稀化气体中的玻色-爱因斯坦凝聚 第2版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

稀化气体中的玻色-爱因斯坦凝聚 第2版 英文PDF格式电子书版下载

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1 Introduction1

1.1 Bose-Einstein condensation in atomic clouds4

1.2 Superfluid 4He7

1.3 Other condensates9

1.4 Overview10

Problems15

References15

2 The non-interacting Bose gas17

2.1 The Bose distribution17

2.1.1 Density of states19

2.2 Thansition temperature and condensate fraction21

2.2.1 Condensate fraction24

2.3 Density profile and velocity distribution25

2.3.1 The semi-classical distribution28

2.4 Thermodynamic quantities33

2.4.1 Condensed phase33

2.4.2 Normal phase35

2.4.3 Specific heat close to Tc36

2.5 Effect of finite particle number38

Problems39

References40

3 Atomic properties41

3.1 Atomic structure41

3.2 The Zeeman effect45

3.3 Response to an electric field50

3.4 Energy scales56

Problems58

References59

4 Trapping and cooling of atoms60

4.1 Magnetic traps61

4.1.1 The quadrupole trap62

4.1.2 The TOP trap64

4.1.3 Magnetic bottles and the Ioffe-Pritchard trap66

4.1.4 Microtraps69

4.2 Influence of laser light on an atom71

4.2.1 Forces on an atom in a laser field75

4.2.2 Optical traps77

4.3 Laser cooling:the Doppler process78

4.4 The magneto-optical trap82

4.5 Sisyphus cooling84

4.6 Evaporative cooling96

4.7 Spin-polarized hydrogen103

Problems106

References107

5 Interactions between atoms109

5.1 Interatomic potentials and the van der Waals interaction110

5.2 Basic scattering theory114

5.2.1 Effective interactions and the scattering length119

5.3 Scattering length for a model potential125

5.4 Scattering between different internal states130

5.4.1 Inelastic processes135

5.4.2 Elastic scattering and Feshbach resonances143

5.5 Determination of scattering lengths151

5.5.1 Scattering lengths for alkali atoms and hydrogen154

Problems156

References156

6 Theory of the condensed state159

6.1 The Gross-Pitaevskii equation159

6.2 The ground state for trapped bosons162

6.2.1 A variational calculation165

6.2.2 The Thomas-Fermi approximation168

6.3 Surface structure of clouds171

6.4 Healing of the condensate wave function175

6.5 Condensates with dipolar interactions176

Problems179

References180

7 Dynamics of the condensate182

7.1 General formulation182

7.1.1 The hydrodynamic equations184

7.2 Elementary excitations188

7.3 Collective modes in traps196

7.3.1 Traps with spherical symmetry197

7.3.2 Anisotropic traps200

7.3.3 Collective coordinates and the variational method204

7.4 Surface modes 21l213

7.5 Free expansion of the condensate213

7.6 Solitons215

7.6.1 Dark solitons216

7.6.2 Bright solitons222

Problems223

References224

8 Microscopic theory of the Bose gas225

8.1 The uniform Bose gas226

8.1.1 The Bogoliubov transformation229

8.1.2 Elementary excitations230

8.1.3 Depletion of the condensate231

8.1.4 Ground-state energy233

8.1.5 States with definite particle number234

8.2 Excitations in a trapped gas236

8.3 Non-zero temperature241

8.3.1 The Hartree-Fock approximation242

8.3.2 The Popov approximation248

8.3.3 Excitations in non-uniform gases250

8.3.4 The semi-classical approximation251

Problems253

References253

9 Rotating condensates255

9.1 Potential flow and quantized circulation255

9.2 Structure of a single vortex257

9.2.1 A vortex in a uniform medium257

9.2.2 Vortices with multiple quanta of circulation261

9.2.3 A vortex in a trapped cloud262

9.2.4 An off-axis vortex265

9.3 Equilibrium of rotating condensates265

9.3.1 Traps with an axis of symmetry266

9.3.2 Rotating traps267

9.3.3 Vortex arrays270

9.4 Experiments on vortices273

9.5 Rapidly rotating condensates275

9.6 Collective modes in a vortex lattice280

Problems286

References288

