Coexistence of topological transition and Anderson localization transition in optical cavity arrays with quasiperiodic disorder

We investigate the topological phase transition and localization properties in an array of optical cavities with periodic or quasiperiodic hopping. In both the commensurate and incommensurate regimes, the occurrence of the topological phase transition is confirmed by numerically calculating the real-space winding number. Moreover, due to the presence of quasiperiodicity, the system undergoes Anderson localization phase transition and exhibits topological Anderson insulators (TAIs) induced by quasiperiodic disorders in the incommensurate regime. Interestingly, unlike gapless and completely localized TAI in random disorder systems, we reveal gapped TAI with bulk states that have distinct localization properties, in addition to the gapless TAI with completely localized states. Furthermore, it is observed that the localized states in the band-center region will become delocalized and then localized again as the quasiperiodic parameter increases. Our findings provide insight into understanding the topology and localization properties of quasiperiodic optical systems.