Monte Carlo Wavefunctions

Abstract

An atom decaying by spontaneous emission, or a field mode which is damped due to absorption or leakage of photons through mirrors, are examples of “open systems” in quantum optics. Such systems must be described by quantities which are more general than a wavefunction, and their dynamics is different from the usual solutions of Schrodinger’s equation. The standard treatment involves the introduction of a system density matrix ρ,and under conditions often fulfilled in quantum optics problems, the Schrodinger equation of motion for the total system+ surroundings wavefunction leads to a linear equation of motion, the so-called master equation, for ρ(t). Recently, a novel treatment of such systems was introduced: provided a stochastic element is included in the evolution, it is possible to apply wavefunctions rather than density matrices. We shall give a brief outline of how these stochastic wavefunctions are introduced and point out some of their main advantages. As an example we shall discuss the application to full quantum calculations on laser cooling. Experiments on laser cooling are now approaching a regime where collective atomic effects become prominent, and as a natural extension we shall comment on the application of wavefunctions to non-linear master equations.