  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.
