Gardiner C.W., Zoller P. — Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics :: Электронная библиотека попечительского совета мехмата МГУ

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Gardiner C.W., Zoller P. — Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics

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Название: Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics

Авторы: Gardiner C.W., Zoller P.

Аннотация:

This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quantum amplifier theory, non-Markovian quantum stochastic processes, quantum input-output theory, and positive P-representations. It is the first book in which quantum noise is described by a mathematically complete theory in a form that is also suited to practical applications. Special attention is paid to non-classical effects, such as squeezing and antibunching. This second edition has been enlarged so as to take account of rapid progress in the field, and now includes two additional chapters, on the stochastic Schrodinger equation and on cascaded quantum systems.

Язык:

Рубрика: Физика/Электромагнетизм/Оптика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2000

Количество страниц: 438

Добавлена в каталог: 03.09.2005

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Предметный указатель

Input-output theory, using fermions      267
Inputs, and quantum stochastic differential equations      148 353
Intensity correlation      252
Intensity correlation antibunched light      253
Intensity correlation laser light      253
Intensity correlation light from two-level atom, driven by antibunched light      409
Intensity correlation thermal light      252 253
Interaction picture      15
Interaction picture and the cumulant expansion      78
Interference fringe      85
Inverted oscillator heat bath      213
Ito calculus, quantum      156
Ito integral, relation to Stratonovich with squeezed white noise      331
Ito table, counting processes      364
Ito table, diffusion processes      374
Ito table, non-vacuum      350
Ito table, number processes      352
Ito table, vacuum      346
Josephson junction      43
Jump probability      363
Kramers' equation, in Wigner function treatment of quantum Brownian motion      183
Lagrange multiplier      37
Laguerre polynomial      118
Lamb shift      43 86 140
Lamb shift in two level atom master equation      279
Lamb shift modification using density of states      279
Lamb — Dicke regime      390 394
Langevin correlation function, as a function of time      59
Langevin equation, derivation of      46
Laser      289
Laser analytic solution of deterministic equations      199
Laser asymptotic expansion in number of atoms      292
Laser co-operativity parameter      293
Laser configuration      289
Laser cooling      387
Laser correlation functions      303
Laser field      20
Laser Fokker — Planck equation derivation      296
Laser Fokker — Planck equation derivation by adiabatic elimination      298
Laser Fokker — Planck equation evaluation of noise terms      299
Laser Fokker — Planck equation stationary solution      301
Laser Fokker — Planck equation use of P-representation      297
Laser Langevin equations      see “laser SDEs”
Laser linewidth      305
Laser macroscopic equations      292
Laser Master equation      296
Laser nature of laser light      304
Laser phase fluctuations      305
Laser phase space methods      315
Laser potential      294 301
Laser potential plotted      295
Laser pump parameter      293
Laser quantum Langevin equations for      290
Laser scaling behaviour of parameters      300
Laser scaling of parameters      198
Laser scaling with number of atoms      311 319
Laser SDEs, solutions      301
Laser SDEs, solutions of linearized form      301
Laser simulated using positive P-representation      197
Laser stationary solutions      293
Laser stochastic differential equation      197
Laser stochastic differential equations in P-representation      301
Laser time dependent macroscopic solutions      294
LC circuit      91
Light beams      237
Light field, classical      19
Light, absorption of      7
Light, emission of      7
Lindblad form of master equation      147
Lindblad form of master equation for cascaded systems      401
Linewidth, spectral      1
Liouville operator      349
Liouvillian operators, in derivation of master equation      135
Local coupling      42
Local oscillator      374
Local oscillator noise      261
Locality, and damping      52
LRC circuit      6 65
LSZ formulation of quantum field theory      56
Macroscopic coherence destruction of in quantum Brownian motion      223
Macroscopic coherence quantum optical situation      225
Macroscopic limit in open quantum systems      222
Mandel's coherent state      258
Mandel's counting formula      254 256 358
Mandel's input-output theory of photodetection      266
Mandel's number state      258
Mandel's photon counting formula      256
Mandel's thermal state      258
Map, completely positive      33
Markov approximation      345
Markov approximation and weak coupling limit      137
Markov approximation in derivation of the master equation      134—135
Markov assumption, in derivation of photon counting formulae      244
Markov interpretation, in quantum Markov process      146
Markov property      130
Master equation      13 18 71 76 349 351
Master equation applying      169
Master equation cascaded quantum system      401
Master equation classical      14
Master equation connection with QSDEs      161
Master equation derivation based on projection operators      135
Master equation derivation from QSDE      162
Master equation derivation from the adjoint equation      77
Master equation duality with stochastic differential equation      130
Master equation equivalence to QSDE      164
Master equation history      130
Master equation laser      296
Master equation Lindblad form      369
Master equation many channels      349
Master equation nonlinear absorber      206
Master equation notation for      141
Master equation number state basis      169
Master equation optical molasses      391
Master equation Pauli      14 18 19
Master equation photon counting      246
Master equation physical basis      131
Master equation projection operator derivation      135
Master equation quantum Brownian motion      80 141 223
Master equation quantum Brownian motion limit      137
Master equation quantum Brownian motion, Wigner function treatment      183
Master equation quantum optical      349 351 366
Master equation quantum optical, derivation of      131
Master equation quantum optical, derived      137
Master equation quantum optical, derived from the adjoint equation      85
Master equation quantum optical, general form      132
Master equation simulation      368
Master equation three-level system      382
Master equation transformation      369
Master equation two-level system      385
Master equation unravelling      366
Master equation weak coupling limit in derivation of      136
Master equation with several frequencies      163
Maxwell's equations      231
Mean square displacement, in quantum Brownian motion      63
Measurement      212
Measurement back action evading      4
Measurement general kinds of      29
Measurement imprecise      25—26
Measurement of the first kind      29
Measurement of the second kind      29
Measurement postulates      26 29
Measurement precise      24
Measurement projection postulate, model derivation      229
Measurement quantum model of      226
Measurement quantum non-demolition      4
Measurements and the density operator      31
Measurements, multitime      33
Measurements, sequences of      33
Mechanical light effects      384
Memory function      47

