Quantum law of rare events for systems with Bose-Einstein statistics

Abstract

In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated states of a classical two-state system. We derive a quantum version of the law for a large number of non-interacting systems (particles) obeying Bose-Einstein statistics. The classical low is significantly modified by quantum interference, which allows, among other effects, for the counter flow of particles back into the densely populated state. Suggested observation of this classically forbidden counter flow effect can be achieved with modern laser-based techniques used for manipulating and trapping of cold atoms.