Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices

The notion of quasi- angular momentum is introduced to label the eigenstates of a Hamiltonian with a discrete rotational symmetry. This concept is recast in an operatorial form where the creation and annihilation operators of a Hubbard Hamiltonian carry units of quasi- angular momentum. Using this formalism, the ground states of ultracold gases of non- interacting fermions in rotating optical lattices are studied as a function of rotation, and transitions between states of different quasi- angular momentum are identified. In addition, previous results for strongly- interacting bosons are re- examined and compared to the results for non- interacting fermions. Quasi- angular momentum can be used to distinguish between these two cases. Finally, an experimentally accessible signature of quasi- angular momentum is identified in the momentum distributions of single-particle eigenstates.