量子光学-第2版

1 Introduction2 Quantisation of the Electromagnetic Field2．1 Field Quantisation2．2 Fock or Number States2．3 Coherent States2．4 Squeezed States2．5 Two-Photon Coherent States2．6 Variance in the Electric Field2．7 Multimode Squeezed States2．8 Phase Properties of the FieldExercisesReferencesFurther Reading3 Coherence Properties of the Electromagnetic Field3．1 Field-Correlation Functions3．2 Properties of the Correlation Functions3．3 Correlation Functions and Optical Coherence3．4 First-Order Optical Coherence3．5 Coherent Field3．6 Photon Correlation Measurements3．7 Quantum Mechanical Fields3．7．1 Squeezed State3．7．2 Squeezed Vacuum3．8 Phase-Dependent Correlation Functions3．9 Photon Counting Measurements3．9．1 Classical Theory3．9．2 Constant Intensity3．9．3 Fluctuating Intensity-Short-Time Limit3．10 Quantum Mechanical Photon Count Distribution3．10．1 Coherent Light3．10．2 Chaotic Light3．10．3 Photo-Electron Current FluctuationsExercisesReferencesFurther Reading4 Representations of the Electromagnetic Field4．1 Expansion in Number States4．2 Expansion in Coherent States4．2．1 PRepresentation4．2．2 Wigner's Phase-Space Density4．2．3 Q Function4．2．4 R Representation4．2．5 Generalized P Representations4．2．6 Positive P RepresentationExercisesReferences5 Quantum Phenomena in Simple Systems in Nonlinear Optics5．1 Single-ModeQuantum Statistics5．1．1 Degenerate Parametric Amplifier5．1．2 Photon Statistics5．1．3 Wigner Function5．2 Two-Mode Quantum Correlations5．2．1 Non-degenerate Parametric Amplifier5．2．2 Squeezing5．2．3 Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox5．2．4 Wigner Function5．2．5 Reduced Density Operator5．3 Quantum Limits to Amplification5．4 Amplitude Squeezed State with Poisson Photon Number StatisticsExercisesReferences6 Stochastic Methods6．1 Master Equation6．2 Equivalent c-Number Equations6．2．1 Photon Number Representation6．2．2 P Representation6．2．3 Properties of Fokker-Planck Equations6．2．4 Steady State Solutions - Potential Conditions6．2．5 Time Dependent Solution6．2．6 Q Representation6．2．7 Wigner Function6．2．8 Generalized P Representation6．3 Stochastic Differential Equations6．3．1 Use of the Positive P Representation6．4 Linear Processes with Constant Diffusion6．5 Two Time Correlation Functions in Quantum Markov Processes．．6．5．1 Quantum Regression Theorem6．6 Application to Systems with a P Representation6．7 Stochastic Unravellings6．7．1 Simulating Quantum TrajectoriesExercisesReferencesFurther Reading7 Input-Output Formulation of Optical Cavities7．1 Cavity Modes7．2 Linear Systems7．3 Two-Sided Cavity7．4 Two Time Correlation Functions7．5 Spectrum of Squeezing7．6 Parametric Oscillator7．7 Squeezing in the Total Field7．8 Fokker-Planck EquationExercisesReferences．Further Reading8 Generation and Applications of Squeezed Light8．1 Parametric Oscillation and Second Harmonic Generation8．1．1 Semi-Classical Steady States and Stability Analysis8．1．2 Parametric Oscillation8．1．3 Second Harmonic Generation8．1．4 Squeezing Spectrum8．1．5 Parametric Oscillation8．1．6 Experiments8．2 Twin Beam Generation and Intensity Correlations8．2．1 Second Harmonic Generation8．2．2 Experiments8．3 Applications of Squeezed Light8．3．1 Interferometric Detection of Gravitational Radiation8．3．2 Sub-Shot-Noise Phase Measurements8．3．3 Quantum InformationExercisesReferencesFurther Reading9 Nonlinear Quantum Dissipative Systems9．1 Optical Parametric Oscillator： Complex P Function9．2 Optical Parametric Oscillator： Positive P Function9．3 Quantum Tunnelling Time9．