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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
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.


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: en

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
"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 $A(\omega)$      215
Added noise $A(\omega)$ 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 $\alpha^{†}$, 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 $\alpha$, 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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