Quantum Phases of Cold Bosonic Atoms in an Optical Lattice with Inhomogeneous Atomic Interactions and Coexistence of Multi Phases

We study cold bosonic atoms on a two-dimensional inhomogeneous optical lattice with site-dependent atomic interactions. With the tight -binding approximation, we derive the extended Bose Hubbard model. Base on the mean-field approximation, the ground states are solved by the exact diagonalization method. We calculate the mean-field order parameter and particle number density for the ground states. We find the coexistence of superfluid phase and Mott-insulator phase on the two-dimensional inhomogeneous optical lattice in appropriate parameter ranges.