  We study the spatial correlations of strongly interacting bosons in a ground
state, confined in two-dimensional square and three-dimensional cubic lattice.
Using combined Bogoliubov method and the quantum rotor approach, we map the
Hamiltonian of strongly interacting bosons onto U(1) phase action in order to
calculate the atom-atom correlations decay along the principal axis and a
diagonal of the lattice plane direction as a function of distance. Lower
tunneling rates lead to quicker decays of the correlations, which character
becomes exponential. Finally, correlation functions allow us to calculate
quantities that are directly bound to experimental outcomes, namely
time-of-flight absorption images and resulting visibility. Our results contain
all the characteristic features present in experimental data (transition from
Mott insulating blob to superfluid peaks, etc.), which emphasizes the usability
of the proposed approach.