4 Dispersive Optical Bistahility9．5 Comment on the Use of the Q and Wigner Representations Exercises9．A Appendix9．A．I Evaluation of Moments for the Complex P function for Parametric Oscillation （9．1 7）9．A．2 Evaluation of the Moments for the Complex P Function for Optical Bistability （9．4 8）ReferencesFurther Reading10 Interaction of Radiation with Atoms10．1 Quantization of the Many-Electron System10．2 Interaction of a Single Two-Level Atom with a Single Mode Field．10．3 Spontaneous Emission from a Two-Level Atom10．4 Phase Decay in a Two-Level System10．5 Resonance FluorescenceExercisesReferencesFurther Reading11 CQED11．1 Cavity QED11．1．1 Vacuum Rabi Splitting11．1．2 Single Photon Sources11．1．3 Cavity QED with N Atoms11．2 Circuit QEDExercisesReferencesFurther Reading12 Quantum Theory of the Laser12．1 Master Equation12．2 Photon Statistics12．2．1 Spectrum of Intensity Fluctuations12．3 Laser Linewidth12．4 Regularly Pumped Laser12．A Appendix： Derivation of the Single-Atom IncrementExercisesReferences13 Bells Inequalities in Quantum Optics13．1 The Einstein-Podolsky-Rosen （EPR） Argument13．2 Bell Inequalities and the Aspect Experiment13．3 Violations of Bell's Inequalities Using a Parametric Amplifier Source13．4 One-Photon InterferenceExercisesReferences14 Quantum Nondemolition Measurements14．1 Concept of a QND Measurement14．2 Back Action Evasion14．3 Criteria for a QND Measurement14．4 The Beam Splitter14．5 Ideal Quadrature QND Measurements14．6 Experimental Realisation14．7 A Photon Number QND SchemeExercisesReferences15 Quantum Coherence and Measurement Theory15．1 Quantum Coherence15．2 The Effect of Dissipation15．2．1 Experimental Observation of Coherence Decay15．3 Quantum Measurement Theory15．3．1 General Measurement Theory15．3．2 The Pointer Basis15．4 Examples of Pointer Observables15．5 Model of a Measurement15．6 Conditional States and Quantum Trajectories15．6．1 Homodyne Measurement of a Cavity FieldExercisesReferences16 Quantum Information16．1 Introduction16．1．1 The Qubit16．1．2 Entanglement16．2 Quantum Key Distribution16．3 Quantum Teleportation16．4 Quantum Computation16．4．1 Linear Optical Quantum Gates16．4．2 Single Photon SourcesExercisesReferencesFurther Reading17 Ion Traps17．1 Introduction17．2 Trapping and Cooling17．3 Novel Quantum States17．4 Trapping Multiple Ions17．5 Ion Trap Quantum Information ProcessingExercisesReferences18 Light Forces18．1 Radiative Forces in the Semiclassical Limit18．2 Mean Force for a Two-Level Atom Initially at Rest18．3 Friction Force for a Moving Atom18．3．1 Laser Standing Wave——Doppler Cooling18．4 Dressed State Description of the Dipole Force18．5 Atomic Diffraction by a Standing Wave18．6 Optical Stern——Gerlach Effect18．7 Quantum Chaos18．7．1 Dynamical Tunnelling18．7．2 Dynamical Localisation18．8 The Effect of Spontaneous EmissionReferencesFurther Reading19 Bose-Einstein Condensation19．1 Hamiltonian： Binary Collision Model19．2 Mean-Field Theory —— Gross-Pitaevskii Equation19．3 Single Mode Approximation19．4 Quantum State of the Condensate19．5 Quantum Phase Diffusion： Collapses and Revivals of the Condensate Phase19．6 Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase19．6．1 Interference of Two Condensates Initially in Number States19．7 Quantum Tunneling of a Two Component Condensate19．7．1 Semiclassical Dynamics19．7．2 Quantum Dynamics19．8 Coherence Properties of Bose-Einstein Condensates19．8．1 1st Order Coherence19．8．2 Higher Order CoherenceExercisesReferencesFurther ReadingIndex