Inhomogeneous BCS-BEC crossover for trapped cold atoms in optical lattices

The BCS-BEC (Bose-Einstein condensation) crossover in a lattice is a powerful paradigm that describes how a superconductor deviates from the Bardeen-Cooper-Schrieffer physics as the attractive interaction increases. Optical lattices loaded with binary mixtures of cold atoms allow one to access this phenomenon experimentally in a clean and controlled way. We show that, however, the possibility to study this phenomenon in actual cold-atoms experiments is limited by the effect of the trapping potential. Real-space dynamical mean-field theory calculations show indeed that interactions and the confining potential conspire to pack the fermions in the center of the trap, which approaches a band insulator when the attraction becomes sizeable. Interestingly, the energy gap is spatially more homogeneous than the superfluid condensate order parameter. We show how this physics reflects in several observables, and we propose an alternative strategy to disentangle the effect of the harmonic potential and measure the intrinsic properties resulting from the interaction strength.