Nonreciprocal exciton-polariton ring lattices

Recent experiments showed the transfer of orbital angular momentum (OAM) from a nonresonant laser onto an exciton-polariton condensate, despite earlier views that the phase information of such a laser should be lost during the process of polariton condensation. We study with a phenomenological theory the interplay of a usual angular momentum independent gain and an angular momentum preserving gain. We find that even when the latter is much smaller, it is enough to favor condensation into a given orbital angular momentum state. This further allows a breaking of symmetry in the system, which further manifests in nonreciprocal one-way propagation in a lattice of coupled rings. Even though we consider only Hermitian reciprocal coupling between rings, the local non-Hermiticity generates an effective nonreciprocal coupling and supports a non-Hermitian topological invariant (winding number) associated to a non-Hermitian skin effect.