Microcanonical and Canonical Fluctuations in Bose-Einstein Condensates -- Fock state sampling approach

TL;DR

This paper introduces the Fock state sampling method to analyze atom number fluctuations in Bose-Einstein condensates, revealing ensemble-dependent suppression, interaction effects, and dependence on trap parameters, clarifying longstanding debates.

Contribution

The paper presents a novel Fock state sampling approach to accurately study fluctuations in weakly interacting Bose gases, resolving ensemble and interaction effects.

Findings

Suppression of fluctuations in microcanonical ensemble compared to canonical

Interactions shift the temperature of peak fluctuations

Fluctuation size depends on atom number and trap aspect ratio

Abstract

The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations furthermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or enhancement of fluctuations.