Novel Superfluidity of Trapped Fermi Atoms Loaded on Optical Lattices

We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes {\it negative} below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a "Mott insulating core" appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left and right hand sides of this core. Furthermore, we show a ground-state phase diagram including the superfluidity on the trapped Fermi atoms loaded on optical lattices.