Correspondence between Transmission Spectrum and Topology of Artificial Atomic Chain in a Cavity

Abstract In this paper, we study the transmission spectrum in a coupled system of topological artificial atomic chain and optical microcavity, with a particular focus on the unique manifestations of topological phases with the larger topological invariant. We establish a theoretical model of an extended Su-Schrieffer-Heeger type artificial atomic chain coupled with a cavity. Besides two peaks induced by cavity mode and bulk dipole, additional peaks for the transmission spectrum arise induced by topological edge states. In particular, the number of additional transmission peaks equals the topological invariant of the atomic chain. In the topological phase with topological invariant $\nu=1$, the system produces additional one transmission peak, while two transmission peaks appear in the topological phase with $\nu=2$. This study reveals the mechanism of coupling between topological edge states and cavity modes, providing a new approach to detect topological phase transitions through optical methods.