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.
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