Spin-1/2 fermions with attractive interaction in an optical lattice

We study attractive fermions in an optical lattice superimposed by a trapping potential, such that fermions may form bosonic molecules. We map the model onto nonlinear field equations depending on the Nambu-Gor'kov propagator. The resulting field equations where solved numerically by a relaxation technique that allowed us to calculate the inhomogeneous densities of fermions and condensed molecules at zero temperature. When the interactions between fermions are strong there is a competition between unbound fermions and bound molecules leading to an unexpected reduction of the non-homogeneous density of fermions at the center of the trap.