Superfluid-insulator transitions of the fermi gas with near-unitary interactions in a periodic potential

We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period a_{L}, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V=V_{c}. We compute the universal ratio V_{c}ma_{L};{2}/variant Planck's over 2pi;{2} at N=infinity in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.