Sqeezing out the entropy of Fermions in an optical lattice.

We point out a new scheme for achieving the strongly correlated system in an optical lattice. By turning the bulk of the trapped fermions into a band insulator, the entropy of the system is expelled to the surface and removed by various means. Our scheme also illustrates a general principle of cooling in a many body system. That is, one can use a gapped state to squeeze out the entropy and then turn it into the desired state after the entropy is removed.