Inhomogeneous Fermi mixtures at Unitarity: Bogoliubov-de Gennes vs. Landau-Ginzburg

TL;DR

This paper develops an inhomogeneous theoretical framework for low-temperature resonantly interacting Fermi mixtures, comparing Bogoliubov-de Gennes and Landau-Ginzburg methods, and successfully matches experimental density profiles.

Contribution

It introduces an improved inhomogeneous theory surpassing local-density approximation, especially for first-order phase transitions, and explores interface phenomena including surface tension and exotic phases.

Findings

Landau-Ginzburg approach better for first-order transitions

Good agreement with experimental density profiles

Stability of Sarma phase at interfaces

Abstract

We present an inhomogeneous theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap that goes beyond the local-density approximation. We compare the Bogoliubov-de Gennes and a Landau-Ginzburg approach and conclude that the latter is more appropriate when dealing with a first-order phase transition. Our approach incorporates the state-of-the-art knowledge on the homogeneous mixture with a population imbalance exactly and gives good agreement with the experimental density profiles of Shin {\it et al}. [Nature {\bf 451}, 689 (2008)]. We calculate the universal surface tension due to the observed interface between the equal-density superfluid and the partially polarized normal state of the mixture. We find that the exotic and gapless superfluid Sarma phase can be stabilized at this interface, even when this phase is unstable in the bulk of the gas.