Bose-Einstein condensate fluctuations versus an interparticle interaction

TL;DR

This paper investigates how interparticle interactions influence Bose-Einstein condensate fluctuations in a nonuniform system, revealing a transition between ideal and interacting regimes and emphasizing boundary effects in large systems.

Contribution

It provides a detailed analysis of BEC fluctuation regimes in a nonuniform trap, highlighting the persistent boundary effects and describing the transition from ideal to Thomas-Fermi regimes.

Findings

Identification of non-Gaussian and Gaussian fluctuation regimes

Discovery of boundary effects persisting in the thermodynamic limit

Description of the crossover between thermal and quantum fluctuations

Abstract

We calculate the Bose-Einstein condensate (BEC) occupation statistics vs. the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics - the anomalous non-Gaussian thermally-dominated fluctuations and the Gaussian quantum-dominated fluctuations - as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations does not vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.