Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

TL;DR

This paper investigates the critical behavior of harmonically confined Bose gases near the phase transition to Bose-Einstein condensation, revealing divergence in derivatives of susceptibilities due to confinement effects.

Contribution

It introduces a mean-field like model for the equation of state that captures the critical properties of confined Bose gases, bridging ideal and interacting regimes.

Findings

Divergence in derivatives of susceptibilities indicates critical behavior.

The model matches the Thomas-Fermi solution at large densities.

Critical properties can be experimentally tested.

Abstract

The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the {\it global} thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.