  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.
