Counting statistics and fluctuations in Bose–Einstein condensation

Abstract

For a system of N Bose atoms, we propose a natural probability distribution for the occupation numbers. The counting statistics only depends on the probabilities of occupation of the single-particle states. Fluctuations of the occupation numbers are related in a simple way with the corresponding probabilities. The case of N ideal bosons trapped in a symmetric three-dimensional harmonic potential is analyzed. In this case, fluctuations of the condensate display a physically expected behavior. When the thermodynamic limit is considered, we obtain analytic expressions for the counting statistics and fluctuations of the ground estate occupation number. The temperature of maximum fluctuations of the ground state occupation number is proposed in order to characterize in an unambiguous way the apparition of a macroscopic condensate fraction.