Three-Component Fermi Gas in a one-dimensional Optical Lattice

TL;DR

This paper explores the phase behavior of a three-component Fermi gas in a 1D optical lattice, revealing four phases with trionic states and conditions for BCS phase stabilization, relevant to recent $^{6}$Li experiments.

Contribution

It identifies four distinct phases with trionic instabilities and analyzes the conditions for BCS phase stabilization in a three-component Fermi gas in a 1D lattice.

Findings

Four phases with trionic instabilities identified

Conditions for BCS phase stabilization at low densities or high anisotropy

Relevance to recent $^{6}$Li atom experiments

Abstract

We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2$k_F$ atomic density waves fluctuations of the three species. At small enough densities or strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally our results are discussed in light of a recent experiment on $^{6}$Li atoms.