Superfluidity And Pairing Phenomena In Ultracold Atomic Fermi Gases In One-Dimensional Optical Lattices. I. Balanced Case

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.