Abstract

Very recently there have been a number of papers discussing the applicability of stochastic methods as an alternative to the usual treatment of master equations in quantum mechanics.^1-5 In this paper we present a wave function approach including a stochastic element to study the evolution of a small system when it is coupled to a reservoir. We show how fluctuations and dissipation originate from quantum jumps occuring randomly during the time evolution of the system, and we present a physical interpretation of the procedure. We demonstrate how this treatment may replace a wide class of master equations, and its use in problems with a large number of states N is discussed. Since the density matrix has N ×N elements, where a wave function is determined by only N variables, there is a computational advantage in using the wave function procedure. This is illustrated by calculations on cooling atoms in a laser field.

© 1992 Optical Society of America