稀化气体中的玻色-爱因斯坦凝聚 第2版 英文PDF电子书下载

1 Introduction 1

1.1 Bose-Einstein condensation in atomic clouds 4

1.2 Superfluid 4He 7

1.3 Other condensates 9

1.4 Overview 10

Problems 15

References 15

2 The non-interacting Bose gas 17

2.1 The Bose distribution 17

2.1.1 Density of states 19

2.2 Thansition temperature and condensate fraction 21

2.2.1 Condensate fraction 24

2.3 Density profile and velocity distribution 25

2.3.1 The semi-classical distribution 28

2.4 Thermodynamic quantities 33

2.4.1 Condensed phase 33

2.4.2 Normal phase 35

2.4.3 Specific heat close to Tc 36

2.5 Effect of finite particle number 38

Problems 39

References 40

3 Atomic properties 41

3.1 Atomic structure 41

3.2 The Zeeman effect 45

3.3 Response to an electric field 50

3.4 Energy scales 56

Problems 58

References 59

4 Trapping and cooling of atoms 60

4.1 Magnetic traps 61

4.1.1 The quadrupole trap 62

4.1.2 The TOP trap 64

4.1.3 Magnetic bottles and the Ioffe-Pritchard trap 66

4.1.4 Microtraps 69

4.2 Influence of laser light on an atom 71

4.2.1 Forces on an atom in a laser field 75

4.2.2 Optical traps 77

4.3 Laser cooling:the Doppler process 78

4.4 The magneto-optical trap 82

4.5 Sisyphus cooling 84

4.6 Evaporative cooling 96

4.7 Spin-polarized hydrogen 103

Problems 106

References 107

5 Interactions between atoms 109

5.1 Interatomic potentials and the van der Waals interaction 110

5.2 Basic scattering theory 114

5.2.1 Effective interactions and the scattering length 119

5.3 Scattering length for a model potential 125

5.4 Scattering between different internal states 130

5.4.1 Inelastic processes 135

5.4.2 Elastic scattering and Feshbach resonances 143

5.5 Determination of scattering lengths 151

5.5.1 Scattering lengths for alkali atoms and hydrogen 154

Problems 156

References 156

6 Theory of the condensed state 159

6.1 The Gross-Pitaevskii equation 159

6.2 The ground state for trapped bosons 162

6.2.1 A variational calculation 165

6.2.2 The Thomas-Fermi approximation 168

6.3 Surface structure of clouds 171

6.4 Healing of the condensate wave function 175

6.5 Condensates with dipolar interactions 176

Problems 179

References 180

7 Dynamics of the condensate 182

7.1 General formulation 182

7.1.1 The hydrodynamic equations 184

7.2 Elementary excitations 188

7.3 Collective modes in traps 196

7.3.1 Traps with spherical symmetry 197

7.3.2 Anisotropic traps 200

7.3.3 Collective coordinates and the variational method 204

7.4 Surface modes 21l 213

7.5 Free expansion of the condensate 213

7.6 Solitons 215

7.6.1 Dark solitons 216

7.6.2 Bright solitons 222

Problems 223

References 224

8 Microscopic theory of the Bose gas 225

8.1 The uniform Bose gas 226

8.1.1 The Bogoliubov transformation 229

8.1.2 Elementary excitations 230

8.1.3 Depletion of the condensate 231

8.1.4 Ground-state energy 233

8.1.5 States with definite particle number 234

8.2 Excitations in a trapped gas 236

8.3 Non-zero temperature 241

8.3.1 The Hartree-Fock approximation 242

8.3.2 The Popov approximation 248

8.3.3 Excitations in non-uniform gases 250

8.3.4 The semi-classical approximation 251

Problems 253

References 253

9 Rotating condensates 255

9.1 Potential flow and quantized circulation 255

9.2 Structure of a single vortex 257

9.2.1 A vortex in a uniform medium 257

9.2.2 Vortices with multiple quanta of circulation 261

9.2.3 A vortex in a trapped cloud 262

9.2.4 An off-axis vortex 265

9.3 Equilibrium of rotating condensates 265

9.3.1 Traps with an axis of symmetry 266

9.3.2 Rotating traps 267

9.3.3 Vortex arrays 270

9.4 Experiments on vortices 273

9.5 Rapidly rotating condensates 275

9.6 Collective modes in a vortex lattice 280

Problems 286

References 288

10 Superfluidity 290

10.1 The Landau criterion 291