10 Superfluidity290

10.1 The Landau criterion291

10.2 The two-component picture294

10.2.1 Momentum carried by excitations294

10.2.2 Normal fluid density295

10.3 Dynamical processes296

10.4 First and second sound300

10.5 Interactions between excitations307

10.5.1 Landau damping308

Problems314

References315

11 Trapped clouds at non-zero temperature316

11.1 Equilibrium properties317

11.1.1 Energy scales317

11.1.2 Transition temperature319

11.1.3 Thermodynamic properties321

11.2 Collective modes325

11.2.1 Hydrodynamic modes above Tc328

11.3 Collisional relaxation above Tc334

11.3.1 Relaxation of temperature anisotropies339

11.3.2 Damping of oscillations342

Problems345

References346

12 Mixtures and spinor condensates348

12.1 Mixtures349

12.1.1 Equilibrium properties350

12.1.2 Collective modes354

12.2 Spinor condensates356

12.2.1 Mean-field description358

12.2.2 Beyond the mean-field approximation360

Problems363

References364

13 Interference and correlations365

13.1 Tunnelling between two wells365

13.1.1 Quantum fluctuations371

13.1.2 Squeezed states373

13.2 Interference of two condensates374

13.2.1 Phase-locked sources375

13.2.2 Clouds with definite particle number381

13.3 Density correlations in Bose gases384

13.3.1 Collisional shifts of spectral lines386

13.4 Coherent matter wave optics390

13.5 Criteria for Bose-Einstein condensation394

13.5.1 The density matrix394

13.5.2 Fragmented condensates397

Problems399

References399

14 Optical lattices401

14.1 Generation of optical lattices402

14.1.1 One-dimensional lattices403

14.1.2 Higher-dimensional lattices406

14.1.3 Energy scales407

14.2 Energy bands409

14.2.1 Band structure for a single particle409

14.2.2 Band structure for interacting particles411

14.2.3 Tight-binding model416

14.3 Stability418

14.3.1 Hydrodynamic analysis421

14.4 Intrinsic non-linear effects423

14.4.1 Loops423

14.4.2 Spatial period doubling427

14.5 From superfluid to insulator431

14.5.1 Mean-field approximation433

14.5.2 Effect of trapping potential439

14.5.3 Experimental detection of coherence439

Problems441

References442

15 Lower dimensions444

15.1 Non-interacting gases445

15.2 Phase fluctuations447

15.2.1 Vortices and the Berezinskii-Kosterlitz-Thouless transition451

15.3 Microscopic theory of phase fluctuations453

15.3.1 Uniform systems455

15.3.2 Anisotropic traps456

15.4 The one-dimensional Bose gas460

15.4.1 The strong-coupling limit461

15.4.2 Arbitrary coupling466

15.4.3 Correlation functions474

Problems479

References480

16 Fermions481

16.1 Equilibrium properties483

16.2 Effects of interactions486

16.3 Superfluidity489

16.3.1 Transition temperature491

16.3.2 Induced interactions496

16.3.3 The condensed phase498

16.4 Pairing with unequal populations506

16.5 Boson-fermion mixtures508

16.5.1 Induced interactions in mixtures509

Problems511

References513

17 From atoms to molecules514

17.1 Bose-Einstein condensation of molecules516

17.2 Diatomic molecules518

17.2.1 Binding energy and the atom-atom scattering length518

17.2.2 A simple two-channel model520

17.2.3 Atom-atom scattering526

17.3 Crossover:From BCS to BEC527

17.3.1 Wide and narrow Feshbach resonances528

17.3.2 The BCS wave function530

17.3.3 Crossover at zero temperature531

17.3.4 Condensate fraction and pair wave function535

17.4 Crossover at non-zero temperature540

17.4.1 Thermal molecules540

17.4.2 Pair fluctuations and thermal molecules543

17.4.3 Density of atoms548

17.4.4 Transition temperature549

17.5 A universal limit550

17.6 Experiments in the crossover region553

17.6.1 Collective modes553

17.6.2 Vortices556

Problems559

References560

Appendix.Fundamental constants and conversion factors562

Index564