Controlling the pair momentum of the FFLO state in a 3D Fermi gas through a 1D periodic potential

TL;DR

This paper explores how a 1D periodic potential can control the direction of the FFLO state's pair momentum in a 3D Fermi gas, revealing a new skewed orientation that enhances pairing overlap.

Contribution

It demonstrates that the FFLO wave vector can be skewed relative to the periodic potential, expanding the understanding of FFLO state configurations in 3D Fermi gases.

Findings

FFLO wave vector can be skewed relative to the periodic potential

Tilting the wave vector increases pairing overlap

Skewed FFLO state offers new experimental signatures

Abstract

The question whether a spin-imbalanced Fermi gas can accommodate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has been the subject of intense study. This state, in which Cooper pairs obtain a nonzero momentum, has hitherto eluded experimental observation. Recently, we demonstrated that the FFLO state can be stabilized in a 3D Fermi gas, by adding a 1D periodic potential. Until now it was assumed that the FFLO wave vector always lies parallel to this periodic potential (FFLO-P). In this contribution we show that, surprisingly, the FFLO wave vector can also lie skewed with respect to the potential (FFLO-S). Starting from the partition sum, the saddle-point free energy of the system is derived within the path-integral formalism. Minimizing this free energy allows us to study the different competing ground states of the system. To qualitatively understand the underlying pairing mechanism, we visualize the Fermi surfaces of the spin up and spin down particles. From this visualization, we find that tilting the FFLO wave vector with respect to the direction of the periodic potential, can result in a larger overlap between the pairing bands of both spin species. This skewed FFLO state can provide an additional experimental signature for observing FFLO superfluidity in a 3D Fermi gas.