  We study the phase diagram of one dimensional spin one-half fermionic cold
atoms. The two ``spin'' species can have different hopping or mass. The phase
diagram at equal densities of the species is found to be very rich, Mott
insulators as well as superfluids. We also briefly discuss coupling 1D systems
together, and some experimental signatures of these phases. In particular, we
compute the spin structure factor in the small momentum limit, which should
allow the spin gap to be detected.

Soft Condensed Matter;Strongly Correlated Electrons