Thermal and quantum fluctuations of confined Bose-Einstein condensate beyond the Bogoliubov approximation

TL;DR

This paper extends a zero-temperature formulation of quantum and thermal fluctuations in confined Bose-Einstein condensates beyond the Bogoliubov approximation to finite temperatures, considering finite-size effects and zero mode operators.

Contribution

It introduces a method to incorporate thermal fluctuations and zero mode operators in finite-size BECs beyond the Bogoliubov approximation, revealing enhanced depletion and thermodynamic effects.

Findings

Enhanced depletion condensate in weak interaction regime

Proper treatment of zero mode operators at finite temperature

Reproduces homogeneous system results in large particle limit

Abstract

The formulation for zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y.Nakamura et al., Phys. Rev. A 89, 013613 (2014)] is extended to finite temperature. Both thermal and quantum fluctuations are considered in a manner consistent with a concept of spontaneous symmetry breakdown for a finite-size system. Therefore, we need a proper treatment of the zero mode operators, which invoke non-trivial enhancements in depletion condensate and thermodynamical quantities such as the specific heat. The enhancements are visible in the weak interaction case. Our approach reproduces the results of a homogeneous system in the Bogoliubov approximation in a large particle number limit.