I Master Equation Methods in Quantum Optics

Abstract

This chapter focuses on master equation methods in quantum optics. Some of the methods have been specifically developed to treat the problems in quantum optics. These include the well known phase space methods. In phase space methods, the c-number distribution functions for quantum systems are introduced, which in many physical situations are found to obey equations of the Fokker–Planck type. In quantum optics, the concern is usually related to the study of a subsystem that is a part of a large system. Master equation methods have found applications in many branches of physics, such as in the theory of relaxation processes. The chapter also explains master equations for open systems. Some of the problems, involving open systems, in quantum optics are those of lasers, the relaxation of oscillators and two-level atoms, super-radiance, and parametric oscillators. In problems such as superradiance, the radiation field plays the role of the reservoir. The chapter describes the derivation of the master equation for the reduced density operator (phase space distribution function) of the sub-system of interest.