Bose-Hubbard model with attractive interactions and inhomogeneous lattice potential

摘要

We consider the Bose-Hubbard model of attractive Bose gas in an optical lattice potential and in an additional inhomogeneous double well magnetic trap potential. We calculate the energy spectrum and the on-site number fluctuation of the system using numerical exact diagonalization procedure. Our results shows very clearly the role played by the degenerate double well minimum of the trap potential on the nature of instability of the attractive Bose-Hubbard model and the phase-transition picture of the system.