Physical interpretation of Monte Carlo wave-function and stochastic Schroedinger equation methods for cavity quantum electrodynamics

The dynamics of open system is frequently modeled in terms of a small system S coupled to a reservoir R, the last having an infinitely larger number of degree of freedom than S. Usually the dynamics of the S variables may be of interest, which can be studied using either Langevin equations, or master equations, or yet the path integral formulation. Useful alternatives for the master equation method are the Monte Carlo Wave-function method (MCWF), and Stochastic Schroedinger Equations (SSE's). The methods MCWF and SSE's recently experienced a fast development both in their theoretical background and applications to the study of the dissipative quantum systems dynamics in quantum optics. Even though these alternatives can be shown to be formally equivalent to the master equation approach, they are often regarded as mathematical tricks, with no relation to a concrete physical evolution of the system. The advantage of using them is that one has to deal with state vectors, instead of density matrices, thus reducing the total amount of matrix elements to be calculated. In this work, we consider the possibility of giving a physical interpretation to these methods, in terms of continuous measurements made on the evolving system. We show that physical realizations of the two methods are indeed possible, for a mode of the electromagnetic field in a cavity interacting with a continuum of modes corresponding to the field outside the cavity. Two schemes are proposed, consisting of a mode of the electromagnetic field interacting with a beam of Rydberg two-level atoms. In these schemes, the field mode plays the role of a small system and the atomic beam plays the role of a reservoir (infinitely larger number of degrees of freedom at finite temperature, the interaction between them being given by the Jaynes-Cummings model