Ground-state densities of repulsive two-component Fermi gases

TL;DR

This paper introduces a computational method using imaginary-time evolution of a nonlinear pseudo-Schrödinger equation to accurately determine ground-state densities of repulsive two-component Fermi gases in various trap geometries, including phase transition analysis.

Contribution

It presents a novel, efficient approach for calculating ground-state densities that incorporates gradient corrections and is adaptable to complex trap configurations.

Findings

Identified critical repulsion strengths for phase transitions.

Demonstrated transitions from identical to separated density profiles.

Validated method across different trap geometries.

Abstract

We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger equation in three dimensions, rather than from the cumbersome variational equations. With the underlying hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic trap. We present transitions from identical density profiles of the two fermion species towards isotropic and anisotropic separations for various confinements, including harmonic and double-well-type traps. Our proposed method is suited for arbitrary trap geometries and can be straightforwardly extended to study dynamics in the light of ongoing experiments on degenerate Fermi gases.