Quantum Theory of Optical Coherence: Selected Papers and Lectures

649 Pages·2007·4.744 MB·English

by  Roy J. Glauber(auth.)

RoyJ.Glauber
QuantumTheoryofOpticalCoherence

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
QuantumTheoryofOpticalCoherence.SelectedPapersandLectures.RoyJ.Glauber.
Copyright(cid:1)c 2007WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40687-6
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
viii
9 OrderedExpansionsinBosonAmplitudeOperators 331
9.1 Introduction 331
9.2 CoherentStatesandDisplacementOperators 333
9.3 CompletenessofDisplacementOperators 337
9.4 OrderedPower-SeriesExpansions 345
9.5 s-OrderedPower-SeriesExpansions 353
9.6 IntegralExpansionsforOperators 358
9.7 CorrespondencesBetweenOperatorsandFunctions 366
9.8 IllustrationofOperator–FunctionCorrespondences 375
AppendixA 377
AppendixB 378
AppendixC 379
AppendixD 380
References 380
10 DensityOperatorsandQuasiprobabilityDistributions 383
10.1 Introduction 383
10.2 OrderedOperatorExpansions 385
10.3 ThePRepresentation 389
10.4 WignerDistribution 393
10.5 TheFunction(cid:1)α|ρ|α(cid:2) 399
10.6 EnsembleAveragesandsOrdering 402
10.7 ExamplesoftheGeneralQuasiprobabilityFunctionW(ααα,s) 408
10.8 AnalogywithHeatDiffusion 416
10.9 Time-ReversedHeatDiffusionandW(ααα,s) 418
10.10 PropertiesCommontoallQuasiprobabilityDistributions 420
References 423
11 CoherenceandQuantumDetection 425
11.1 Introduction 425
11.2 TheStatisticalPropertiesoftheElectromagneticField 426
11.3 TheIdealPhotonDetector 428
11.4 CorrelationFunctionsandCoherence 429
11.5 OtherCorrelationFunctions 432
11.6 TheCoherentStates 434
11.7 ExpansionsinTermsofCoherentStates 437
11.8 AFewGeneralObservations 439
11.9 TheDampedHarmonicOscillator 440
11.10 TheDensityOperatorfortheDampedOscillator 444
11.11 IrreversibilityandDamping 447
11.12 TheFokker–PlanckandBlochEquations 449
ix
11.13 TheoryofPhotodetection. ThePhotonCounterViewedasaHarmonic
Oscillator 453
11.14 TheDensityOperatorforthePhotonCounter 459
References 462
12 QuantumTheoryofCoherence 463
12.1 Introduction 463
12.2 ClassicalTheory 468
12.3 QuantumTheory 471
12.4 IntensityandCoincidenceMeasurements 474
12.5 Coherence 487
12.6 CoherentStates 495
12.7 ThePRepresentation 499
12.8 ChaoticStates 514
12.9 WavepacketStructureofChaoticField 521
References 530
13 TheInitiationofSuperfluorescence 531
13.1 Introduction 531
13.2 BasicEquationsforaSimpleModel 532
13.3 OnsetofSuperfluorescence 534
References 536
14 Amplifiers,AttenuatorsandSchro¨dingersCat 537
14.1 Introduction: TwoParadoxes 537
14.2 AQuantum-MechanicalAttenuator: TheDampedOscillator 542
14.3 AQuantumMechanicalAmplifier 548
14.4 SpecificationofPhotonPolarizationStates 558
14.5 MeasuringPhotonPolarizations 561
14.6 UseoftheCompoundAmplifier 563
14.7 SuperluminalCommunication? 565
14.8 InterferenceExperimentsandSchro¨dinger’sCat 569
References 575
15 TheQuantumMechanicsofTrappedWavepackets 577
15.1 Introduction 577
15.2 EquationsofMotionandTheirSolutions 578
15.3 TheWaveFunctions 581
15.4 PeriodicFieldsandTrapping 584
15.5 InteractionWiththeRadiationField 587
15.6 SumRules 590
15.7 RadiativeEquilibriumandInstability 592
References 594
x
16 DensityOperatorsforFermions 595
16.1 Introduction 595
16.2 Notation 597
16.3 CoherentStatesforFermions 597
16.3.1 DisplacementOperators 597
16.3.2 CoherentStates 599
16.3.3 IntrinsicDescriptionsofFermionicStates 600
16.4 GrassmannCalculus 601
16.4.1 Differentiation 601
16.4.2 EvenandOddFunctions 601
16.4.3 ProductRule 602
16.4.4 Integration 602
16.4.5 IntegrationbyParts 603
16.4.6 CompletenessoftheCoherentStates 604
16.4.7 CompletenessoftheDisplacementOperators 604
16.5 Operators 605
16.5.1 TheIdentityOperator 605
16.5.2 TheTrace 606
16.5.3 PhysicalStatesandOperators 606
16.5.4 PhysicalDensityOperators 607
16.6 δFunctionsandFourierTransforms 608
16.7 OperatorExpansions 610
16.8 CharacteristicFunctions 612
16.8.1 Thes-OrderedCharacteristicFunction 613
16.9 s-OrderedExpansionsforOperators 614
16.10 QuasiprobabilityDistributions 616
16.11 MeanValuesofOperators 618
16.12 PRepresentation 619
16.13 CorrelationFunctionsforFermions 620
16.14 ChaoticStatesoftheFermionField 621
16.15 CorrelationFunctionsforChaoticFieldExcitations 624
16.16 Fermion-CountingExperiments 626
16.17 SomeElementaryExamples 628
16.17.1 TheVacuumState 628
16.17.2 APhysicalTwo-ModeDensityOperator 629
References 631
Index 632