  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.
