量子光学中的统计方法

Volume 1. Master Equations and Fokker-Planck Equations

1. Dissipation in Quantum Mechanics

The Master Equation Approach

1.1 Introduction

1.2 Inadequacy of an Ad Hoc Approach

1.3 System Plus R,eservoir Approach

1.3.1 The Schrodinger Equation in Integro-Differential Form

1.3.2 Born and Markov Approximations

1.3.3 The Markov Approximation and Reservoir Correlations

1.4 The Damped Harmonic Oscillator

1.4.1 Master Equation for the Damped Harmonic Oscillator

1.4.2 Some Limitations

1.4.3 Expectation Values and Commutation Relations

1.5 Two-Time Averages and the Quantum Regression Formula

1.5.1 Formal R,esults

1.5.2 Quantum Regression for a Complete Set of Operators

1.5.3 Correlation Functions for the Damped Harmonic Oscillator

2. Two-Level Atoms and Spontaneous Enussion

2.1 Two-Level Atom as a Pseudo-Spin System

2.2 Spontaneous Emission in the Master Equation Approach

2.2.1 Master Equation for a R,adiatively Damped Two-Level Atom

2.2.2 The Einstein A Coefficient

2.2.3 Matrix Element Equations, Correlation Functions, and Spontaneous Emission Spectrum

2.2.4 Phase Destroying Processes

2.3 Resonance Fluorescence

2.3.1 The Scattered Field

2.3.2 Master Equation for a Two-Level Atom

Driven by a Classical Field

2.3.3 Optical Bloch Equations and Dressed States

2.3.4 The Fluorescence Spect.rum

2.3.5 Seconcl-Order Coherence

2.3.6 Photon Antibunching and Squeezing

3. Quantum-Classical Correspondence for the Electromagnetic Field I:

The Glauber-Sudarshan P Representation

3.1 The Glauber-Sudarshan P Representation

3.1.1 Coherent States

3.1.2 Diagonal Representation for the Density Operator Using Coherent States

3.1.3 Examples: Coherent States, Thermal States, and Fock States

3.1.4 Fokker-Planck Equation for the Damped Harmonic Oscillator

3.1.5 Solution of the Fokker-Planck Equation

3.2 The Characteristic Function for Normal-Ordered Averages

3.2.1 Operator Averages and the Characteristic Function

3.2.2 Derivation of the Fokker-Planck Equation Using the Characteristic Function

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Volume 2. Modern Topics

The material in the first volume of this book is standard and I have clianged little in revising it for the second edition. My main task has been to correct the numerous errors that, having escaped detection in the original manuscript were brought to my attention after the book came to print. My thanks to all those who have helped in this enterprise by informing me of an insidious misspelling, a mistake in an equation, or a mislabeled figure. A few other superficial changes have been made; I have reworked many of the figures and "prettied up" the typesetting in one or two spots.