10.2 The two-component picture 294

10.2.1 Momentum carried by excitations 294

10.2.2 Normal fluid density 295

10.3 Dynamical processes 296

10.4 First and second sound 300

10.5 Interactions between excitations 307

10.5.1 Landau damping 308

Problems 314

References 315

11 Trapped clouds at non-zero temperature 316

11.1 Equilibrium properties 317

11.1.1 Energy scales 317

11.1.2 Transition temperature 319

11.1.3 Thermodynamic properties 321

11.2 Collective modes 325

11.2.1 Hydrodynamic modes above Tc 328

11.3 Collisional relaxation above Tc 334

11.3.1 Relaxation of temperature anisotropies 339

11.3.2 Damping of oscillations 342

Problems 345

References 346

12 Mixtures and spinor condensates 348

12.1 Mixtures 349

12.1.1 Equilibrium properties 350

12.1.2 Collective modes 354

12.2 Spinor condensates 356

12.2.1 Mean-field description 358

12.2.2 Beyond the mean-field approximation 360

Problems 363

References 364

13 Interference and correlations 365

13.1 Tunnelling between two wells 365

13.1.1 Quantum fluctuations 371

13.1.2 Squeezed states 373

13.2 Interference of two condensates 374

13.2.1 Phase-locked sources 375

13.2.2 Clouds with definite particle number 381

13.3 Density correlations in Bose gases 384

13.3.1 Collisional shifts of spectral lines 386

13.4 Coherent matter wave optics 390

13.5 Criteria for Bose-Einstein condensation 394

13.5.1 The density matrix 394

13.5.2 Fragmented condensates 397

Problems 399

References 399

14 Optical lattices 401

14.1 Generation of optical lattices 402

14.1.1 One-dimensional lattices 403

14.1.2 Higher-dimensional lattices 406

14.1.3 Energy scales 407

14.2 Energy bands 409

14.2.1 Band structure for a single particle 409

14.2.2 Band structure for interacting particles 411

14.2.3 Tight-binding model 416

14.3 Stability 418

14.3.1 Hydrodynamic analysis 421

14.4 Intrinsic non-linear effects 423

14.4.1 Loops 423

14.4.2 Spatial period doubling 427

14.5 From superfluid to insulator 431

14.5.1 Mean-field approximation 433

14.5.2 Effect of trapping potential 439

14.5.3 Experimental detection of coherence 439

Problems 441

References 442

15 Lower dimensions 444

15.1 Non-interacting gases 445

15.2 Phase fluctuations 447

15.2.1 Vortices and the Berezinskii-Kosterlitz-Thouless transition 451

15.3 Microscopic theory of phase fluctuations 453

15.3.1 Uniform systems 455

15.3.2 Anisotropic traps 456

15.4 The one-dimensional Bose gas 460

15.4.1 The strong-coupling limit 461

15.4.2 Arbitrary coupling 466

15.4.3 Correlation functions 474

Problems 479

References 480

16 Fermions 481

16.1 Equilibrium properties 483

16.2 Effects of interactions 486

16.3 Superfluidity 489

16.3.1 Transition temperature 491

16.3.2 Induced interactions 496

16.3.3 The condensed phase 498

16.4 Pairing with unequal populations 506

16.5 Boson-fermion mixtures 508

16.5.1 Induced interactions in mixtures 509

Problems 511

References 513

17 From atoms to molecules 514

17.1 Bose-Einstein condensation of molecules 516

17.2 Diatomic molecules 518

17.2.1 Binding energy and the atom-atom scattering length 518

17.2.2 A simple two-channel model 520

17.2.3 Atom-atom scattering 526

17.3 Crossover:From BCS to BEC 527

17.3.1 Wide and narrow Feshbach resonances 528

17.3.2 The BCS wave function 530

17.3.3 Crossover at zero temperature 531

17.3.4 Condensate fraction and pair wave function 535

17.4 Crossover at non-zero temperature 540

17.4.1 Thermal molecules 540

17.4.2 Pair fluctuations and thermal molecules 543

17.4.3 Density of atoms 548

17.4.4 Transition temperature 549

17.5 A universal limit 550

17.6 Experiments in the crossover region 553

17.6.1 Collective modes 553

17.6.2 Vortices 556

Problems 559

References 560

Appendix.Fundamental constants and conversion factors 562

Index 564