Spin density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

TL;DR

This paper develops a spin-density functional theory to analyze imbalanced attractive Fermi gases in elongated traps, revealing how interactions and polarization influence phase separation and exotic pairing states.

Contribution

It introduces an accurate parametrization of the ground state energy for the spin-polarized Gaudin-Yang model within a density-functional framework.

Findings

Identification of a two-shell structure with FFLO phase at the center

Demonstration of the impact of interactions on density profiles

Validation of the theoretical approach against recent results

Abstract

We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikov-type phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.