Topological edge/corner states and polaritons in dimerized/trimerized superconducting qubits in a cavity

We investigate a two-level topological system with an alternating XX coupling in a photon cavity. It is mapped to a free boson model equally coupled to a photon, whose interaction is highly nonlocal. We analyze the Su-Schrieffer-Heeger model and the breathing kagome model. Intriguing phenomena occur in the topological phase due to hybridization between the photon field and the topological edge or corner state. As the photon coupling increases, the symmetric edge or corner state is smoothly transformed into a polariton state coupled with the edge or corner state. Simultaneously, the photon state is smoothly transformed into the symmetric edge state or the C₃-symmetric corner state. Furthermore, a state is detached from the bulk band and smoothly transformed into a polariton due to hybridization with the photon field.