Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices, Part I: Balanced case

TL;DR

This paper investigates superfluidity and pairing in balanced ultracold Fermi gases within one-dimensional optical lattices, revealing pseudogap phenomena, the dependence of transition temperature on lattice parameters, and unique low-temperature behaviors.

Contribution

It introduces a pairing fluctuation theory for 1D optical lattices, highlighting how lattice effects influence superfluid transition temperature and pairing properties, distinct from 3D systems.

Findings

Pseudogap phenomena are widespread beyond the BCS regime.

Superfluid transition temperature $T_c$ decreases with pairing strength in the BEC regime.

$T_c$ at unitarity increases with lattice constant $d$ and hopping $t$.

Abstract

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures, and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature $T_c$ decreases with pairing strength in the BEC regime, where it approaches asymptotically $T_c = \pi an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast growing (absolute value of the) fermionic chemical potential $\mu$ and pairing gap $\Delta$, which depends exponentially on the ratio $d/a$. Importantly, $T_c$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on $T_c$ is identified. The superfluid density exhibits $T^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.