Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

We study ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the current-current correlations, which provides the information about conductivity of the system. The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice. In the phase-ordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.