1 Introduction
2 Quantisation of the Electromagnetic Field
2．1 Field Quantisation
2．2 Fock or Number States
2．3 Coherent States
2．4 Squeezed States
2．5 Two-Photon Coherent States
2．6 Variance in the Electric Field
2．7 Multimode Squeezed States
2．8 Phase Properties of the Field
Exercises
References
Further Reading
3 Coherence Properties of the Electromagnetic Field
3．1 Field-Correlation Functions
3．2 Properties of the Correlation Functions
3．3 Correlation Functions and Optical Coherence
3．4 First-Order Optical Coherence
3．5 Coherent Field
3．6 Photon Correlation Measurements
3．7 Quantum Mechanical Fields
3．7．1 Squeezed State
3．7．2 Squeezed Vacuum
3．8 Phase-Dependent Correlation Functions
3．9 Photon Counting Measurements
3．9．1 Classical Theory
3．9．2 Constant Intensity
3．9．3 Fluctuating Intensity-Short-Time Limit
3．10 Quantum Mechanical Photon Count Distribution
3．10．1 Coherent Light
3．10．2 Chaotic Light
3．10．3 Photo-Electron Current Fluctuations
Exercises
References
Further Reading
4 Representations of the Electromagnetic Field
4．1 Expansion in Number States
4．2 Expansion in Coherent States
4．2．1 PRepresentation
4．2．2 Wigner's Phase-Space Density
4．2．3 Q Function
4．2．4 R Representation
4．2．5 Generalized P Representations
4．2．6 Positive P Representation
Exercises
References
5 Quantum Phenomena in Simple Systems in Nonlinear Optics
5．1 Single-ModeQuantum Statistics
5．1．1 Degenerate Parametric Amplifier
5．1．2 Photon Statistics
5．1．3 Wigner Function
5．2 Two-Mode Quantum Correlations
5．2．1 Non-degenerate Parametric Amplifier
5．2．2 Squeezing
5．2．3 Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox
5．2．4 Wigner Function
5．2．5 Reduced Density Operator
5．3 Quantum Limits to Amplification
5．4 Amplitude Squeezed State with Poisson Photon Number Statistics
Exercises
References
6 Stochastic Methods
6．1 Master Equation
6．2 Equivalent c-Number Equations
6．2．1 Photon Number Representation
6．2．2 P Representation
6．2．3 Properties of Fokker-Planck Equations
6．2．4 Steady State Solutions - Potential Conditions
6．2．5 Time Dependent Solution
6．2．6 Q Representation
6．2．7 Wigner Function
6．2．8 Generalized P Representation
6．3 Stochastic Differential Equations
6．3．1 Use of the Positive P Representation
6．4 Linear Processes with Constant Diffusion
6．5 Two Time Correlation Functions in Quantum Markov Processes．．
6．5．1 Quantum Regression Theorem
6．6 Application to Systems with a P Representation
6．7 Stochastic Unravellings
6．7．1 Simulating Quantum Trajectories
Exercises
References
Further Reading
7 Input-Output Formulation of Optical Cavities
7．1 Cavity Modes
7．2 Linear Systems
7．3 Two-Sided Cavity
7．4 Two Time Correlation Functions
7．5 Spectrum of Squeezing
7．6 Parametric Oscillator
7．7 Squeezing in the Total Field
7．8 Fokker-Planck Equation
Exercises
References．
Further Reading
8 Generation and Applications of Squeezed Light
8．1 Parametric Oscillation and Second Harmonic Generation
8．1．1 Semi-Classical Steady States and Stability Analysis
8．1．2 Parametric Oscillation
8．1．3 Second Harmonic Generation
8．1．4 Squeezing Spectrum
8．1．5 Parametric Oscillation
8．1．6 Experiments
8．2 Twin Beam Generation and Intensity Correlations
8．2．1 Second Harmonic Generation
8．2．2 Experiments
8．3 Applications of Squeezed Light
8．3．1 Interferometric Detection of Gravitational Radiation
8．3．2 Sub-Shot-Noise Phase Measurements
8．3．3 Quantum Information
Exercises
References
Further Reading
9 Nonlinear Quantum Dissipative Systems
9．1 Optical Parametric Oscillator： Complex P Function
9．2 Optical Parametric Oscillator： Positive P Function
