Critical properties of a trapped interacting Bose gas

Abstract

We develop a practical theoretical formalism for studying the critical properties of a trapped Bose-Einstein condensate using the projected Gross-Pitaevskii equation. We show that this approach allows us investigate the behavior of the correlation length, condensate mode and its number fluctuations about the critical point. Motivated by recent experiments [Science {\bf 315}, 1556 (2007)] we calculate the critical exponent for the correlation length, observe clear finite-size effects, and develop characteristic length scales to characterize the finite-size influences. We extend the Binder cumulant to the trapped system and discuss an experimental method for measuring number fluctuations.

10 pages, 9 figures

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• Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates
• The stochastic projected Gross-Pitaevskii equation
• A comparison between microscopic methods for finite temperature Bose gases
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• Temporal correlations of elongated Bose gases at finite temperature
• Interaction effects on dynamic correlations in non-condensed Bose gases
• Dynamics of quantum vortices at finite temperature
• Fluctuational susceptibility of ultracold bosons in the vicinity of condensation