Condensation of N bosons. III. Analytical results for all higher moments of condensate fluctuations in interacting and ideal dilute Bose gases via the canonical ensemble quasiparticle formulation - art. no. 053606

We consider equilibrium canonical-ensemble fluctuations of the Bose-Einstei n condensate (BEC) in a trap using the particle-number conserving operator formalism of Girardeau and Arnowitt [Phys. Rev. 113, 755 (1959)] and the co ncept of the canonical-ensemble quasiparticles. We find explicit expression s for the characteristic function and all cumulants of the ground-state occ upation statistics both for the dilute weakly interacting and ideal Bose ga ses. We present analytical formulas for the moments of the ground-state occ upation fluctuations in the weakly interacting and ideal Bose gases in a bo x ("homogeneous gas") as well as in the ideal Bose gas in an arbitrary powe r-law trap, in particular, in an arbitrary harmonic trap. We calculate the effect of Bogoliubov coupling between quasiparticles on suppression of the ground-state occupation fluctuations at moderate temperatures and their enh ancement at very low temperatures. We clarify a crossover between ideal-gas and weakly interacting gas statistics, which is governed by a pair-correla tion, squeezing mechanism. The important conclusion is that in most cases t he ground-state occupation fluctuations are anomalously large and are not G aussian even in the thermodynamic limit.