Normal and anomalous densities in Bose-Einstein condensates with optical lattices

We study the quantum phase transition from the superfluid to the Mott insulator state in two-and three-dimensional Bose-Einstein condensate with optical lattices using Bose-Hubbard Hamiltonian within the generalized Hatree-Fock-Bogoliubov 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.