We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized processes and compute the corresponding phase diagram. It substantially deviates from the single-band Bose–Hubbard model and predicts strong changes of the superfluid-to-Mott-insulator transition. In general, the presented beyond-Hubbard physics plays an essential role in bosonic lattice systems and has an observable influence on experiments with tunable interactions.
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.
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.