  We study the quantum phase transition from the superfluid to the Mott
insulator state in two and three dimensional Bose-Einstein condensate (BEC)
with optical lattices using Bose-Hubbard Hamiltonian within the Generalized
Hatree-Fock-Bogoliubov (GHFB) approximation. The behavior of the depletion and
the anomalous fraction has been investigated in the Mott insulator phase. We
found that at T = 0, these quantities become significant in two and three
dimensions. It is shown also that the dimensionality of the lattice enhances
the anomalous density.
