Physical Foundations of Quantum Electronics by David Klyshko

Contents......Page 14
Preface......Page 6
Foreword......Page 8
List of Notation and Acronyms......Page 10
1. Introduction......Page 22
1.1.2 Population inversion......Page 23
1.1.3 Feedback and the lasing condition......Page 24
1.1.4 Saturation and relaxation......Page 25
1.2 History of quantum electronics......Page 26
1.2.2 Radio spectroscopy......Page 27
1.2.3 Masers......Page 28
1.2.4 Lasers......Page 29
1.3.1 Physics of lasers......Page 30
1.3.3 New trends in nonlinear optics......Page 31
1.3.5 Optics of nonclassical light......Page 32
2.1 Amplitude and probability of a transition......Page 36
2.1.1 Unperturbed atom......Page 37
2.1.2 Atom in an alternating field......Page 39
2.1.3 Perturbation theory......Page 40
2.1.4 Linear approximation......Page 41
2.2.1 Dipole approximation......Page 42
2.2.2 Transition probability......Page 43
2.2.3 Finite level widths......Page 45
2.3.1 Relation between intensity and field amplitude......Page 47
2.3.2 Cross-section of resonance interaction......Page 48
2.3.4 Photon kinetics......Page 49
2.3.5 Coefficient of resonance absorption......Page 50
2.3.6 Amplification bandwidth......Page 51
2.3.7  Degeneracy of the levels......Page 52
2.4.1 Correlation functions......Page 54
2.4.2 Transition rate......Page 55
2.4.4  Spectral field density......Page 56
2.5 Field as a thermostat......Page 57
2.5.1 Spontaneous transitions......Page 58
2.5.2 Natural bandwidth......Page 59
2.5.3 Number of photons, spectral brightness, and brightness temperature......Page 60
2.5.4  Relaxation time......Page 62
3.1.1 Observables......Page 64
3.1.2 Density matrix of a pure state......Page 65
3.1.3 Mixed states......Page 66
3.1.4  More general definition of the density matrix......Page 68
3.1.5 Properties of the density matrix......Page 69
3.1.6  Density matrix and entropy......Page 70
3.1.7  Density matrix of an atom......Page 71
3.2.1 Equilibrium populations......Page 72
3.2.2 Two-level system and the negative temperature......Page 73
3.2.3  Populations in semiconductors......Page 74
3.2.4  Inversion in semiconductors......Page 76
3.3.1 Non-equilibrium systems......Page 77
3.3.2 Von Neumann equation......Page 78
3.3.4 Evolution of a closed system......Page 79
3.3.5 Transverse and longitudinal relaxation......Page 80
3.3.6 Interaction picture......Page 83
3.3.7  Perturbation theory......Page 85
4.1 Definition and general properties of susceptibility......Page 88
4.1.1 Symmetry......Page 89
4.1.2 The role of causality......Page 90
4.1.3 Absorption of a given field......Page 91
4.1.4  Susceptibility of the vacuum......Page 92
4.1.5  Thermodynamic approach......Page 93
4.2.1 Dispersion law......Page 96
4.2.2 The effect of absorption......Page 97
4.2.3 Classical theory of dispersion......Page 98
4.2.4 Quantum theory of dispersion......Page 100
4.2.5  Oscillator strength......Page 102
4.2.6 Isolated resonance......Page 103
4.2.7  Polaritons......Page 106
4.3.1 Applicability of the model......Page 110
4.3.2 Kinetic equations......Page 111
4.3.3 Saturation......Page 112
4.3.4  Lineshape in the presence of saturation......Page 113
4.4.1 Kinetic equations for the mean values......Page 116
4.4.2 Pauli matrices and expansion of operators......Page 117
4.4.3 The Bloch vector and the Bloch sphere......Page 120
4.4.4 Higher moments and distributions .......Page 121
4.4.5 Bloch equations......Page 122
4.4.6 Equation for polarization......Page 124
4.4.7 Magnetic resonance......Page 125
5. Non-Stationary Optics......Page 128
5.1.1 Atom as a gyroscope......Page 129
5.1.2 Analytical solution......Page 131
5.1.3  Nutation......Page 133
5.1.4 Self-induced transparency......Page 135
5.2 Emission of an atom......Page 136
5.2.1 Emission of a dipole......Page 137
5.2.2 Probability of a spontaneous transition......Page 138
5.2.3  Normally ordered emission......Page 139
5.2.4 Relation between spontaneous and thermal emission......Page 141
5.2.6  Quantum beats......Page 142
5.2.7  Resonance fluorescence......Page 145
5.3.1 Superradiance......Page 148
5.3.2 Analogy with phase transitions......Page 151
5.3.3 Photon echo......Page 152
6. Nonlinear Optics......Page 156
