Ordered states of Rydberg-dressed ultracold quantum gases in optical lattices

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We investigate long-range ordered states and quasiparticle excitations of Rydberg-dressed quantum gases in optical lattices. Our non-perturbative theoretical approach, based on an extended Hubbard model, allows us to address the full parameter range from far-detuned weak dressing to resonant Rydberg excitation. It includes collective many-body interactions induced by dressing, which are beyond descriptions based on effective pair potentials. Using dynamical mean-field theory (DMFT), we calculate superfluid, supersolid, density- and spin-ordered phases, as well as their critical temperatures and entropies. We investigate the influence of geometric lattice frustration on the phase diagram, which is expected to lead to novel correlated states. We determine collective modes, such as the Higgs-amplitude mode, and quasiparticle dispersions of the dressed system, applying a generalized bosonic quasiparticle-theory. The additional influence of dissipation and dephasing for realistic Rydberg laser excitation schemes is addressed within a Lindblad master equation, solved non-perturbatively, which allows us to calculate the full out-of-equilibrium steady-state phase diagram, and to search for novel ordered states which are stabilized by dissipation.