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Quantum Vortex States in Bose Hubbard Model With Rotation

We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square, rectangular and triangular. Using numerical exact diagonalization method we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We show how the geometry of the lattice plays crucial role in determining the maximum number of vortex states as well as the general characteristics of these states such as, the average angular momentum $<L_z>$, the current at the perimeter of the lattice, phase winding, the relation between the maximum phase difference, the maximum current and also the saturation of the current between the two neighboring lattice points. The effect of the two- and three-body interactions between the particles, both attractive and repulsive, also depends on the geometry of the lattice as the current flow or the lattice current depends on the interactions. We also consider the effect of the spatial inhomogeneity introduced by the presence of an additional confining harmonic trap potential. It is shown that the curvature of the trap potential and the position of the minimum of the trap potential with respect to the axis of rotation or the center of the lattice have a significant effect on the general characteristics these vortex states.