Imbalanced Fermi superfluid in a one-dimensional optical potential

TL;DR

This paper investigates the effects of population imbalance on superfluidity in a two-state Fermi mixture within a one-dimensional optical lattice, providing analytical solutions and phase diagrams.

Contribution

It offers analytical solutions for the free energy, gap, and number equations in an imbalanced Fermi superfluid in a lattice, including effects beyond mean-field in the BEC limit.

Findings

Phase separation occurs in layered structures.

Derived phase diagrams for superfluid and normal phases.

Analytical expressions for phase boundaries.

Abstract

The superfluid properties of a two-state Fermi mixture in an optical lattice are profoundly modified when an imbalance in the population of the two states is present.We present analytical solutions for the free energy, and for the gap and number equations in the saddle-point approximation describing resonant superfluidity in the quasi-two-dimensional gas. Inhomogeneities due to the trapping potentials can be taken into account using the local density approximation. Analyzing the free energy in this approximation, we find that phase separation occurs in the layers. The phase diagram of the superfluid and normal phases is derived and analytical expressions for the phase lines are presented. We complete the investigation by accounting for effects beyond mean-field in the BEC limit where the system is more properly described as a Bose-Fermi mixture of atoms and molecules.