Abstract

We simulate quantum degenerate Bose gases at finite temperatures in a grand canonical ensemble and use the Bose-Hubbard model which can describe the dynamics of ultracold bosonic atoms in optical and magnetic lattices. We study ultracold atoms with the gauge P-representation in 1D with 1, 2 (double well), 3, 7 and 11 sites and study quantum correlations and other physical quantities at different  temperatures across the superfluid to Mott insulator quantum phase transition. Moreover, using a truncated number-state basis and the gauge P-representation, we  show  that  the Mott  lobes are not present unless  the  temperature  is below a certain value.