Conductivity of Strongly Correlated Bosons in the Simple Cubic Lattice - Magnetic Field and Hopping Anisotropy Effects

We investigate optical conductivity in three dimensional system of bosons under strong magnetic field. In particular, we consider Bose Hubbard model in the strongly correlated limit, where Mott insulator phase emerges. For chosen rational number of magnetic flux per cell we show that response of the system gains complex peaks behavior on the order of frequency corresponding to on-site boson repulsive interaction. Moreover, when anisotropy in hopping energy for the direction parallel to magnetic field is tuned up, the non-monotonous behavior of the optical conductivity could appear. The obtained results can be experimentally probed in the system of ultracold atoms loaded on an optical lattice.