Quantized vortex states of strongly interacting bosons in a rotating optical lattice

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of 2 pi in the phase winding of the condensate wave function. A lattice of size LxL can have at most L-1 quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.