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1 Introduction1

1.1 Scope and aims of this book1

1.2 History2

1.3 The contents of this book7

References8

Suggestions for further reading8

2 Field quantization10

2.1 Quantization of a single-mode field10

2.2 Quantum fluctuations of a single-mode field15

2.3 Quadrature operators for a single-mode field17

2.4 Multimode fields18

2.5 Thermal fields25

2.6 Vacuum fluctuations and the zero-point energy29

2.7 The quantum phase33

Problems40

References41

Bibliography42

3 Coherent states43

3.1 Eigenstates of the annihilation operator and minimum uncertainty states43

3.2 Displaced vacuum states48

3.3 Wave packets and time evolution50

3.4 Generation of coherent states52

3.5 More on the properties of coherent states53

3.6 Phase-space pictures of coherent states56

3.7 Density operators and phase-space probability distributions59

3.8 Characteristic functions65

Problems71

References72

Bibliography73

4 Emission and absorption of radiation by atoms74

4.1 Atom-field interactions74

4.2 Interaction of an atom with a classical field76

4.3 Interaction of an atom with a quantized field82

4.4 The Rabi model87

4.5 Fully quantum-mechanical model；the Jaynes-Cummings model90

4.6 The dressed states99

4.7 Density-operator approach：application to thermal states102

4.8 The Jaynes-Cummings model with large detuning：a dispersive interaction105

4.9 Extensions of the Jaynes-Cummings model107

4.10 Schmidt decomposition and von Neumann entropy for the Jaynes-Cummings model108

Problems110

References113

Bibliography114

5 Quantum coherence functions115

5.1 Classical coherence functions115

5.2 Quantum coherence functions120

5.3 Young’s interference124

5.4 Higher-order coherence functions127

Problems133

References133

Bibliography134

6 Beam splitters and interferometers135

6.1 Experiments with single photons135

6.2 Quantum mechanics of beam splitters137

6.3 Interferometry with a single photon143

6.4 Interaction-free measurement144

6.5 Interferometry with coherent states of light146

Problems147

References149

Bibliography149

7 Nonclassical light150

7.1 Quadrature squeezing150

7.2 Generation of quadrature squeezed light165

7.3 Detection of quadrature squeezed light167

7.4 Amplitude（or number）squeezed states169

7.5 Photon antibunching171

7.6 Schrodinger cat states174

7.7 Two-mode squeezed vacuum states182

7.8 Higher-order squeezing188

7.9 Broadband squeezed light189

Problems190

References192

Bibliography194

8 Dissipative interactions and decoherence195

8.1 Introduction195

8.2 Single realizations or ensembles？196

8.3 Individual realizations200

8.4 Shelving and telegraph dynamics in three-level atoms204

8.5 Decoherence207

8.6 Generation of coherent states from decoherence：nonlinear optical balance208

8.7 Conclusions210

Problems211

References211

Bibliography212

9 Optical test of quantum mechanics213

9.1 Photon sources：spontaneous parametric down-conversion214

9.2 The Hong-Ou-Mandel interferometer217

9.3 The quantum eraser219

9.4 Induced coherence222

9.5 Superluminal tunneling of photons224

9.6 Optical test of local realistic theories and Bell’s theorem226

9.7 Franson’s experiment232

9.8 Applications of down-converted light to metrology without absolute standards233

Problems235

References236

Bibliography237

10 Experiments in cavity QED and with trapped ions238

10.1 Rydberg atoms238

10.2 Rydberg atom interacting with a cavity field241

10.3 Experimental realization of the Jaynes-Cummings model246

10.4 Creating entangled atoms in CQED249

10.5 Formation of Schrodinger cat states with dispersive atom-field interactions and decoherence from the quantum to the classical250

10.6 Quantum nondemolition measurement of photon number254

10.7 Realization of the Jaynes-Cummings interaction in the motion of a trapped ion255

10.8 Concluding remarks258

Problems259

References260

Bibliography261

11 Applications of entanglement：Heisenberg-limited interferometry and quantum information processing263

11.1 The entanglement advantage264

11.2 Entanglement and interferometric measurements265

11.3 Quantum teleportation268

11.4 Cryptography270

11.5 Private key crypto-systems271

11.6 Public key crypto-systems273

11.7 The quantum random number generator274

11.8 Quantum cryptography275

11.9 Future prospects for quantum communication281

11.10 Gates for quantum computation281

11.11 An optical realization of some quantum gates286

11.12 Decoherence and quantum error correction289

Problems290

References291

Bibliography293

Appendix A The density operator，entangled states，the Schmidt decomposition，and the von Neumann entropy294

A.1 The density operator294

A.2 Two-state system and the Bloch sphere297

A.3 Entangled states298

A.4 Schmidt decomposition299

A.5 von Neumann entropy301

A.6 Dynamics of the density operator302

References303

Bibliography303

Appendix B Quantum measurement theory in a（very small） nutshell304

Bibliography307

Appendix C Derivation of the effective Hamiltonian for dispersive（far off-resonant）interactions308

References311

Appendix D Nonlinear optics and spontaneous parametric down-conversion312

References313

Index314