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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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| Предметный указатель |
"Out" fields, defined 151 353
A posteriori dynamics 366 382
A posteriori state 362
A priori state 362 366
Absorber, non-linear 190
Absorption of light 7
Absorption, as a result of detection 247
Added noise  215
Added noise absence of in degenerate parametric amplifier 221
Adiabatic elimination, in laser theory 290 298 320
Adjoint equation 71
Adjoint equation commutative noise for 74
Adjoint equation computation of correlation functions 74
Adjoint equation defined 73 75
Adjoint equation derivation of 72
Adjoint equation eigenfunction methods 337
Adjoint equation equivalence to Langevin equation 74
Adjoint equation general form 75
Adjoint equation simulation methods 337
Adjoint equation using squeezed light 335
Amplifier 212
Amplifier degenerate parametric, P-function treatment 179
Amplifier degenerate parametric, Q-function treatment 181
Amplifier degenerate parametric, QSDE for 220
Amplifier degenerate parametric, Wigner function treatment 182
Amplifier harmonic oscillator 177
Amplifier input-output theory 212
Amplifier noise 177
Amplifier noise temperature 217
Amplifier phase conjugating 220
Amplifier QSDE for 215
Amplifier signal to noise ratio 217
Amplifier treated by P-, Q- and Wigner representations 176
Amplitude correlation function for output field from a two level atom 283
Anharmonic oscillator and dispersive optical bistability 310
Anharmonic oscillator, simulation using positive P-representation 203 7
Anharmonicity and quantum optical master equation 88
Antibunched light 253
Antibunched light driving a two level atom 408
Antibunched light driving an atom 398
Antibunching 253
Antibunching in output light from two level atom 284
Antinormally ordered products and Q-function 107
Atom antibunched light 398
Atom driven, using cascaded system 404
Atom driving with antibunched light, treated using cascaded systems 407
Atom driving with squeezed light 398
Atom driving with squeezed light, treated using cascaded systems 405 406
Atom interaction of light with 276
Atom interaction with electromagnetic field 43
Atom two level 14 276 276
Atom two level in EM field, master equation 278
Atom two level, driving with antibunched light 407
Atom two level, driving with squeezed light 404
Atom two level, driving with thermal light 410
Atom two level, in EM field 278
Atomic decay 1 61
Attenuators, input-output theory 212
Back action evading measurement 4
Baker — Hausdorff theorem 99 111 115
Baker — Hausdorff theorem derivation 128
Balanced homodyne and heterodyne detection 263
Bargmann states 101
Bayes theorem, quantum 27
Beams of light 237
Black body radiation 5
Black body radiation measurement of spectrum by absorption 5
Boltzmann distribution 10
Boltzmann distribution as stationary solution of the quantum optical master equation 88
Bose field 345
Bose — Einstein distribution 38
Boundary condition at end of transmission line 55
Boundary condition between "in" and "out" fields 152
Brownian motion, quantum 11
Brownian particle 42 57
Brownian particle quantum Langevin equation for 62
Bunched light 253
Canonical commutation relation 11 43 54 343
Canonical momentum 51
Carnot cycle 39
Cascaded quantum systems 398
Cascaded quantum systems coupling equations 399
Cascaded quantum systems imperfect coupling 402
Cascaded quantum systems in quantum network 413
Cascaded quantum systems Lindblad form of master equation 401
Cascaded quantum systems master equation 401
Cascaded quantum systems numerical methods for 407
Cascaded quantum systems quantum Ito equations 400
Cascaded quantum systems relation to input-output formalism 399
Cascaded quantum systems Stochastic Schr odinger equation 401
Causality 55
Causality and commutators for inputs and outputs 153
Cavity QED 414
Chapman — Kolmogorov equation 146
Characteristic functional, counting processes 359 366
Characteristic functional, diffusion processes 372 376
Characteristic operator, counting processes3 59
