Dissipation in Quantum Mechanics: The Master Equation Approach

Abstract

This book deals with various quantum-statistical methods and their application to problems in quantum optics. The development of these methods arose out of the need to deal with dissipation in quantum optical systems. Thus, dissipation in quantized systems is a theme unifying the topics covered in the book. Two elementary systems provide the basic building blocks for a number of applications: the damped harmonic oscillator, which describes a single mode of the electromagnetic field in a lossy cavity (a cavity with imperfect mirrors), and the damped two-level atom. The need for a quantized treatment for the damped field mode arose originally in the context of the quantum theory of the maser and the laser. The damped two-level atom is, of course, of very general and fundamental interest, since it is just the problem of spontaneous emission. The book is structured around these two illustrative examples and their use in building quantum-theoretic treatments of resonance fluorescence and the single-mode laser. A second volume will extend the applications to the degenerate parametric oscillator and cavity quantum electrodynamics (cavity QED.). Discussion of the examples will guide the development of fundamental formalism. When we meet such things as master equations, phase-space representations, Fokker—Planck equations and stochastic differential equations, and the related methods of analysis, we will always have a specific application at hand with which to illustrate the formalism. Although formal methods will be introduced essentially from first principles, in places the treatment will necessarily be rather cursory. Ample references to the literature will hopefully offset any deficiencies.