Correlation Effects in Ultracold Two-Dimensional Bose Gases

TL;DR

This paper investigates correlation effects in ultracold 2D Bose gases, deriving an effective interaction, analyzing mean-field and renormalization group theories, and highlighting the importance of correlations near criticality.

Contribution

It introduces a renormalization group approach to improve mean-field descriptions of 2D Bose gases, resolving unphysical density discontinuities near the BKT transition.

Findings

Mean-field theory shows a density discontinuity near the BKT transition.

Renormalization group approach removes the unphysical discontinuity.

Correlation effects are significant even in the normal phase approaching criticality.

Abstract

We study various properties of an ultracold two-dimensional (2D) Bose gas that are beyond a mean-field description. We first derive the effective interaction for such a system as realized in current experiments, which requires the use of an energy dependent $T$-matrix. Using this result, we then solve the mean-field equation of state of the modified Popov theory, and compare it with the usual Hartree-Fock theory. We show that even though the former theory does not suffer from infrared divergences in both the normal and superfluid phases, there is an unphysical density discontinuity close to the Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field description by using a renormalization group approach and show how the density discontinuity is resolved. The flow equations in two dimensions, in particular, of the symmetry-broken phase, already contain some unique features pertinent to the 2D XY model, even though vortices have not been included explicitly. We also compute various many-body correlators, and show that correlation effects beyond the Hartree-Fock theory are important already in the normal phase as criticality is approached. We finally extend our results to the inhomogeneous case of a trapped Bose gas using the local-density approximation and show that close to criticality, the renormalization group approach is required for the accurate determination of the density profile.