Novel pairing in the Hubbard model with confinement potential

We explore a novel type of pairing in the repulsive Hubbard model with a confinement potential. Such an undertaking situation including the confinement potential is realized in a part of intense spatial modulations observed in High-Tc cuprate superconductors, while an atomic Fermi gas loaded on an optical lattice is described by the Hubbard model with the confinement potential. In this paper, applying the exact diagonalization method to a one-dimensional Hubbard model with the confinement potential, we find that, when U exceeds a critical value, the binding energy of two Fermi atoms becomes 'negative, indicating that an attractive interaction effectively works between two fermions. In this case, a 'Mott core' appears in the confinement center, where each site is occupied by one atom, and the Cooper-pair function strongly develops between fermions in the left and right hand sides of this core.