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When a Bose–Einstein condensate is set to rotate, superfluid vortices will be formed, which finally condense into a vortex lattice as the rotation frequency further increases. We show that the dipole-dipole interactions renormalize the short-range interaction strength and result in a distinction between interactions of parallel-polarized atoms and interactions of antiparallel-polarized atoms. This effect may lead to a spontaneous breakdown of the rapidly rotating Bose condensate into a novel anti-ferromagnetic-like vortex lattice. The upward-polarized Bose condensate forms a vortex lattice, which is staggered against a downward-polarized vortex lattice. A phase diagram related to the coupling strength is obtained.

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., 5 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, 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., 5 pages, 4 figures