Non-equilibrium dynamics of ultra cold lattice gases with inter-site interactions

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Recent experiments on dipolar and Rydberg-dressed gases in optical lattices open promising perspectives for the simulation of lattice models with inter-site interactions. The combination of energy conservation, finite band-width, and inter-site interactions is expected to lead to a wealth of new non-equilibrium phenomena absent in systems with only on-site interactions. Even moderate inter-site interactions are expected to lead to the formation of clusters of many particles, which may hinder or totally preclude the motion in the lattice. We will study this motion in detail, and evaluate its consequences for on-going experiments. Moreover, the dynamics of holons, i.e. empty sites, doped within an insulator may become strikingly different to that of individual particles. We will analyze this dynamics, including holon-induced particle ejection, dynamically-maintained bulk- and edge-holons, and interaction-induced lattice reconfiguration. We will as well investigate the adiabatic realization of the Haldane-insulator phase, a phase with a non-local string-order that constitutes one the most relevant novel features in extended Bose-Hubbard models. Our results are expected to impact on on-going experiments, which whom we will maintain a close collaboration.