QUANTUM OPTICS

Contents......Page 1
1. Introduction......Page 14
2.1 Field Quantisation......Page 20
2.2 Fock or Number States......Page 23
2.3 Coherent States......Page 25
2.4 Squeezed States......Page 28
2.5 Two-Photon Coherent States......Page 31
2.6 Variance in the Electric Field......Page 33
2.7 Multimode Squeezed States......Page 35
2.8 Phase Properties of the Field......Page 36
Exercises......Page 39
3.1 Field-Correlation Functions......Page 42
3.2 Properties of the Correlation Functions......Page 44
3.3 Correlation Functions and Optical Coherence......Page 45
3.4 First-Order Optical Coherence......Page 47
3.5 Coherent Field......Page 51
3.6 Photon Correlation Measurements......Page 52
3.7 Quantum Mechanical Fields......Page 54
3.7.1 Squeezed States......Page 55
3.8 Phase-Dependent Correlation Functions......Page 57
3.9.1 Classical Theory......Page 59
3.9.3 Fluctuating Intensity - Short-Time Limit......Page 61
3.10 Quantum Mechanical Photon Count Distribution......Page 64
3.10.2 Chaotic Light......Page 65
3.10.3 Photo-Electron Current Fluctuations......Page 66
Exercises......Page 68
4.1 Expansion in Number States......Page 70
4.2.1 P Representation......Page 71
a) Correlation Functions......Page 73
b) Covariance Matrix......Page 74
c) Characteristic Function......Page 75
4.2.2 Wigner's Phase-Space Density......Page 76
c) Number State......Page 77
4.2.3 Q Function......Page 78
4.2.4 P Representation......Page 79
4.2.5 Generalized P Representations......Page 81
4.2.6 Positive P Representation......Page 84
Exercises......Page 85
5.1.1 Degenerate Parametric Amplifier......Page 86
5.1.3 Wigner Function......Page 88
5.2.1 Non-degenerate Parametric Amplifier......Page 90
5.2.2 Squeezing......Page 93
5.2.3 Quadrature Correlations and the Einstein- Podolsky-Rosen Paradox......Page 94
5.2.4 Wigner Function......Page 95
5.2.5 Reduced Density Operator......Page 96
5.3 Quantum Limits to Amplification......Page 98
5.4 Amplitude Squeezed State with Poisson Photon Number Statistics......Page 99
Problems......Page 102
6.1 Master Equation......Page 104
6.2.1 Photon Number Representation......Page 111
6.2.2 P Representation......Page 112
6.2.4 Steady State Solutions - Potential Conditions......Page 114
6.2.5 Time Dependent Solution......Page 116
6.2.6 Q Representation......Page 117
6.2.7 Wigner Function......Page 119
6.2.8 Generalized P Represention......Page 121
a) Complex P Representation......Page 122
b) Positive P Representation......Page 123
6.3 Stochastic Differential Equations......Page 124
6.4 Linear Processes with Constant Diffusion......Page 128
6.5 Two Time Correlation Functions in Quantum Markov Processes......Page 130
6.6 Application to Systems with a P Representation......Page 131
Exercises......Page 132
7.1 Cavity Modes......Page 134
7.2 Linear Systems......Page 137
7.3 Two-Sided Cavity......Page 139
7.4 Two Time Correlation Functions......Page 140
7.6 Parametric Oscillator......Page 142
7.8 Fokker-Planck Equation......Page 145
Exercises......Page 148
8.1 Parametric Oscillation and Second Harmonic Generation......Page 150
8.1.2 Parametric Oscillation......Page 152
8.1.3 Second Harmonic Generation......Page 153
8.1.4 Squeezing Spectrum......Page 154
8.1.5 Parametric Oscillation......Page 155
8.1.6 Experiments......Page 156
8.2 Twin Beam Generation and Intensity Correlations......Page 159
8.2.1 Second Harmonic Generation......Page 163
8.2.2 Experiments......Page 165
8.2.3 Dispersive Optical Bistability......Page 166
8.3.1 Interferometric Detection of Gravitational Radiation......Page 171
8.3.2 Sub-Shot-Noise Phase Measurements......Page 185
Exercises......Page 187
9.1 Optical Parametric Oscillator: Complex P Function......Page 190
9.2 Optical Parametric Oscillator: Positive P Function......Page 195
9.3 Quantum Tunnelling Time......Page 199
9.4 Dispersive Optical Bistability......Page 204
Exercises......Page 206
9.A.1 Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17)......Page 207
9.A.2 Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48)......Page 208
10.1 Quantization of the Electron Wave Field......Page 210
10.2 Interaction Between the Radiation Field and the Electron Wave Field......Page 212
10.3 Interaction of a Two-Level Atom with a Single Mode Field......Page 217
10.4 Quantum Collapses and Revivals......Page 218
10.5 Spontaneous Decay of a Two-Level Atom......Page 219
10.6 Decay of a Two-Level Atom in a Squeezed Vacuum......Page 221
10.7 Phase Decay in a Two-Level System......Page 223
Exercises......Page 224
11.1 Master Equation......Page 226
11.2 Spectrum of the Fluorescent Light......Page 230
11.3 Photon Correlations......Page 234
11.4 Squeezing Spectrum......Page 238
Exercises......Page 241
12.1 Master Equation......Page 242
12.2 Photon Statistics......Page 245
12.2.1 Spectrum of Intensity Fluctuations......Page 246
12.3 Laser Linewidth......Page 248
12.4 Regularly Pumped Laser......Page 249
12.A Appendix: Derivation of the Single-Atom Increment......Page 253
Exercises......Page 257
13.1 Optical Bistability......Page 258
13.2 Nondegenerate Four Wave Mixing......Page 265
13.3 Experimental Results......Page 271
Exercises......Page 272
14.1 The Einstein-Podolsky-Rosen (EPR) Argument......Page 274
14.2 Bell Inequalities and the Aspect Experiment......Page 275
14.3 Violations of Bell's Inequalities Using a Parametric Amplifier Source......Page 281
14.4 One-Photon Interference......Page 286
Exercises......Page 292
15. Quantum Nondemolition Measurements......Page 294
15.1 Concept of a QND measurement......Page 295
15.3 Criteria for a QND Measurement......Page 297
15.4 The Beam Splitter......Page 300
15.5 Ideal Quadrature QND Measurements......Page 303
15.6 Experimental Realisation......Page 304
15.7 A Photon Number QND Scheme......Page 307
Exercises......Page 309
16.1 Quantum Coherence......Page 310
16.2 The Effect of Fluctuations......Page 316
16.3 Quantum Measurement Theory......Page 319
16.4 Examples of Pointer Observables......Page 323
16.5 Model of a Measurement......Page 324
Exercises......Page 326
17. Atomic Optics......Page 328
17.1 Young's Interference with Path Detectors......Page 329
17.1.1 The Feynman Light Microscope......Page 332
17.2 Atomic Diffraction by a Standing Light Wave......Page 334
17.3 Optical Stern-Gerlach Effect......Page 338
17.4 Quantum Non-Demolition Measurement of the Photon Number by Atomic Beam Deflection......Page 343
17.5 Measurement of Atomic Position......Page 347
17.5.1 Atomic Focussing and Contractive States......Page 350
17.A Appendix......Page 352
References......Page 354
Subject Index......Page 5