Vortex lattices in rotating atomic bose gases with dipolar interactions

We show that dipolar interactions have dramatic effects on the ground states of rotating atomic Bose gases in the weak-interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean field, or high filling factor, ground state undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, ``stripe,{''} and ``bubble{''} phases. We also study the effects of dipolar interactions on the quantum fluids at low filling factors. We show that the incompressible Laughlin state at filling factor nu=1/2 is replaced by compressible stripe and bubble phases.