  We propose a model to realize a fermionic superfluid state in an optical
lattice circumventing the cooling problem. Our proposal exploits the idea of
tuning the interaction in a characteristically low entropy state, a
band-insulator in an optical bilayer system, to obtain a superfluid. By
performing a detailed analysis of the model including fluctuations and
augmented by a variational quantum Monte Carlo calculations of the ground
state, we show that the superfluid state obtained has high transition
temperature of the order of the hopping energy. Our system is designed to
suppress other competing orders such as a charge density wave. We suggest a
laboratory realization of this model via an orthogonally shaken optical lattice
bilayer.
