Superfluidity of p-wave and s-wave atomic Fermi gases in optical lattices

We consider p-wave pairing of single hyperfine state and s-wave pairing of two hyperfine states ultracold atomic gases trapped in quasi-two-dimensional optical lattices. First, we analyse superfluid properties of p-wave and s-wave symmetries in the strictly weak coupling BCS regime where we discuss the order parameter, chemical potential, critical temperature, atomic compressibility and superfluid density as a function of filling factor for tetragonal and orthorhombic optical lattices. Second, we analyse superfluid properties of p-wave and s-wave superfluids in the evolution from BCS to BEC regime at low temperatures ($T \approx 0$), where we discuss the changes in the quasiparticle excitation spectrum, chemical potential, atomic compressibility, Cooper pair size and momentum distribution as a function of filling factor and interaction strength for tetragonal and orthorhombic optical lattices.