Theory of quasi-one dimensional imbalanced Fermi gases

TL;DR

This paper develops a theoretical framework for quasi-one-dimensional imbalanced Fermi gases, revealing the nature of the FFLO state as a two-component Luttinger liquid and analyzing its phase transitions.

Contribution

It introduces an effective field theory based on Bethe ansatz that captures spin-charge mixing and characterizes the FFLO state as a two-component Luttinger liquid, providing a detailed phase diagram.

Findings

FFLO state is a two-component Luttinger liquid with fractional excitations.

Inter-tube tunneling leads to either a polarized Fermi liquid or FFLO superfluid.

Superfluid transition temperature scales with intertube coupling.

Abstract

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D `tubes') with spin imbalance, where strong intratube quantum fluctuations invalidate mean field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against inter-tube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.