Critical temperature of a trapped Bose gas: comparison of theory and experiment

TL;DR

This paper uses the Projected Gross-Pitaevskii equation to accurately predict the critical temperature shift in a trapped Bose gas, aligning well with experimental data and highlighting the importance of critical fluctuations.

Contribution

First application of a classical field method to quantitatively compare theoretical predictions with experimental measurements of Bose gas critical temperature shifts.

Findings

PGPE results differ from mean-field theories

Results agree closely with experimental data

Beyond mean-field effects require higher precision or stronger interactions

Abstract

We apply the Projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature $T_c$ of a harmonically confined Bose gas as reported in Gerbier \emph{et al.} [Phys. Rev. Lett. \textbf{92}, 030405 (2004)]. The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.