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

TL;DR

This paper introduces the concept of quasi-angular momentum for labeling eigenstates in rotating optical lattices, compares fermionic and bosonic gases, and suggests experimental signatures for detecting quasi-angular momentum.

Contribution

It develops a formalism for quasi-angular momentum in Hubbard models and compares behaviors of bosons and fermions in rotating lattices.

Findings

Transitions between quasi-angular momentum states are identified.

Quasi-angular momentum distinguishes between bosonic and fermionic gases.

Experimental signatures in momentum distributions are proposed.

Abstract

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.