Quantum theory of optical coherence

658 Pages·2007·4.001 MB·English

by  Roy J. Glauber

Roy J. Glauber
Quantum Theory of Optical Coherence
Selected Papers and Lectures
WILEY-VCH Verlag GmbH & Co. KGaA

RoyJ.Glauber
QuantumTheoryofOpticalCoherence
II
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Roy J. Glauber
Quantum Theory of Optical Coherence
Selected Papers and Lectures
WILEY-VCH Verlag GmbH & Co. KGaA
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v
Contents
1 TheQuantumTheoryofOpticalCoherence 1
1.1 Introduction 1
1.2 ElementsofFieldTheory 2
1.3 FieldCorrelations 7
1.4 Coherence 10
1.5 CoherenceandPolarization 15
Appendix 18
References 20
2 OpticalCoherenceandPhotonStatistics 23
2.1 Introduction 23
2.1.1 ClassicalTheory 27
2.2 InterferenceExperiments 30
2.3 IntroductionofQuantumTheory 35
2.4 TheOne-AtomPhotonDetector 38
2.5 Then-AtomPhotonDetector 46
2.6 PropertiesoftheCorrelationFunctions 51
2.6.1 SpaceandTimeDependenceoftheCorrelationFunctions 54
2.7 DiffractionandInterference 56
2.7.1 SomeGeneralRemarksonInterference 58
2.7.2 First-OrderCoherence 59
2.7.3 FringeContrastandFactorization 64
2.8 InterpretationofIntensityInterferometerExperiments 66
2.8.1 HigherOrderCoherenceandPhotonCoincidences 67
2.8.2 FurtherDiscussionofHigherOrderCoherence 70
2.8.3 TreatmentofArbitraryPolarizations 71
2.9 CoherentandIncoherentStatesoftheRadiationField 75
2.9.1 Introduction 75
2.9.2 Field-TheoreticalBackground 77
2.9.3 CoherentStatesofaSingleMode 80
vi
2.9.4 ExpansionofArbitraryStatesinTermsofCoherentStates 86
2.9.5 ExpansionofOperatorsinTermsofCoherentStateVectors 89
2.9.6 GeneralPropertiesoftheDensityOperator 92
2.9.7 ThePRepresentationoftheDensityOperator 94
2.9.8 TheGaussianDensityOperator 100
2.9.9 DensityOperatorsfortheField 104
2.9.10 CorrelationandCoherencePropertiesoftheField 109
2.10 RadiationbyaPredeterminedCharge–CurrentDistribution 117
2.11 Phase-SpaceDistributionsfortheField 121
2.11.1 ThePRepresentationandtheMomentProblem 123
2.11.2 APositive-Definite“PhaseSpaceDensity” 124
2.11.3 Wigner’s“PhaseSpaceDensity” 127
2.12 CorrelationFunctionsandQuasiprobabilityDistributions 132
2.12.1 FirstOrderCorrelationFunctionsforStationaryFields 134
2.12.2 CorrelationFunctionsforChaoticFields 136
2.12.3 QuasiprobabilityDistributionfortheFieldAmplitude 139
2.12.4 QuasiprobabilityDistributionfortheFieldAmplitudesatTwoSpace-Time
Points 145
2.13 ElementaryModelsofLightBeams 148
2.13.1 ModelforIdealLaserFields 153
2.13.2 ModelofaLaserFieldWithFiniteBandwidth 156
2.14 InterferenceofIndependentLightBeams 164
2.15 PhotonCountingExperiments 170
References 181
3 CorrelationFunctionsforCoherentFields 183
3.1 Introduction 183
3.2 CorrelationFunctionsandCoherenceConditions 184
3.3 CorrelationFunctionsasScalarProducts 186
3.4 ApplicationtoHigherOrderCorrelationFunctions 189
3.5 FieldsWithPositive-DefinitePFunctions 191
References 195
4 DensityOperatorsforCoherentFields 197
4.1 Introduction 197
4.2 EvaluationoftheDensityOperator 199
4.3 FullyCoherentFields 205
4.4 UniquePropertiesoftheAnnihilationOperatorEigenstates 209
References 216
5 ClassicalBehaviorofSystemsofQuantumOscillators 217
References 220
vii
6 QuantumTheoryofParametricAmplificationI 221
6.1 Introduction 221
6.2 TheCoherentStatesandthePRepresentation 223
6.3 ModeloftheParametricAmplifier 227
6.4 ReducedDensityOperatorfortheAMode 233
6.5 InitiallyCoherentState: PRepresentationfortheAMode 234
6.6 InitiallyCoherentState;Moments,MatrixElements,andExplicit
RepresentationforρA(t) 238
6.7 SolutionsforanInitiallyChaoticBMode 241
6.8 SolutionforInitialn-QuantumStateofAMode;BModeChaotic 244
6.9 GeneralDiscussionofAmplificationWithBModeInitiallyChaotic 249
6.10 DiscussionofPRepresentation: CharacteristicFunctionsInitially
Gaussian 252
6.11 SomeGeneralPropertiesofP(α,t) 258
Appendix 260
References 261
7 QuantumTheoryofParametricAmplificationII 263
7.1 Introduction 263
7.2 TheTwo-ModeCharacteristicFunction 265
7.3 TheWignerFunction 267
7.4 DecoupledEquationsofMotion 271
7.5 CharacteristicFunctionsExpressedinTermsofDecoupledVariables 273
7.6 W andPExpressedinTermsofDecoupledVariables 275
7.7 ResultsforChaoticInitialStates 278
7.8 CorrelationsoftheModeAmplitudes 283
References 286
8 PhotonStatistics 287
8.1 Introduction 287
8.2 ClassicalTheory 288
8.3 QuantumTheory: Introduction 290
8.4 IntensityandCoincidenceMeasurements 293
8.5 FirstandHigherOrderCoherence 297
8.6 TheCoherentStates 300
8.7 ExpansionsinTermsoftheCoherentStates 307
8.8 CharacteristicFunctionsandQuasiprobabilityDensities 313
8.9 SomeExamples 319
8.10 PhotonCountingDistributions 322
References 329