Nesting and lifetime effects in the FFLO state of quasi-one-dimensional imbalanced Fermi gases

TL;DR

This paper investigates the stability and phase transitions of the FFLO state in quasi-one-dimensional imbalanced Fermi gases, considering effects of induced interactions and quasiparticle lifetime, revealing conditions for direct and intermediate phase transitions.

Contribution

It provides a detailed analysis of how induced interactions and quasiparticle lifetime influence the phase diagram and stability of the FFLO state in 1D Fermi gases, identifying a quantum critical point.

Findings

Direct transition from fully polarized to FFLO state with induced interactions.

Existence of a quantum critical point at finite Fermi mismatch for short quasiparticle lifetimes.

Transition from FFLO to a partially polarized normal state as mismatch increases.

Abstract

Motivated by the recent experimental realization of a candidate to the Fulde-Ferrell (FF) and the Larkin-Ovchinnikov (LO) states in one dimensional (1D) atomic Fermi gases, we study the quantum phase transitions in these enigmatic, finite momentum-paired superfluids. We focus on the FF state and investigate the effects of the induced interaction on the stability of the FFLO phase in homogeneous spin-imbalanced quasi-1D Fermi gases at zero temperature. When this is taken into account we find a direct transition from the fully polarized to the FFLO state. Also, we consider the effect of a finite lifetime of the quasi-particles states in the normal-superfluid instability. In the limit of long lifetimes, the lifetime effect is irrelevant and the transition is directly from the fully polarized to the FFLO state. We show, however, that for sufficiently short lifetimes there is a quantum critical point (QCP), at a finite value of the mismatch of the Fermi wave-vectors of the different quasi-particles, that we fully characterize. In this case the transition is from the FFLO phase to a normal partially polarized state with increasing mismatch.