6.1 Nonlinear susceptibilities: definitions and general properties......Page 158
6.1.1 Nonlinear susceptibilities......Page 159
6.1.2  Various definitions......Page 160
6.1.4  Transparent matter......Page 162
6.1.5 The role of the material symmetry......Page 165
6.2 Models of optical anharmonicity......Page 166
6.2.1 Anharmonicity of a free electron......Page 167
6.2.2  Light pressure .......Page 170
6.2.3 Striction anharmonicity......Page 173
6.2.4 Anharmonic oscillator......Page 175
6.2.5 Raman anharmonicity......Page 178
6.2.6 Temperature anharmonicity......Page 183
6.2.7 Electrocaloric anharmonicity......Page 185
6.2.8 Orientation anharmonicity......Page 187
6.2.9  Quantum theory of nonlinear polarization......Page 190
6.2.10  Probability of multi-photon transitions......Page 194
6.3.1 Initial relations......Page 198
6.3.2 Classification of nonlinear effects......Page 199
6.3.3 The role of linear and nonlinear dispersion......Page 202
6.3.4  One-dimensional approximation......Page 203
6.3.5 The Manley-Rowe relation and the permutation symmetry......Page 208
6.3.6  Derivation of one-dimensional equations......Page 210
6.4.1 Nonlinear absorption......Page 212
6.4.2 Doppler-free spectroscopy......Page 216
6.4.3 Raman amplification......Page 218
6.4.4 Spontaneous and stimulated scattering......Page 220
6.4.5 Self-focusing......Page 222
6.4.6  Self-focusing length......Page 224
6.5 Parametric interactions......Page 228
6.5.1 Undepleted-pump approximation the near field......Page 229
6.5.2 The far field......Page 231
6.5.3 Three-wave interaction......Page 233
6.5.4 Frequency up-conversion......Page 234
6.5.5 Parametric amplification and oscillation......Page 235
6.5.6 Backward interaction......Page 237
6.5.7 Second harmonic generation......Page 238
6.5.8 The scattering matrix......Page 240
6.5.9  Parametric down-conversion......Page 241
6.5.10  Light scattering by polaritons......Page 246
6.5.11 Four-wave interactions......Page 247
6.5.12 Nonlinear spectroscopy......Page 249
6.5.13 Dynamical holography and phase conjugation......Page 250
7. Statistical Optics......Page 258
7.1.1 The Kirchho  law for a single mode......Page 260
7.1.2 The Kirchho  law for a negative temperature......Page 262
7.1.3 Noise of a multimode amplifier......Page 266
7.1.4 Equilibrium and spontaneous radiation; superfluorescence......Page 267
7.1.5 Gain and bandwidth of a cavity amplifier......Page 269
7.1.6 The Kirchho  law for a cavity amplifier. The Townes equation......Page 272
7.2 Basic concepts of the statistical optics......Page 273
7.2.1 Analytical signal......Page 274
7.2.2 Random intensity......Page 275
7.2.3 Correlation functions......Page 277
7.2.4 Temporal coherence......Page 278
7.2.5 Spatial coherence......Page 280
7.2.6 Coherence volume and the degeneracy factor......Page 281
7.2.7 Statistics of photocounts and the Mandel formula......Page 283
7.2.8 Photon bunching......Page 286
7.2.9 Intensity correlation......Page 287
7.2.10 Second-order coherence (added by the Editors)......Page 291
7.3.1 Maxwell’s equations in the k, t representation......Page 294
7.3.2 Canonical field variables......Page 299
7.3.3  Hamiltonian of the field and the matter......Page 301
7.3.4  Dipole approximation......Page 304
7.4.1 Commutation relations......Page 306
7.4.2 Quantization of macroscopic field in matter......Page 308
7.5  States of the field and their properties......Page 309
7.5.1 Dirac’s notation......Page 310
7.5.2 Energy states......Page 312
7.5.3 Coherent states......Page 315
7.5.4 Coordinate and momentum states......Page 319
7.5.5 Squeezed states......Page 323
7.5.6 Mixed states......Page 326
7.5.7 Entangled states (added by the Editors)......Page 331
7.6.1 Photon statistics......Page 335
7.6.2 Photon bunching and anti-bunching......Page 339
7.6.3 Statistics of photoelectrons......Page 344
7.7  Interaction of an atom with quantized field......Page 348
7.7.1 Absorption and emission probabilities......Page 349
7.7.2 Spontaneous emission......Page 350
7.7.3 Interaction of stationary systems......Page 352
7.7.4 Spectral representation......Page 354
7.7.5 Equilibrium systems. FDT......Page 356
Bibliography......Page 358
Index......Page 364