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The notion of quasi-angular momentum is introduced to label the eigenstatesof a Hamiltonian with a discrete rotational symmetry. This concept is recast inan operatorial form where the creation and annihilation operators of a HubbardHamiltonian carry units of quasi-angular momentum. Using this formalism, theground states of ultracold gases of non-interacting fermions in rotatingoptical lattices are studied as a function of rotation, and transitions betweenstates of different quasi-angular momentum are identified. In addition,previous results for strongly-interacting bosons are re-examined and comparedto the results for non-interacting fermions. Quasi-angular momentum can be usedto distinguish between these two cases. Finally, an experimentally accessiblesignature of quasi-angular momentum is identified in the momentum distributionsof single-particle eigenstates.

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