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

TL;DR

This paper derives a quantum analogue of the classical Poisson law for rare events in Bose-Einstein systems, highlighting quantum interference effects like counter flow, with potential experimental observation using cold atom techniques.

Contribution

It introduces a quantum version of the law of rare events for Bose-Einstein systems, incorporating quantum interference effects absent in classical models.

Findings

Quantum interference modifies classical Poisson statistics.

Counter flow of particles into dense states is possible.

Experimental observation feasible with cold atom techniques.

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.