9．3 Quantum Tunnelling Time
9．4 Dispersive Optical Bistahility
9．5 Comment on the Use of the Q and Wigner Representations Exercises
9．A Appendix
9．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）
References
Further Reading
10 Interaction of Radiation with Atoms
10．1 Quantization of the Many-Electron System
10．2 Interaction of a Single Two-Level Atom with a Single Mode Field．
10．3 Spontaneous Emission from a Two-Level Atom
10．4 Phase Decay in a Two-Level System
10．5 Resonance Fluorescence
Exercises
References
Further Reading
11 CQED
11．1 Cavity QED
11．1．1 Vacuum Rabi Splitting
11．1．2 Single Photon Sources
11．1．3 Cavity QED with N Atoms
11．2 Circuit QED
Exercises
References
Further Reading
12 Quantum Theory of the Laser
12．1 Master Equation
12．2 Photon Statistics
12．2．1 Spectrum of Intensity Fluctuations
12．3 Laser Linewidth
12．4 Regularly Pumped Laser
12．A Appendix： Derivation of the Single-Atom Increment
Exercises
References
13 Bells Inequalities in Quantum Optics
13．1 The Einstein-Podolsky-Rosen （EPR） Argument
13．2 Bell Inequalities and the Aspect Experiment
13．3 Violations of Bell's Inequalities Using a Parametric Amplifier Source
13．4 One-Photon Interference
Exercises
References
14 Quantum Nondemolition Measurements
14．1 Concept of a QND Measurement
14．2 Back Action Evasion
14．3 Criteria for a QND Measurement
14．4 The Beam Splitter
14．5 Ideal Quadrature QND Measurements
14．6 Experimental Realisation
14．7 A Photon Number QND Scheme
Exercises
References
15 Quantum Coherence and Measurement Theory
15．1 Quantum Coherence
15．2 The Effect of Dissipation
15．2．1 Experimental Observation of Coherence Decay
15．3 Quantum Measurement Theory
15．3．1 General Measurement Theory
15．3．2 The Pointer Basis
15．4 Examples of Pointer Observables
15．5 Model of a Measurement
15．6 Conditional States and Quantum Trajectories
15．6．1 Homodyne Measurement of a Cavity Field
Exercises
References
16 Quantum Information
16．1 Introduction
16．1．1 The Qubit
16．1．2 Entanglement
16．2 Quantum Key Distribution
16．3 Quantum Teleportation
16．4 Quantum Computation
16．4．1 Linear Optical Quantum Gates
16．4．2 Single Photon Sources
Exercises
References
Further Reading
17 Ion Traps
17．1 Introduction
17．2 Trapping and Cooling
17．3 Novel Quantum States
17．4 Trapping Multiple Ions
17．5 Ion Trap Quantum Information Processing
Exercises
References
18 Light Forces
18．1 Radiative Forces in the Semiclassical Limit
18．2 Mean Force for a Two-Level Atom Initially at Rest
18．3 Friction Force for a Moving Atom
18．3．1 Laser Standing Wave——Doppler Cooling
18．4 Dressed State Description of the Dipole Force
18．5 Atomic Diffraction by a Standing Wave
18．6 Optical Stern——Gerlach Effect
18．7 Quantum Chaos
18．7．1 Dynamical Tunnelling
18．7．2 Dynamical Localisation
18．8 The Effect of Spontaneous Emission
References
Further Reading
19 Bose-Einstein Condensation
19．1 Hamiltonian： Binary Collision Model
19．2 Mean-Field Theory —— Gross-Pitaevskii Equation
19．3 Single Mode Approximation
19．4 Quantum State of the Condensate
19．5 Quantum Phase Diffusion： Collapses and Revivals of the Condensate Phase
19．6 Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase
19．6．1 Interference of Two Condensates Initially in Number States
19．7 Quantum Tunneling of a Two Component Condensate
19．7．1 Semiclassical Dynamics
19．7．2 Quantum Dynamics
19．8 Coherence Properties of Bose-Einstein Condensates
19．8．1 1st Order Coherence
19．8．2 Higher Order Coherence
Exercises
References
Further Reading
Index
鄂公网安备 42010302001612号 