Minimum uncertainty states, coherent states as      97
Mode functions for electromagnetic field      232
Mollow hierarchy      381
Moments, normally ordered      267
Multitime averages, computation of in quantum Markov process      143
Multitime measurement, expression as correlation function      34
Multitime measurements      33
Multitime structure, of quantum Markov process      143
Negative temperature      213
Negative temperature bath, QSDE      218
Noise added      215
Noise Hamiltonian      181
Noise inputs and outputs      43 55
Noise interpretation of inputs and outputs      57
Noise local oscillator      261
Noise operators classical limit of      59
Noise operators correlation function of      59
Noise operators thermal      57
Noise outputs and inputs      43 55
Noise sources of several frequencies, in QSDEs      160
Noise sources, commutation relations for      49—50
Noise temperature      217
Noise vacuum      43
Non-classical light, characterization of      412
Non-exclusive multitime probability density      358
Non-linear couplings      45
Nonlinear absorber, master equation      206
Normal product      5
Normal product defined      102
Normally ordered moments and Mandel's formula      267
Normally ordered moments and quantum characteristic function      111
Number processes      351
Number states, of harmonic oscillator      93
Nyquist's Theorem      4
Off-diagonal elements, rapid damping      171
Operator correspondence, for Wigner function      124
Operator correspondences for P-function      123
Operator correspondences for Q-function      123
Operator correspondences, and equations of motion      122
Operator identities, for generalized P-representations      189
Operator ordering in multitime averages      144
Optical bistability      306
Optical bistability absorptive limit      309
Optical bistability dispersive limit      310
Optical Bloch equations      378
Optical Bloch equations Generalized      390
Optical Bloch equations two-level system      380
Optical molasses      387 394
Optical potential      387
Optical pumping      388 390
Ornstein — Uhlenbeck process, complex      172
Output      43
Output correlation functions      165
Output field      52
Output noise      55
Outputs, and quantum stochastic differential equations      148
P-function coherent state      113
P-function Gaussian      114
P-function Gaussian density operator      120
P-function number state      113
P-function power series for      114
P-function relationship to Q-function      112
P-function thermal state      113
P-representation      90 112
P-representation complex      184
P-representation complex, contours for      195
P-representation complex, Fokker — Planck equation      191
P-representation complex, operator identities for      191
P-representation complex, potential solutions      195
P-representation complex, stationary solutions      195
P-representation Fokker — Planck equation      172
P-representation generalized      183
P-representation generalized, existence theorems      184
P-representation generalized, operator identities for      189
P-representation Glauber — Sudarshan      184
P-representation limitations of classical interpretation1      74
P-representation positive      184
P-representation positive, applications      195
P-representation positive, boundary terms      193
P-representation positive, definition by quantum characteristic function      187
P-representation positive, existence of      186
P-representation positive, Fokker — Planck equation      192
P-representation positive, linearization      196
P-representation positive, non-uniqueness      195
P-representation positive, operator identities for      190
P-representation SDE      173
P-representation stochastic simulation      197
P-representation time correlation functions      174
P-representation use in master equation      172
P-representation—general form of time correlation functions      176
Parametric amplifier, degenerate, QSDE for      220
Parametric oscillator, bistable behaviour      211
Parametric oscillator, positive P-representation treatment      196
Parametric oscillator, real submanifold      210
Particle in a potential, quantum Langevin equation for      47
Partition function canonical      37
Partition function grand canonical      38
Pauli master equation      14 18 19
Pauli master equation, relation to quantum optical master equation      163
Pauli matrices      277
Pauli matrices properties      277
Phase conjugating amplifier      219
Phase damping      171
Phase fluctuations, in laser light      305
Phase space methods      90
Phase space methods Haken, Risken and Weidlich      311
Phase space methods laser      310 313
Phase space methods Smith and Gardiner      313
Phase space representations, of harmonic oscillator density operator      106
Photodetection      238
Photodetection absorption as a result of detection      247
Photodetection input-output model using Fermi electrons      267
Photodetection input-output theory of      264
Photodetection one atom model      265
Photodetection physical basis of formulae for      239
Photodetection spatially distributed input-output model      273
Photodetector, inefficient, model for      258
Photon counting      230 238 351 354
Photon counting absorption as a result of      247
Photon counting formulae      248
Photon counting formulae, derivation of      243
Photon counting master equation and QSDE for      246
Photon counting physical basis of formulae for      239
Photon number operator      254
Photon, concept of      236
Planck distribution      13
Planck function      16
Planck spectrum      4 5
Planck spectrum and stochastic electrodynamics      127
Planck's radiation law      8 9
Polarization identity      35
Positive map      33
Positive P-representation      see “P-representation positive”
Positive P-representation, escape of trajectory in simulations      201
Positive P-representation, guidelines for simulations      209
Positive P-representation, in cascaded quantum systems      405
Positive P-representation, numerical signatures of presence of boundary terms      202 204
Precise measurement      24
Probability amplitude      28
Product, normal      5
Projection operator      27
Projection operator in derivation of master equation      135
Projection operator non-diagonal coherent state      184
Projection postulate, derived in a model of quantum measurement      229
Projection postulate, von Neumann's      229
Projector      25
Pump parameter, for the laser      293
Pure state      22
Pure state analysis of resonant light scattering      379
q-bit, defined      412

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