本书从相空间的角度，用基于半经典的方法来理解量子光学这一快速发展的领域。它首先介绍令人惊奇的结果，然后给出清晰的解释。本书非常详细地介绍了第一个光学实验，此项发现导致量子光学成为一个庞大的研究领域。它试图用力学振子之于标准波，类似的方法解释物质和波的纠缠。书中从量子光学的角度，对经典光学的一些实验予以新的诠释；对原子间的相互作用也进行了详细讨论。为方便阅读，本书提供了上百页的相关数学背景知识。每章结尾，给出一些具有挑战性的问题。

本书对于从事量子光学研究的研究者，具有很高的参考价值。

What's Quantum Optics?

 1.1 On the Road to Quantum Optics

 1.2 Resenance Fluorescence

1.2.1 Elastic Peak: Light as a Wave

1.2.2 Mollow-Three-Peak Spectrum

1.2.3 Anti-Bunching

 1.3 Squeezing the Fluctuations

1.3.1 What is a Squeezed State?

1.3.2 Squeezed States in the Optical Parametric Oscillator

1.3.3 Oscillatory Photon Statistics

1.3.4 Interference in Phase Space

 1.4 Jaynes-Cummings-Paul Model

1.4.1 Single Two-Level Atom plus a Single Mode

1.4.2 Time Scales

 1.5 Cavity QED

1.5.1 An Amazing Maser

1.5.2 Cavity QED in the Optical Domain

 1.6  de Broglie Optics

1.6.1 Electron and Neutron Optics

1.6.2 Atom Optics

1.6.3 Atom Optics in Quantized Light Fields

 1.7 Quantum Motion in Paul Traps

1.7.1 Analogy to Cavity QED

1.7.2 Quantum Information Processing

 1.8 Two-Photcn Interferometry and More

 1.9 Outline of the Book

2 Ante

 2.1 Position and Momentum Eigenstates

2.1.1 Properties of Eigenstates

2.1.2 Derivative of Wave Function

2.1.3 Fourier Transform Connects x- and p-Space

 2.2 Energy Eigenstate

2.2.1 Arbitrary Representation

2.2.2 Position Representation

 2.3 Density Operator: A Brief Introduction

2.3.1 A State Vector is not Enough!

2.3.2 Definition and Properties

2.3.3 Trace of Opelator

2.3.4 Examples cf a Density Operator

 2.4 Time Evolution of Quantum States

2.4.1 Motion of a Wave Packet

2.4.2 Time Evolution due to Interaction

2.4.3 Time Dependent Hamiltonian

2.4.4 Time Evolution of Density Operator

3 Wigner Function

 3.1 Jump Start of the Wigner Function

 3.2 Properties of the Wigner Function

3.2.1 Marginals

3.2.2 Overlap of Quantum States as Overlap in Phase Space

3.2.3 Shape of Wigner Function

 3.3 Time Evolution of Wigner Function

3.3.1 von Neumann Equation in Phase Space

3.3.2 Quantum Liouville Equation

 3.4 Wigner Function Determined by Phase Space

3.4.1 Definition of Moyal Function

3.4.2 Phase Space Equations for Moyal Functions

 3.5 Phase Space Equations for Energy Eigenstates

3.5.1 Power Expansion in Planck's Constant

3.5.2 Model Differential Equation

 3.6  Harmonic Oscillator

3.6.1 Wigner Function as Wave Function

3.6.2 Phase Space Enforces Eneigy Quantization

 3.7 Evaluation cf Quantum Mechanical Averages

3.7.1 Operator Ordering

3.7.2 Examples of Weyl-Wigner Ordering

4 Quantum States in Phase Space

 4.1 Energy Eigenstate

4.1.1 Simple Phase Space Representation

4.1.2 Large-m Limit

4.1.3 Wigner Function

 4.2 Ccherent State

4.2.1 Definition cf a Coherent State

4.2.2 Energy Distribution

4.2.3 Time Evolution

 4.3 Squeezed State

4.3.1 Definition of a Squeezed State

4.3.2 Energy Distribution: Exact Treatment

4.3.3 Energy Distribution: Asymptotic Treatment

4.3.4 Limit Towards Squeezed Vacuum

 ……

5 Waves a la WKB

6 WKB and Berry Phase

7 Interference in Phase space

8 Applications of Interference in Phase Space

9 Wave Packet Dynamics

10 Fidld Quantization

11 Field States

12 Phase Space Functions

13 Optical Interferometry

14 Atom-Field Interaction

15 Jaynes-Cummings-Paul Model: Dynamics

16 State Prepartion and Entanglement

17 Paul Trap

18 Damping and Amplification

19 Atom Optics in Quantized Light Fields

20 Wigner Funcations in Atom Optics

Index