量子光学中的统计方法

9 The Degenerate Parametric Oscillator Ⅰ: Squeezed States

9.1 Introduction

9.2 Degenerate Parametric Amplification and Squeezed States

9.2.1 Degenerate Parametric Amplification Without Pump Depletion

9.2.2 Quantum Fluctuations and Squeezed States

9.2.3The Degenerate Parametric Oscjllator

9.2.4 Master Equation for the Degenerate Parametric Oscillator

9.2.5 Cavity Output Fields

9.3 The Spectrum of Squeezing

9.3.1Intracavity Field Fluctuations

9.3.2 Defirution of the Spectrum of Squeezing

9.3.3 Homodyne Detection: The Source-Field Spectrum of Squeezing

9.3.4 The Source-Field Spectrum of Squeezing with Unit Efficiency

9.3.5 Free-Field Coritributions

9.3.6 Vacuum Fluctuations

9.3.7 Squeezing in the Wigner Representation: A Comment on Interpretation

10 The Degenerate Parametric Oscillator Ⅱ： Phase-Space Analysis in the Small-Noise Limit

10.1 Phase-Space Formalism for the Degenerate Parametric Oscillator

10.1.1 Phase-Space Equation of Motion in the P Representation

10.1.2 Phase-Space Equations of Motion in the Q and Wigner R,epresentations

10.2 Squeezing: Quantum Fluctuations in the Small-Noise Limit

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11 The Positive P Representation

12 The Degenerate Parametric Oscillator Ⅲ: Phase-Space Analysis Outside the Small-Noise Limit .

13 Cavity QED I: Simple Calculations

14 Many Atoms in a Cavity Ⅰ: Macroscopic Theory

15 Many Atoms in a Cavity Ⅱ: Quantum Fluctuations in the Small-Noise Limit

16 Cavity QED II: Quantum Fluctuations

17 Quantum Trajectories Ⅰ: Background and Interpretation

18 Quantum Tajectories Ⅱ: The Degenerate Parametric Oscillator

19 Quantum Trajectories Ⅲ: More Examples

References

Index

The subtitle, Nonclassical Fields, is perhaps not as accurate as it might be as a summary of content; or to put it another way, if my aim from the start had been to write a book on this topic, parts of that book would differ significantly from what follows here. Possibly the most important thing missing, and something that should be said, is that there are two quite distinct paths to a definition of nonclassicality in quantum optics. The first is grounded in the existence, or otherwise, of a nonsingular and positrve Glauber-Sudarshan P function. The physical grounding is in the treatment of optical measurements, specifically the photoelectric effect: for a given optical field, can the photoelectron counting statistics, including all correlations, be reproduced by a Poisson process of photoelectron generation driven by a classicallight intensity, allowed most generally to be stochastic? Viewed at a more informallevel, the question asks whether or not the infamous proposal of Bohr, Kramers, and Slater for the interaction of classical light and quantized atoms can be upheld in the presence of the observable photoelectron counting statistics.