Multistable localized states in highly photonic polariton rings with a quasiperiodic modulation

We present a theoretical study of an exciton-polariton annular microcavity with an additional quasiperiodic structure along the ring which is implemented in the form of a bicosine dependence. We demonstrate that for a sufficiently strong quasiperiodic modulation, the microcavity features a sharp mobility edge separating a cluster of localized states from the rest of the spectrum consisting of states extended over the whole ring. Localized modes can be excited using a resonant pump whose topological charge determines the phase distribution of excited patterns. Repulsive polariton interactions make the resonance peaks distinctively asymmetric and enable the formation of multistable states which feature the attractor-like dynamical behavior and hysteresis. We also demonstrate that the localized states can be realized in a biannular cavity that consists of two rings, each having periodic modulation, such that the periods of two modulations are different.