We propose a Hamiltonian of ultracold spinless atom in optical lattices including the two-body interaction of nearest neighbors, which reduces to the Bose-Hubbard model in weak-interaction limit. An atom-pair hopping term appearing in the Hamiltonian explains naturally the recent experimental observation of correlated tunneling in a double-well trap with strong atom-atom interactions and moreover leads to a dynamic process of atom-pair tunneling where strongly interacting atoms can tunnel back and forth as a fragmented pair. Finally a dynamics of oscillations induced by the atom-pair tunneling is found in the strong interaction regime, where the Bose-Hubbard model gives rise to the insulator state with fixed time-averaged value of atom-occupation number only. Quantum phase transitions between two quantum phases characterized by degenerate and nondegenerate ground states are shown to be coinciding with the Landau second-order phase-transition theory. In the system of finite atom number the degeneracy of ground states can be removed by quantum tunneling for the even number of atoms but not for the odd number.

• Received 21 April 2008

DOI:https://doi.org/10.1103/PhysRevA.79.033617