Effective multi-body induced tunneling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice

We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair tunneling, and nearest-neighbor interaction processes of higher orders. An alternative description of the same model can be formulated in terms of occupation-dependent Bose-Hubbard parameters. These multiparticle effects can be enhanced using Feshbach resonances, leading to corrections which are well within experimental reach and of significance to the phase diagram of ultracold bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism of interacting atoms on a local lattice site and show that this cannot be explained only by a spatial broadening of Wannier orbitals on a single-particle level, which neglects correlations.Comment: 16 pages, 6 figure

Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands

The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is energy absorption rate when the lattice depth is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid

Multi-orbital and density-induced tunneling of bosons in optical lattices

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.Comment: 21 pages, 7 figure