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
