Thermodynamics of Trapped Imbalanced Fermi Gases at Unitarity

TL;DR

This paper develops a Landau-Ginzburg-like theoretical framework to describe the low-temperature behavior of trapped imbalanced Fermi gases at unitarity, accurately capturing inhomogeneities and interface properties beyond local-density approximations.

Contribution

It introduces a self-energy inclusive approach that accounts for strong interactions and inhomogeneities, providing improved agreement with experimental density profiles and insights into interface surface tension.

Findings

Good agreement with experimental density profiles.

Calculated universal surface tension of the superfluid-normal interface.

Discussed metastable states explaining superfluid core deformation.

Abstract

We present a theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap, that goes beyond the local-density approximation. The theory corresponds essentially to a Landau-Ginzburg-like approach that includes self-energy effects to account for the strong interactions at unitarity. We show diagrammatically how these self-energy effects arise from fluctuations in the superfluid order parameter. Gradient terms of the order parameter are included to account for inhomogeneities. This approach incorporates the state-of-the-art knowledge of the homogeneous mixture with a population imbalance exactly and gives good agreement with the experimental density profiles of Shin et al. [Nature 451, 689 (2008)]. This allows us to calculate the universal surface tension of the interface between the equal-density superfluid and the partially polarized normal state of the mixture. We also discuss the possibility of a metastable state to explain the deformation of the superfluid core that is seen in the experiment of Partridge et al. [Science 311, 503 (2006)].