Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps

TL;DR

This paper develops a density-functional theory for strongly correlated two-component Fermi gases in elongated traps, capturing interaction effects near Feshbach resonances and predicting observable density wave phenomena.

Contribution

It introduces a Kohn-Sham DFT approach using the Gaudin-Yang model as a reference for inhomogeneous Q1D Fermi gases, incorporating local-density approximations for exchange and correlation energies.

Findings

Repulsive interactions reduce shell structure amplitude.

Attractive interactions promote atomic-density waves.

Predicted phenomena are observable in small atomic clouds.

Abstract

Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas {\it via} a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to a hundred atoms.