Characteristic operator, diffusion processes 373
chemical potential 38 39
Circuit, LRC 6
Classical light field 19
Classical limit, of noise operators 59
Co-operativity parameter, for the laser 293
Coherence, of light fields 240
Coherent signal, homodyne and heterodyne detection 261
Coherent state 90
Coherent state classical limit 96
Coherent state driven oscillator wavefunction 104
Coherent state eigenstate of destruction operator a 97
Coherent state electromagnetic field, correlation function 241
Coherent state expansion of an operator in terms of 101
Coherent state expansion of arbitrary states in terms of 101
Coherent state minimum uncertainty state 97
Coherent state Poissonian number state distribution of 103
Coherent state properties 99
Coherent state quasi-classical state 97
Coherent state solution of the harmonic oscillator 98
Coherent state wavefunction for 103
Coincidence probability in terms of QSDE solutions 250
Coincidence probability, photon counting 248 358
Coincidence probability, relation to elementary probability 249
Commutation relations for noise sources 49
Commutation relations preservation of 67
Commutation relations, canonical 11 43 54
Commutation relations, equal times 45
Completely positive map 33
Complex impedance 67
Complex P-function, for an ideal squeezed state 323
Conditional dynamics 362
Conditional state 362
Consistency requirements for quantum noise theory 10
Consistency with quantum mechanics 11
Continuous measurement 342
Correlation function 24 34
Correlation function adjoint equation 74
Correlation function electromagnetic field in coherent state 241
Correlation function light fields 240
Correlation function noise operators 59
Correlation function normalized 242
Correlation function of system, inputs and outputs 164
Correlation function time ordered 35
Correlation function time ordered, in P-representation 174
Correlation functions, simulations 369
Correlation time, thermal 60
Coulomb gauge 231
Coupling constants, to harmonic oscillator heat bath 48
Coupling, unidirectional 398
Creation operator 12
Creation operator  , defined 93
Cumulant expansion range of validity 79
| Cumulant expansion van Kampen's 77
Cumulant expansion, and quasiclassical Langevin equation 127
Damping radiation 43 51 55
Damping, and locality 52
Decay, atomic 1
Degenerate parametric amplifier correlation functions for the output field3 29
Degenerate parametric amplifier internal mode properties 326
Degenerate parametric amplifier internal mode quadrature phases 327
Degenerate parametric amplifier maximum squeezing 329
Degenerate parametric amplifier normally ordered variances 327
Degenerate parametric amplifier output field 328
Degenerate parametric amplifier P-function treatment 179
Degenerate parametric amplifier Q-function treatment 181
Degenerate parametric amplifier QSDE for 220
Degenerate parametric amplifier squeezed white noise limit of output field 330
Degenerate parametric amplifier squeezing in 221
Degenerate parametric amplifier Wigner function treatment 182
Degenerate parametric amplifier, and squeezing 323
Delay function 368
Delay function three-level system 382
Delta function, transverse 235
Density operator 14 21
Density operator and measurement 31
Density operator canonical 37
Density operator damping of off-diagonal elements 171
Density operator factorizable 58
Density operator Gaussian 118
Density operator grand canonical 38
Density operator in terms of Q-function 109
Density operator initial factorization of 131
Density operator properties 22
Density operator reduced 16 40 132
Density operator stochastic 349 366 375
Density operator unravelling of system 361
Density operator, reduced 349
Destruction operator 12
Destruction operator  , defined 93
Detection, generalized 32
Diagonalization of density operator, by coupling to noise 223
Diffusion matrix, non-positive-definite 184
Diffusion processes 371
Dissipation 41
Driven harmonic oscillator, P-function method for 124
Driving field and quantum Langevin equation 88
Driving field and quantum optical master equation 87
Duality, wave-particle 9
Effect 26
Effective Hamiltonian 348 350
