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| Gardiner C.W. — Quantum Noise |
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| Предметный указатель |
Ito integral, relation to Stratonovich with squeezed white noise 335
Johnson, J.B. 4 347
Josephson junction 43 58
Jung, R. 348
Kac, M. 10 11 90 347 348
Kimble, H.J. 339 349 350
Kinsler, P. 212 349
Klauder, J.R. 348
Koch, R.H. 6 137 347 348
Kramers' equation, in Wigner function treatment of quantum Brownian motion 194
Kubo, R. 348
Lagrange multiplier 37
Laguerre polynomial 128
Lamb shift 43 87 150
Lamb shift in two level atom master equation 283
Lamb shift, modification using density of states 283
Landau, L.D. 36 347
Landauer, R. 45 348
Langevin correlation function, as a function of time 59
Langevin equation, derivation of 46
Laser 292
Laser field 20
Laser Fokker — Planck equation, derivation 300
Laser Fokker — Planck equation, derivation by adiabatic elimination 302
Laser Fokker — Planck equation, evaluation of noise terms 303
Laser Fokker — Planck equation, stationary solution 305
Laser Fokker — Planck equation, use of P-representation 301
Laser Langevin equations see "Laser SDEs"
Laser potential 305
Laser potential, plotted 299
Laser SDEs, solutions 305
Laser SDEs, solutions of linearised form 306
Laser, asymptotic expansion in number of atoms 296
Laser, co-operativity parameter 297
Laser, configuration 293
Laser, correlation functions 307
Laser, linewidth 310
Laser, macroscopic equations 296
Laser, Master equation 300
Laser, nature of laser light 308
Laser, phase fluctuations 310
Laser, phase space methods 315
Laser, potential 298
Laser, pump parameter 297
Laser, quantum Langevin equations for 294
Laser, scaling behaviour of parameters 304
Laser, scaling with number of atoms 315 323
Laser, stationary solutions 297
Laser, stochastic differential equations in P-representation 305
Laser, time dependent macroscopic solutions 298
Lax, M. 13 140 157 294 347 349 349
LC circuit 100
Leggett, A.J. 91 348
Lehmann, H. 348
Lewenstein, m. 350
Lifshitz, I.M. 36 347
Light beams 239
Light field, classical 19
Light, absorption of 7
Light, emission of 7
Linewidth, spectral 1
Liouvillian operators, in derivation of master equation 145
Local coupling 42
Local oscillator noise 264
Locality, and damping 52
Louisell, W. 88 140 294 347 349 348 349
LRC circuit 6 66
LSZ formulation of quantum field theory 57
Lugiato, L.A. 350
Macroscopic coherence, destruction of in quantum Brownian motion 225
Macroscopic coherence, quantum optical situation 227
Macroscopic limit in open quantum systems 224
Macroscopic quantum coherence, using the adjoint equation 90
Mandel's counting formula 257 258
Mandel's counting formula, coherent state 260
Mandel's counting formula, input-output theory of photodetection 269
Mandel's counting formula, number state 260
Mandel's counting formula, photon counting formula 258
Mandel's counting formula, thermal state 261
Map, completely positive 32
Markov approximation 91
Markov approximation and weak coupling limit 147
Markov approximation in derivation of the master equation 144—145
Markov assumption, in derivation of photon counting formulae 246
Markov interpretation, in quantum Markov process 156
Markov property 140
Marshall, T.W. 348
Martinis, J.M. 348
Master equation 13 18 72 77
Master equation with several frequencies 173
Master equation, applying 180
Master equation, classical 14
Master equation, connection with QSDEs 171
Master equation, derivation based on projection operators 145
Master equation, derivation from QSDE 172
Master equation, derivation from the adjoint equation 78
Master equation, duality with stochastic differential equation 140
Master equation, equivalence to QSDE 174
Master equation, history 140
Master equation, laser 300
Master equation, notation for 151
Master equation, number state basis 180
Master equation, Pauli 14 18 19
Master equation, photon counting 248
Master equation, physical basis 141
Master equation, projection operator derivation 145
Master equation, quantum Brownian motion 81 151 224
Master equation, quantum Brownian motion limit 147
Master equation, quantum Brownian motion, Wigner function treatment 194
Master equation, quantum optical, derivation of 141
Master equation, quantum optical, derived 147
Master equation, quantum optical, derived from the adjoint equation 86
Master equation, quantum optical, general form 144
Master equation, weak coupling limit in derivation of 146
Maxwell's equations 233
Mazur, P. 347 348
McKenna, J. 348
McNeil, K.J. 349
Mean square displacement, in quantum Brownian motion 63
Measurement 213
Measurement of the first kind 29
Measurement of the second kind 29
Measurement postulates 26 29
Measurement, back action evading 4
Measurement, general kinds of 29
Measurement, imprecise 25-26
measurement, precise 25
Measurement, projection postulate, model derivation 231
Measurement, quantum model of 228
Measurement, quantum non-demolition 4
Measurements and the density operator 31
Measurements, multitime 33
Measurements, sequences of 33
Memory function 48
Milburn, G.J. 349
Minimum uncertainty states, coherent states as 107
Mode functions for electromagnetic field 234
Moments, normally ordered 269
Mortimer, I.K. 208 349
Multitime averages, computation of in quantum Markov process 153
Multitime measurement, expression as a correlation function 34
Multitime measurements 33
Multitime structure, of quantum Markov process 153
Narducci, L.M. 350
Negative temperature 215
Negative temperature bath, QSDE 220
Noise input 43
Noise inputs and outputs 55
Noise interpretation of inputs and outputs 57
Noise operators, classical limit of 59
| Noise operators, correlation function of 59
Noise operators, thermal 58
Noise output 43
Noise sources of several frequencies, in QSDEs 170
