Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light

TL;DR

This paper investigates grand-canonical fluctuations in weakly interacting Bose-Einstein condensates of light, revealing that fluctuations vanish at zero temperature but remain higher than canonical predictions at finite temperatures, highlighting ensemble inequivalence.

Contribution

It provides a phenomenological description of condensate fluctuations using exact recurrence relations for weakly interacting gases in a harmonic trap.

Findings

Fluctuations vanish at zero temperature, similar to ideal gases in canonical ensemble.

At finite temperatures, fluctuations are significantly higher than canonical ensemble predictions.

The study demonstrates non-equivalence of ensembles in weakly interacting Bose gases.

Abstract

Grand-canonical fluctuations of Bose-Einstein condensates of light are accessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014).]. We phenomenologically describe these fluctuations by using the grand-canonical ensemble for a weakly interacting Bose gas at thermal equilibrium. For a two-dimensional harmonic trap, we use two models for which the canonical partition functions of the weakly interacting Bose gas are given by exact recurrence relations. We find that the grand-canonical condensate fluctuations for weakly interacting Bose gases vanish at zero temperature, thus behaving qualitatively similar to an ideal gas in the canonical ensemble (or micro-canonical ensemble) rather than the grand-canonical ensemble. For low but finite temperatures, the fluctuations remain considerably higher than for the canonical ensemble, as predicted by the ideal gas in the grand-canonical ensemble, thus clearly showing that we are not in a regime in which the ensembles are equivalent.