Superfluid-Insulator Transitions of the Fermi Gas with Near-Unitary Interactions in a Periodic Potential

Abstract

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 $V_{c}m{a}_L^2/{\hslash }^2$ at $N=\infty$ 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.