Ebook: Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations

The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker--Planck equations. Particular attention is given to the theory of optical bistability formulated in terms of the positive P-representation, and the theory of small bistable systems. This is a textbook at an advanced graduate level. It is intended as a bridge between an introductory discussion of the master equation method and problems of current research.

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The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker--Planck equations. Particular attention is given to the theory of optical bistability formulated in terms of the positive P-representation, and the theory of small bistable systems. This is a textbook at an advanced graduate level. It is intended as a bridge between an introductory discussion of the master equation method and problems of current research.

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The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker--Planck equations. Particular attention is given to the theory of optical bistability formulated in terms of the positive P-representation, and the theory of small bistable systems. This is a textbook at an advanced graduate level. It is intended as a bridge between an introductory discussion of the master equation method and problems of current research.
Content:
Front Matter....Pages I-XXIII
Dissipation in Quantum Mechanics: The Master Equation Approach....Pages 1-28
Two-Level Atoms and Spontaneous Emission....Pages 29-74
Quantum—Classical Correspondence for the Electromagnetic Field I: The Glauber—Sudarshan P Representation....Pages 75-99
Quantum—Classical Correspondence for the Electromagnetic Field II: P, Q, and Wigner Representations....Pages 101-145
Fokker—Planck Equations and Stochastic Differential Equations....Pages 147-193
Quantum—Classical Correspondence for Two-Level Atoms....Pages 195-255
The Single-Mode Homogeneously Broadened Laser I: Preliminaries....Pages 257-304
The Single-Mode Homogeneously Broadened Laser II: Phase-Space Analysis....Pages 305-348
Back Matter....Pages 349-368

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The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker--Planck equations. Particular attention is given to the theory of optical bistability formulated in terms of the positive P-representation, and the theory of small bistable systems. This is a textbook at an advanced graduate level. It is intended as a bridge between an introductory discussion of the master equation method and problems of current research.
Content:
Front Matter....Pages I-XXIII
Dissipation in Quantum Mechanics: The Master Equation Approach....Pages 1-28
Two-Level Atoms and Spontaneous Emission....Pages 29-74
Quantum—Classical Correspondence for the Electromagnetic Field I: The Glauber—Sudarshan P Representation....Pages 75-99
Quantum—Classical Correspondence for the Electromagnetic Field II: P, Q, and Wigner Representations....Pages 101-145
Fokker—Planck Equations and Stochastic Differential Equations....Pages 147-193
Quantum—Classical Correspondence for Two-Level Atoms....Pages 195-255
The Single-Mode Homogeneously Broadened Laser I: Preliminaries....Pages 257-304
The Single-Mode Homogeneously Broadened Laser II: Phase-Space Analysis....Pages 305-348
Back Matter....Pages 349-368
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