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.I 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 ConstantIntensity
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 P Representation
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
Keferences
5 Quantum Phenomena in Simple Systems in Nonlinear Optics
5.1 Single—Mode Quantum 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 ofSqueezing
7.6 Parametric Oscillator
7.7 Squeezing in the Total Field
7.8 Fokker—Pianck 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.I Optical Parametric Oscillator：Complex P Function
9.2 Optical Parametric Oscillator：Positive P Function
9.3 Quantum Tunnelling Time
9.4 Dispersive Optical Bistability.
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（9.17）
9.A.2 Evaluation of the Moments for the Complex P Function for Optical Bistability（9.48）
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 aTwo—Level Atom.
10.4 Phase Decay in a Two—Level System
10.5 Resonance Fluorescence
Exercises
References
Further Reading
1l CQED
1.1.1 Cavity QED
1.1.1 I Vacuum Rabi Splitting
1.1.1.2 Single Photon Sources
1.1.1.3 Cavity QED with N Atoms
1.1.2 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
14 Quantum Nondemolition Measurements
15 Quantum Coherence and Measurement Theory
16 Quantum Information.
17 Ion Traps
18 Light Forces
19 Bose—Einstein Condensation
Index
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