Two-component repulsive Fermi gases with population imbalance in elongated harmonic traps

TL;DR

This paper analytically investigates the phase diagram and density profiles of a one-dimensional two-component repulsive Fermi gas with population imbalance, revealing a characteristic two-shell structure and finite susceptibility.

Contribution

It provides an analytical phase diagram and density profiles for the imbalanced Fermi gas in harmonic traps using Bethe Ansatz and local density approximation.

Findings

Identifies three phases: balanced, fully polarised, and partially polarised.

Shows a two-shell structure with specific phase distribution in the trap.

Demonstrates finite susceptibility across different parameters.

Abstract

We study the two-component repulsive Fermi gas with imbalanced populations in one dimension. Starting from the Bethe Ansatz solution we calculate analytically the phase diagram for the homogeneous system. We show that three phases appear: the balanced phase, the fully polarised phase and the partially polarised phase. By means of the local density approximation and the equation of state for the homogeneous system we calculate the density profile for the harmonically confined case. We show that a two-shell structure appears: at the center of the cloud we find the partially polarised phase and at the edges the fully polarised one. The radii of the inner and outer shells are calculated for different values of the polarisation and the coupling strength. We calculate the dependence of the magnetisation on the polarisation for different values of the coupling strength and we show that the susceptibility is always finite.