Number Statistics of Ultracold Bosons in Optical Lattice

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. $\mathbf{\text{96}}$, 090401 (2006)]. We also perform quantum Monte Carlo simulations to 1D system with external harmonic trap. The results qualitatively agree with the experiments.