1 Introduction 1
1.1 Scope and aims of this book 1
1.2 History 2
1.3 The contents of this book 7
References 8
Suggestions for further reading 8
2 Field quantization 10
2.1 Quantization of a single-mode field 10
2.2 Quantum fluctuations of a single-mode field 15
2.3 Quadrature operators for a single-mode field 17
2.4 Multimode fields 18
2.5 Thermal fields 25
2.6 Vacuum fluctuations and the zero-point energy 29
2.7 The quantum phase 33
Problems 40
References 41
Bibliography 42
3 Coherent states 43
3.1 Eigenstates of the annihilation operator and minimum uncertainty states 43
3.2 Displaced vacuum states 48
3.3 Wave packets and time evolution 50
3.4 Generation of coherent states 52
3.5 More on the properties of coherent states 53
3.6 Phase-space pictures of coherent states 56
3.7 Density operators and phase-space probability distributions 59
3.8 Characteristic functions 65
Problems 71
References 72
Bibliography 73
4 Emission and absorption of radiation by atoms 74
4.1 Atom-field interactions 74
4.2 Interaction of an atom with a classical field 76
4.3 Interaction of an atom with a quantized field 82
4.4 The Rabi model 87
4.5 Fully quantum-mechanical model；the Jaynes-Cummings model 90
4.6 The dressed states 99
4.7 Density-operator approach：application to thermal states 102
4.8 The Jaynes-Cummings model with large detuning：a dispersive interaction 105
4.9 Extensions of the Jaynes-Cummings model 107
4.10 Schmidt decomposition and von Neumann entropy for the Jaynes-Cummings model 108
Problems 110
References 113
Bibliography 114
5 Quantum coherence functions 115
5.1 Classical coherence functions 115
5.2 Quantum coherence functions 120
5.3 Young’s interference 124
5.4 Higher-order coherence functions 127
Problems 133
References 133
Bibliography 134
6 Beam splitters and interferometers 135
6.1 Experiments with single photons 135
6.2 Quantum mechanics of beam splitters 137
6.3 Interferometry with a single photon 143
6.4 Interaction-free measurement 144
6.5 Interferometry with coherent states of light 146
Problems 147
References 149
Bibliography 149
7 Nonclassical light 150
7.1 Quadrature squeezing 150
7.2 Generation of quadrature squeezed light 165
7.3 Detection of quadrature squeezed light 167
7.4 Amplitude（or number）squeezed states 169
7.5 Photon antibunching 171
7.6 Schrodinger cat states 174
7.7 Two-mode squeezed vacuum states 182
7.8 Higher-order squeezing 188
7.9 Broadband squeezed light 189
Problems 190
References 192
Bibliography 194
8 Dissipative interactions and decoherence 195
8.1 Introduction 195
8.2 Single realizations or ensembles？ 196
8.3 Individual realizations 200
8.4 Shelving and telegraph dynamics in three-level atoms 204
8.5 Decoherence 207
8.6 Generation of coherent states from decoherence：nonlinear optical balance 208
8.7 Conclusions 210
Problems 211
References 211
Bibliography 212
9 Optical test of quantum mechanics 213
9.1 Photon sources：spontaneous parametric down-conversion 214
9.2 The Hong-Ou-Mandel interferometer 217
9.3 The quantum eraser 219
9.4 Induced coherence 222
9.5 Superluminal tunneling of photons 224
9.6 Optical test of local realistic theories and Bell’s theorem 226
9.7 Franson’s experiment 232
9.8 Applications of down-converted light to metrology without absolute standards 233
Problems 235
References 236
Bibliography 237
10 Experiments in cavity QED and with trapped ions 238
10.1 Rydberg atoms 238
10.2 Rydberg atom interacting with a cavity field 241
10.3 Experimental realization of the Jaynes-Cummings model 246
10.4 Creating entangled atoms in CQED 249
10.5 Formation of Schrodinger cat states with dispersive atom-field interactions and decoherence from the quantum to the classical 250
10.6 Quantum nondemolition measurement of photon number 254
10.7 Realization of the Jaynes-Cummings interaction in the motion of a trapped ion 255
10.8 Concluding remarks 258
Problems 259
References 260
Bibliography 261
11 Applications of entanglement：Heisenberg-limited interferometry and quantum information processing 263
11.1 The entanglement advantage 264
11.2 Entanglement and interferometric measurements 265
11.3 Quantum teleportation 268
11.4 Cryptography 270
11.5 Private key crypto-systems 271
11.6 Public key crypto-systems 273
11.7 The quantum random number generator 274
11.8 Quantum cryptography 275
11.9 Future prospects for quantum communication 281
11.10 Gates for quantum computation 281
11.11 An optical realization of some quantum gates 286
11.12 Decoherence and quantum error correction 289
Problems 290
References 291
Bibliography 293
Appendix A The density operator，entangled states，the Schmidt decomposition，and the von Neumann entropy 294
A.1 The density operator 294
A.2 Two-state system and the Bloch sphere 297
A.3 Entangled states 298
A.4 Schmidt decomposition 299
A.5 von Neumann entropy 301
A.6 Dynamics of the density operator 302
References 303
Bibliography 303
Appendix B Quantum measurement theory in a（very small） nutshell 304
Bibliography 307
Appendix C Derivation of the effective Hamiltonian for dispersive（far off-resonant）interactions 308
References 311
Appendix D Nonlinear optics and spontaneous parametric down-conversion 312
References 313
Index 314