Quantum law of rare events for systems with bosonic symmetry

In classical physics, the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, the unidirectional transfer of a 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 noninteracting systems (particles) obeying Bose-Einstein statistics. The classical law is significantly modified by quantum interference, which allows, among other effects, for the counterflow of particles back into the densely populated state. The suggested observation of this classically forbidden counterflow effect can be achieved with modern laser-based techniques used for manipulating and trapping cold atoms.