Effective Hamiltonian optical molasses 391
Effective Hamiltonian three-level system 382
Effective Hamiltonian two-level system 378 386
Electromagnetic field, optical 235
Electromagnetic field, quantization 230 233
Electromagnetic field, quantization in an infinite volume 234
Electron number operator 266
Elementary Probability Density 357
Elementary probability in photon counting 249
Elementary probability in photon counting in terms of QSDE solutions 251
Elementary probability in photon counting relation to coincidence probability 249
Emission of light 7
Energy level 7
Entangled state 355
entropy 35 36
Entropy maximization 36
EPD see “Exclusive Probability Density” 357
Equations of motion, and operator correspondences 122
Equilibrium, thermodynamic 36
Exclusive probability density 357
Exclusive probability density counting processes 361
Exclusive probability density two-level system 381
Fermi — Dirac distribution 39
Fermi's "golden rule" 9
Field interpretation of noise inputs and outputs 51
Fields, input and output 52
First Markov approximation 49 150
First Markov approximation and commutation relations for noise sources 50
Fluctuations 41
Fokker — Planck equation, and classical Langevin equation 71
FPE see “Fokker-Planck equation”
Fringe, optical 242
Gain 213
Gauge processes 351
Gauge transformation 231
Gaussian density operator 118
Gaussian density operator definition 119
Gaussian density operator higher moments for 121
Gaussian density operator P-, Q- and Wigner function for 120
Gaussian density operator quantum characteristic function for 119
Gaussian diffusive measurement 372
Gaussian variable, classical, higher moments for 121
General kinds of measurement 29
Generalized Optical Bloch Equations 385
Generalized P-representation see “P-representation generalized”
Golden Rule 9
Hanbury — Brown Twiss effect 252
harmonic oscillator 38 91
Harmonic oscillator cannot be treated as two level system2 76
Harmonic oscillator damped 6
Harmonic oscillator damped, and quantum Langevin equation1 52
Harmonic oscillator damped, example of destruction of quantum coherence 225
Harmonic oscillator damped, master equation treatment 169
Harmonic oscillator energy eigenvalues 93
Harmonic oscillator heat bath 44
Harmonic oscillator Heisenberg picture 95
Harmonic oscillator in cascaded quantum system 404
Harmonic oscillator mean energy of 67
Harmonic oscillator number states 93
Harmonic oscillator P-representation of 172—176
Harmonic oscillator phase damped 171
Harmonic oscillator quantum Langevin equation for 65
Harmonic oscillator squeezed states of 322
Harmonic oscillator wavefunctions in momentum space 95
Harmonic oscillator wavefunctions in position space 93
Heat bath 39 41 42
Heat bath fermionic 267
Heat bath field interpretation of 43 51
Heat bath initial independence of system 57
Heat bath inverted 213
Heat bath negative temperature 213 218
Heat bath of Harmonic oscillators 44
Heat bath of two level atoms 140
Heisenberg picture 72 92
Heisenberg's uncertainty principle 1 322
Hermite polynomial, Roderigues' formula 95
Heterodyne detection 259
Heterodyne detection balanced 263
Heterodyne detection coherent signal 261
Heterodyne detection local oscillator noise 261
Heterodyne detection mean detected signal 260
Heterodyne detection variance of detected signal 260
Heterodyne detection with imperfect photodetectors 262
Heterodyne measurement of spectrum of quantum noise 6
Homodyne current 371 376
Homodyne current stochastic 375
Homodyne detection 259 342 371
Homodyne detection balanced 263
Homodyne detection coherent signal 261
Homodyne detection local oscillator noise 261
Homodyne detection mean detected signal 260
Homodyne detection variance of detected signal 260
Homodyne detection with imperfect photodetectors 262
Imprecise measurement 25—26
Input 43
Input and driving field 87
Input field 52 353
Input noise 55
Input-output theory 353
Input-output theory, cascaded quantum systems 399
Input-output theory, of amplifiers and attenuators 212
Input-output theory, of photodetection 264
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