Contents
Preface
Chapter 1 Interaction between Electromagnetic Fields and an Atom 1
1.1 The quantized atom-field Hamiltonian in a classical picture 1
1.1.1 Energy quantization of the atom 5
1.1.2 Energy quantization of the electromagnetic field 6
1.1.3 Energy quantization of interaction 8
1.2 Atom-field interactions of two-level atom 13
1.3 Atom-field interaction for three-level atom 17
1.4 The semiclassical atom-field Hamiltonian 20
1.4.1 Comparison with the quantization field 21
1.4.2 Quantization of the electronic waves: Atomic dipole between atomic levels 22
1.5 The Gauge transformation of atom-field Hamiltonian 24
Chapter 2 Maxwell-Bloch Model and Jaynes-Cummings Model for Atom-field Interaction 30
2.1 The different models for electromagnetic fields and two-level atom 31
2.1.1 Semiclassical model: Maxwell-Bloch model or Rabi model 31
2.1.2 The quantum model: Jaynes-Cummings model 36
2.2 The solutions of Maxwell-Bloch model 39
2.2.1 The wave function method 39
2.2.2 Density matrix method 57
2.3 The solutions of Jaynes-Cummings model 88
2.3.1 JCM with rotating wave approximation 88
2.3.2 JCM beyond rotating wave approximation 137
2.3.3 JCM driven by quantum and classical fields 145
Chapter 3 The Quantum Coherence E.ects of the Multi-level Atom 147
3.1 Three-level atom models 147
3.2 Dark state and the coherent population trapping 148
3.2.1 The resonant case for dark state 151
3.2.2 Quantum beat 155
3.2.3 Electromagnetically induced transparency 159
3.3 The laser 164
Chapter 4 The Radiation Spectrum of Atoms in the Electromagnetic Fields 170
4.1 The atom-field system in the environment 170
4.1.1 The system and the environment 173
4.1.2 A cavity mode in the environment: Heisenberg-Langevin approach 175
4.1.3 An atom in the environment: The quantum Langevin equation 184
4.1.4 An atom in the environment: The density operator method 190
4.2 The resonance °uorescence spectrum of two-level atoms 202
4.2.1 Spontaneous emission of a two-level atom 203
4.2.2 Resonance °uorescence from a driven two-level atom 206
Chapter 5 Dicke Model and Tavis-Cummings Model for Atom-field Interaction 216
5.1 The Hamiltonian of interaction between electromagnetic field and a collection of atoms 216
5.2 The level structures of the TCM 217
5.2.1 Energy levels of two-atom model 220
5.2.2 Energy levels of three-atom model 222
5.2.3 Energy levels of N-atom model 224
5.3 The solutions of the TCM 226
5.3.1 One atom case 226
5.3.2 Two atoms case 227
5.4 Superradiance and phase transition of Dicke model 229
5.4.1 Superradiant phenomenon 229
5.4.2 Superradiant phase transition 232
Chapter 6 The Electromagnetic Waves in Atomic Media 242
6.1 Electric field wave in the vacuum 243
6.2 Electric field waves in the dielectric medium 245
6.2.1 The medium equation 246
6.2.2 The electric field wave in one-dimensional dispersive medium 249
6.2.3 The electric field wave in two-level atomic medium 251
6.3 Pulse-area theorem 254
Chapter 7 The Interaction between Electromagnetic Fields and a Moving Atom 259
7.1 The Hamiltonian with atomic center of mass motion 259
7.1.1 Hamiltonian of atom-field interaction with atomic motion 259
7.1.2 The semiclassical Hamiltonian 261
7.1.3 The dynamics of a moving two-level atom in a monochromatic EM field 265
7.2 Complex dynamics of atom in varying lattice: The double resonance model 275
7.2.1 The Hamiltonian of the double resonance model 275
7.2.2 Classical dynamics of the atom 278
7.2.3 Quantum symmetry and the lattice wave of the system 301
7.2.4 Floquet theory for periodic driving 305
7.2.5 System with spatial and temporal period: Lattice waves 310
7.3 Mechanical e.ect of light field 314
7.3.1 The mechanical force induced by dipole interaction 314
7.3.2 A full theory of optical force 315
7.4 Maxwell-Bloch model with external freedom 320
7.4.1 The Bloch equations with external freedom in one-dimensional case 324
7.4.2 Typical models and solutions of Bloch equations with external motion 327
7.5 Atom cooling and trapping 335
7.5.1 The radiation pressure force 337
7.5.2 Doppler cooling 338
7.5.3 The dipole force for trapping 341
7.6 Hybrid model: A driven two-level atom in a cavity field 342
Chapter 8 The Interaction between Electromagnetic Fields and Mechanical Modes 344
8.1 The cavity optomechanics model 345
8.1.1 The traditional model and Langevin equation of motion 353
8.1.2 The Modified Hamiltonian and Langevin equation 354
8.1.3 The linearization method 355
8.2 The classical dynamics of optomechanical system 357
8.2.1 Steady states: The nonlinear static responses 357
8.2.2 The nonlinear dynamics and the self-sustained oscillation 359
8.2.3 The instability and the cha
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