Geometrically induced complex tunnelings for ultracold atoms carrying orbital angular momentum

We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two-dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring states with variation of the winding number are complex. In particular, we demonstrate that in a triangular ring configuration the complex nature of the cross-couplings can be used to geometrically engineer spatial dark states to manipulate the transport of orbital angular momentum states via quantum interference.