosons 149
6.2.1 A variational calculation 151
6.2.2 The Thomas–Fermi approximation 154
6.3 Surface structure of clouds 158
6.4 Healing of the condensate wave function 161

Problems 163
References 163
7 Dynamics of the condensate 165
7.1 General formulation 165
7.1.1 The hydrodynamic equations 167
7.2 Elementaryexcitations 171
7.3 Collective modes in traps 178
7.3.1 Traps with spherical symmetry 179
7.3.2 Anisotropic traps 182
7.3.3 Collective coordinates and the variational method 186
7.4 Surface modes 193
7.5 Free expansion of the condensate 195
7.6 Solitons 196
Problems 201
References 202
8 Microscopic theory of the Bose gas 204
8.1 Excitations in a uniform gas 205
8.1.1 The Bogoliubov transformation 207
8.1.2 Elementaryexcitations 209
8.2 Excitations in a trapped gas 214
8.2.1 Weak coupling 216
8.3 Non-zero temperature 218
8.3.1 The Hartree–Fock approximation 219
8.3.2 The Popov approximation 225
8.3.3 Excitations in non-uniform gases 226
8.3.4 The semi-classical approximation 228
8.4 Collisional shifts of spectral lines 230
Problems 236
References 237
9 Rotating condensates 238
9.1 Potential flow and quantized circulation 238
9.2 Structure of a single vortex 240
9.2.1 A vortex in a uniform medium 240
9.2.2 A vortex in a trapped cloud 245
9.2.3 Off-axis vortices 247
9.3 Equilibrium of rotating condensates 249
9.3.1 Traps with an axis of symmetry 249
9.3.2 Rotating traps 251

9.4 Vortex motion 254
9.4.1 Force on a vortex line 255
9.5 The weakly-interacting Bose gas under rotation 257
Problems 261
References 262
10 Superfluidity 264
10.1 The Landau criterion 265
10.2 The two-component picture 267
10.2.1 Momentum carried byexcitations 267
10.2.2 Normal fluid density268
10.3 Dynamical processes 270
10.4 First and second sound 273
10.5 Interactions between excitations 280
10.5.1 Landau damping 281
Problems 287
References 288
11 Trapped clouds at non-zero temperature 289
11.1 Equilibrium properties 290
11.1.1 Energyscales 290
11.1.2 Transition temperature 292
11.1.3 Thermodynamic properties 294
11.2 Collective modes 298
11.2.1 Hydrodynamic modes above Tc 301
11.3 Collisional relaxation above Tc 306
11.3.1 Relaxation of temperature anisotropies 310
11.3.2 Damping of oscillations 315
Problems 318
References 319
12 Mixtures and spinor condensates 320
12.1 Mixtures 321
12.1.1 Equilibrium properties 322
12.1.2 Collective modes 326
12.2 Spinor condensates 328
12.2.1 Mean-field description 330
12.2.2 Beyond the mean-field approximation 333
Problems 335
References 336

13 Interference and correlations 338
13.1 Interference of two condensates 338
13.1.1 Phase-locked sources 339
13.1.2 Clouds with definite particle number 343
13.2 Densitycorrelations in Bose gases 348
13.3 Coherent matter wave optics 350
13.4 The atom laser 354
13.5 The criterion for Bose–Einstein condensation 355
13.5.1 Fragmented condensates 357
Problems 359
References 359
14F ermions 361
14.1 Equilibrium properties 362
14.2 Effects of interactions 366
14.3 Superfluidity370
14.3.1 Transition temperature 371
14.3.2 Induced interactions 376
14.3.3 The condensed phase 378
14.4 Boson–fermion mixtures 385
14.4.1 Induced interactions in mixtures 386
14.5 Collective modes of Fermi superfluids 388
Problems 391
References 392

Download book




Tags:

About author

Mahesh Loves to write about admission process in US and help prospective students.

0 comments

Leave a Reply

Related Posts with Thumbnails