Attractive Fermi gases with unequal spin populations in highly elongated traps

TL;DR

This paper studies imbalanced attractive Fermi gases in one-dimensional traps, predicting a two-shell structure with a superfluid core and analyzing how the cloud size and polarization depend on interaction strength.

Contribution

It introduces a theoretical framework combining local density approximation with Bethe-ansatz solutions to describe phase separation in 1D Fermi gases with spin imbalance.

Findings

Predicted a two-shell structure with a superfluid core and polarized wings.

Calculated the cloud size and critical polarization as functions of interaction strength.

Identified the superfluid phase as FFLO type in the partially polarized core.

Abstract

We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one dimensional configurations. The ground state properties are determined within local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the FFLO type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell, are calculated as a function of the coupling strength.