Fulde-Ferrell-Larkin-Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases

TL;DR

This paper systematically explores quantum phases in a one-dimensional spin-polarized Fermi gas, revealing the dominance of FFLO states over phase separation, contrasting with three-dimensional predictions, and proposes experimental detection methods.

Contribution

The study compares three theoretical methods to map the phase diagram, demonstrating the prevalence of FFLO states in 1D and challenging 3D phase separation predictions.

Findings

FFLO phase dominates most of the 1D phase diagram.

Second-order phase transition from BCS to FFLO state.

Two-energy-gap structure in density of states as an experimental signature.

Abstract

We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.