Table of Contents
Preface v
Chapter 1 Introduction 1
References 7
Part I Toward Strongly Correlated Systems 9
Chapter 2 Atomic Structure 11
2.1 Electronic levels of alkali-metal atoms 11
2.2 Fine structure 13
2.3 Hyperfine structure 14
2.4 Zeeman effect 16
Chapter 3 Atom-Light Interaction 21
3.1 Atom-light interaction Hamiltonian 21
3.2 Spontaneous emission 25
3.3 Stimulated absorption and emission 29
3.4 The optical Bloch equations 34
3.5 Light forces on atoms 37
References 41
Chapter 4 Laser Cooling and Trapping 43
4.1 Beam deceleration 44
4.2 Doppler cooling 47
4.3 Evaporative cooling 50
4.4 Magnetic trapping 55
4.5 Optical trapping 59
References 62
Chapter 5 Interaction Between Atoms 65
5.1 Interaction potential between alkali-metal atoms 66
5.2 Two-atom scattering in free space 69
5.3 Effective interaction 74
References 81
Chapter 6 Feshbach Resonance 83
6.1 Basic physics of the Feshbach resonance 84
6.2 Magnetic Feshbach resonance 92
6.3 Optical Feshbach resonance 97
References 100
Part II Ultracold Fermi Gases 103
Chapter 7 Background and Experimental Achievements 105
7.1 Brief introduction to experimental achievements 106
7.2 BCS-BEC crossover 113
7.3 Overview 117
References 118
Chapter 8 BCS-BEC Crossover 121
8.1 Cooper instability 121
8.2 BCS theory 123
8.3 Description of BCS-BEC crossover on the mean-field level 130
8.4 Feshbach resonance and the two-channel model 136
8.5 Narrow Feshbach resonance 143
8.6 BCS-BEC crossover in a harmonic trapping potential 145
References 151
Chapter 9 Beyond-Mean-Field Descriptions 153
9.1 NSR scheme 154
9.2 Path integral and saddle point expansion 157
9.3 Extension of the NSR scheme based on the T-matrix formalism 165
References 170
Chapter 10 Polarized Fermi Gas 173
10.1 Mean-field results 175
10.2 Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase 180
10.3 Polarized Fermi gas in a trap 182
References 184
Chapter 11 Synthetic Gauge Field 187
11.1 Implementing synthetic gauge field 187
11.2 Synthetic spin-orbit coupling 191
11.3 Exotic pairing states under spin-orbit coupling 195
References 201
Part III Quantum Simulation with Cold Atoms 203
Chapter 12 Optical Lattice and Band Structure 205
12.1 Construction of optical lattices 206
12.2 Band structure 210
References 213
Chapter 13 Simulation of the Bose-Hubbard Model 215
13.1 Introduction to the Bose-Hubbard model 215
13.2 Simulation of the Bose-Hubbard model in optical lattices 218
References 223
Chapter 14 Dynamical Process 225
14.1 Quench dynamics in the Bose-Hubbard model 225
14.2 Thermalization in an optical lattice 229
References 239
Chapter 15 Disordered Systems 241
15.1 Disorder in free space 242
15.2 Disorder in an optical lattice 244
References 250
Chapter 16 Simulation of Spin Systems 253
16.1 General phases of spin systems 253
16.2 Simulate spin systems in an optical lattice 264
References 274
