Atomic density fluctuations in Bose-Einstein condensates

A Yukawa-like equation, introduced to evaluate the first order correlation function in a Bose-Einstein condensate, can be used to evaluate the atomic density fluctuations. It does not require a few mode approximation. We apply this approach to calculate the atomic fluctuations of a condensate of attractive atoms in a double-well potential. The atomic system undergoes a spatial symmetry breaking above a critical number Nc of atoms. Near Nc the atomic fluctuation dN inside a single well becomes very large and experimentally observable by a phase-contrast imaging technique. dN is related to the collective mode temperature, which may be different from the condensate temperature measured by means of the thermal tails. A one-dimensional array of wells is also considered.