Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice

TL;DR

This paper investigates a 1D polarized Fermi gas in an optical lattice, revealing phase separation, FFLO states, and various phases depending on density and magnetization, using density matrix renormalization group simulations.

Contribution

It provides a detailed characterization of phase behavior and FFLO states in a 1D polarized Fermi gas with strong attraction, using numerical methods.

Findings

Phase separation into superconducting and metallic regions at low density.

Identification of FFLO states with finite momentum pairing.

Multiple phases including Fock, metallic, and polarized states at high density.

Abstract

We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low density regime, the system phase-separates into a well defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of tightly bound bosonic pairs with a finite center-of-mass momentum that scales linearly with the magnetization. In the large density limit, the system allows for four phases: in the core, we either find a Fock state of localized pairs or a metallic shell with free spin-down fermions moving in a fully filled background of spin-up fermions. As the magnetization increases, the Fock state disappears to give room for a metallic phase, with a partially polarized superconducting FFLO shell and a fully polarized metallic cloud surrounding the core.