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Physical Review A

Extended Bose-Hubbard model with pair hopping induced by a quadratically coupled optomechanical system

Yue-Xin Huang, Xiang-Fa Zhou, Guang‐Can Guo, Yong-Sheng Zhang

Published Oct 24, 2016• 4 citations
Publisher

Abstract

We present a scheme to realize the (extended) Bose-Hubbard model in an $N$-coupled optomechanical system. By treating the cavities as intermediary and eliminating them adiabatically with the condition of large detuning or fast decay, we can obtain the effective Hamiltonian for the $N$ oscillators, with the regular terms in the Bose-Hubbard model, i.e., the pair tunnelings and the density-density interactions. Then we verify and provide the condition for our approximation with numerical results. Due to the existence of the pair tunnelings and the density-density interactions, we can investigate the density wave and supersolid phases in our model. Moreover, we also discuss the competition between the regular tunneling and the pair tunneling.

DOI
10.1103/physreva.94.043842

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We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on (d>1)(d>1)(d>1)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping ttt. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.
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.