Noise sources, commutation relations for 49—50
Noise temperature 218
Noise, added 217
Noise, Hamiltonian 192
Noise, local oscillator 264
Noise, vacuum 43
Non-linear couplings 45
Normal product 5
Normal product, defined 112
Normally ordered moments and Mandel's formula 269
Normally ordered moments and quantum characteristic function 121
Number states, of harmonic oscillator 102
Nyquist's Theorem 4
Nyquist, H. 4 347
Off diagonal elements, rapid damping 183
Operator correspondence, for Wigner function 134
Operator correspondences for P-function 133
Operator correspondences for Q-function 134
Operator correspondences, and equations of motion 132
Operator identities, for generalised P-representations 200
Operator ordering in multitime averages 154
Optical bistability 310
Optical bistability, absorptive limit 313
Optical bistability, dispersive limit 314
Ornstein — Uhlenbeck process, complex 184
Orozco, L.A. 350
Out fields, defined 161
Output 43
Output correlation functions 175
Output field 53
Output noise 55
Outputs, and quantum stochastic differential equations 158
P-function, coherent state 123 123
P-function, Gaussian 124
P-function, Gaussian density operator 130
P-function, number state 124
P-function, power series for 124
P-function, relationship to Q-function 122
P-function, thermal state 123
P-representation 99 122
P-representation, complex 195
P-representation, complex, contours for 205
P-representation, complex, Fokker — Planck equation 202
P-representation, complex, operator identities for 201
P-representation, complex, potential solutions 205
P-representation, complex, stationary solutions 205
P-representation, Fokker — Planck equation 183
P-representation, general form of time correlation functions 187
P-representation, generalised 195
P-representation, generalised, existence theorems 196
P-representation, generalised, operator identities for 200
P-representation, Glauber — Sudarshan 195
P-representation, limitations of classical interpretation 185
P-representation, positive 196
P-representation, positive, applications 207
P-representation, positive, boundary terms 204
P-representation, positive, definition by quantum characteristic function 199
P-representation, positive, existence of 197
P-representation, positive, Fokker — Planck equation 203
P-representation, positive, linearisation 207
P-representation, positive, non-uniqueness 205
P-representation, positive, operator identities for 201
P-representation, SDE 184
P-representation, stochastic simulation 207
P-representation, time correlation functions 185
P-representation, use in master equation 183
Parametric amplifier, degenerate, QSDE for 221
Parametric oscillator, bistable behaviour 212
Parametric oscillator, positive P-representation stationary solution 210
Parametric oscillator, positive P-representation treatment 208
Parametric oscillator, real submanifold 209
Parkins, A.S. 75 91 339 341 347 348 350
Particle in a potential, quantum Langevin equation for 47
Partition function, canonical 37
Partition function, grand canonical 37
path integral 91
Pauli master equation 14 18 19
Pauli master equation, relation to quantum optical master equation 174
Pauli matrices 280
Pauli matrices, properties 280
Pauli, W. 9 14 347
Phase conjugating amplifier 221
Phase damping 182
Phase fluctuations, in laser light 310
Phase space methods 99
Phase space methods, Haken, Risken and Weidlich 315
Phase space methods, laser 315 317
Phase space methods, Smith and Gardiner 317
Phase space representations, of harmonic oscillator density operator 116
Photodetection 240
Photodetection, absorption as a result of detection 250
Photodetection, input-output model using Fermi electrons 270
Photodetection, input-output theory of 267
Photodetection, one atom model 268
Photodetection, physical basis of formulae for 241
Photodetection, spatially distributed input-output model 273
Photodetector, inefficient, model for 261
Photon counting 232 240
Photon counting, absorption as a result of 250
Photon counting, formulae 251
Photon counting, formulae, derivation of 245
Photon counting, master equation and QSDE for 248
Photon counting, physical basis of formulae for 241
Photon number operator 257
Photon, concept of 238
Planck distribution 13
Planck function 16
Planck spectrum 4 5
Planck spectrum and stochastic electrodynamics 138
Planck's radiation law 8 9
Planck, M. 232 349
Polarisation identity 35
Positive map 32
Positive P-representation see "P-representation positive"
Precise measurement 25
Probability amplitude 28
Product, normal 5
Projection operator 27
Projection operator in derivation of master equation 145
Projection operator, non-diagonal coherent state 195
Projection postulate, von Neumann's 231
Projection postulate, von Neumann's, derived in a model of quantum measurement 231
Projector 25
Pump parameter, for the laser 297
Pure state 22
Q-function 117
Q-function and antinormally ordered products 117
Q-function as a quasiprobability 119
Q-function, coherent state 118
Q-function, density operator in terms of 119
Q-function, Gaussian density operator 130
Q-function, number state 118
Q-function, relationship to P-function 122
Q-function, thermal state 118
q-representation 117
QSDE see "Quantum stochastic differential equation"
Quadrature phase 191 222
Quantisation of the electromagnetic field 232
Quantum Bayes theorem 27
Quantum Bayes theorem, amplitude interpretation 28
Quantum Brownian motion 11 62—66
Quantum Brownian motion, example of macroscopic limit 224
Quantum Brownian motion, free particle, using the master equation 81
Quantum Brownian motion, limit of the master equation 147
Quantum Brownian motion, master equation 81 151 224
Quantum Brownian motion, particle in a potential, using the master equation 81
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