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We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atomic interaction and atom-light coupling induces a rich phase diagram. A novel "superradiant solid" (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance (SR) transition, here both the Solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by the large scale quantum Monte Carlo simulations., Comment: 5 pages,4 figures

We analyze the hard-core Bose-Hubbard model with both the three-body and nearest neighbor repulsions on the triangular lattice. The phase diagram is achieved by means of the semi-classical approximation and the quantum Monte Carlo simulation. For a system with only the three-body interactions, both the supersolid phase and one third solid disappear while the two thirds solid stably exists. As the thermal behavior of the bosons with nearest neighbor repulsion, the solid and the superfluid undergo the 3-state Potts and the Kosterlitz-Thouless type phase transitions, respectively. In a system with both the frustrated nearest neighbor two-body and three-body interactions, the supersolid and one third solid revive. By tuning the strength of the three-body interactions, the phase diagram is distorted, because the one-third solid and the supersolid are suppressed., Comment: 6 pages, 11 figures

We study the effect of impurities in a supersolid phase in comparison to the behavior in the solid and superfluid phases. A supersolid phase has been established for interacting hardcore bosons on a triangular lattice which may be realizable by ultracold atomic gases. Static vacancies are considered in this model which always lower the magnitude of the order parameter in the solid or superfluid phases. In the supersolid phase, however, the impurities directly affect both order parameters simultaneously and thereby reveal an interesting interplay between them. In particular the solid order may be enhanced at the cost of a strong reduction of the superfluidity, which shows that the two order parameters cannot be in a simple superposition. We also observe an unusual impurity pinning effect in the solid ordered phase, which results in two distinct states separated by a first-order transition., Comment: 5 pages, 5 figures, final version. More information at http://www.physik.uni-kl.de/eggert/papers/index.html

Spatiotemporal evolution of a confined Bose-Einstein condensate is studied by numerically integrating the time-dependent Gross-Pitaevskii equation. Self-interference between the successively expanding and reflecting nonlinear matter waves results in spiral atomic density profile, which subsequently degenerates into an embedding structure: The inner part preserves memory of the initial states while the outer part forms a sequence of necklacelike rings. The phase plot reveals a series of discrete concentric belts. The large gradients between adjacent belts indicate that the ring density notches are dark solitons. In the dynamical process, a scenario of vortex-antivortex pairs are spontaneously created and annihilated, whereas the total vorticity keeps invariant., Comment: 4 pages, 4 figures

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large scale quantum Monte Carlo simulations. We present the ground state phase diagrams for both the hard-core case and the soft-core case. For the hard-core case, the transition between $\rho=1/2$ solid and the superfluid is first order and the supersolid state is unstable towards phase separation. For the soft-core case, due to the presence of the multiple occupation, a stable particle induced supersolid (SS-p) phase emerges when $1/2<\rho<1$. The transition from the solid at $\rho=1/2$ to the SS-p is second order with the superfluid density scaling as $ \rho_{s} \sim \rho-1/2 $. The SS-p has the same diagonal order as the solid at $ \rho=1/2 $. As the chemical potential increasing further, the SS-p will turn into a solid where two bosons occupying each site of a sublattice through a first order transition. We also calculate the critical exponents of the transition between $\rho=1/2$ solid and superfluid at the Heisenberg point for the hard core case. We find the dynamical critical exponent $z=0.15$, which is smaller than results obtained on smaller lattices. This indicates that $ z $ approaches zero in the thermodynamic limit, so the transition is also first order even at the Heisenberg point., Comment: 6pages, 6figures

We study the number statistics of ultracold bosons in optical Lattice using the slave particle technique and quantum Monte Carlo simulations. For homogeneous Bose-Hubbard model, we use the slave particle technique to obtain the number statistics near the superfluid to normal-liquid phase transition. The qualitatively behavior agree with the recent experiment probing number fluctuation [Phys. Rev. Lett. \textbf{96}, 090401 (2006)]. We also perform quantum Monte Carlo simulations to 1D system with external harmonic trap. The results qualitatively agree with the experiments., Comment: 5 pages, 4 figures

We study the softcore extended Bose Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground state phase diagram of the system exhibits a very fruitful structure. Except the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\rho=1/3,2/3$ and $\rho=1$ are identified. Two of them (CDW II and CDW III) are newly predicted. In incommensurate fillings, superfluid, spuersolid as well as phase separation states are detected . As in the case for the hardcore bosons, a supersolid phase exists in $1/3<\rho<2/3$ while it is unstable towards the phase separation in $\rho<1/3$. However, this instability is refrained in $2/3<\rho<1$ due to the softening of the bosons and then a supersolid phase survives., Comment: 4 pages, 5 figures