Quantum Critical Point in Strongly Correlated ${}^{87}$Rb Atoms in Optical Lattice

In this paper, the Bosonic projected variational method is proposed to study the strongly correlated ${}^{87}\mathrm{R}\mathrm{b}$ atoms in optical lattice. A global phase diagram is obtained by this method. There exist two characteristic lattice depths $V$ for ${}^{87}\mathrm{R}\mathrm{b}$ atoms in optical lattice : one is $% V=9.5E_r$ to label the maximum height of the ‘zero-momentum’ peak of condensation, the other is the quantum critical point for the superfluid-insulator (SI) transition at $V=12.3E_r$. As a result of strongly correlated effect for lattice Bosons, the suppressed superfluid state is predicted near the SI transition with the suppressed superfluid density and the very slowly velocity of the sound-like excitons.