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The superfluidity and pairing phenomena in ultracold atomic Fermi gases havebeen of great interest in recent years, with multiple tunable parameters. Herewe study the BCS-BEC crossover behavior of balanced two-component Fermi gasesin a one-dimensional optical lattice, which is distinct from the simplethree-dimensional (3D) continuum and a fully 3D lattice often found in acondensed matter system. We use a pairing fluctuation theory which includesself-consistent feedback effects at finite temperatures, and find widespreadpseudogap phenomena beyond the BCS regime. As a consequence of the latticeperiodicity, the superfluid transition temperature $T_c$ decreases with pairingstrength in the BEC regime, where it approaches asymptotically $T_c = \pian/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) thefermion density (mass). In addition, the quasi-two dimensionality leads to fastgrowing (absolute value of the) fermionic chemical potential $\mu$ and pairinggap $\Delta$, 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. Thesuperfluid density exhibits $T^{3/2}$ power laws at low $T$, away from theextreme BCS limit. These predictions can be tested in future experiments.

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