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

We consider a gas of spin-1/2 fermions with interactions near the unitary limit. In an applied periodic potential, 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 amplitude of the lattice potential. We map out the universal phase diagram at $N=\infty$ in a model with Sp($2N$) spin symmetry, and compute the universal ratio between the critical lattice amplitude and molecule recoil energy. As the interactions between fermions are varied, the insulator evolves smoothly between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent ultra-cold atom experiments.