Topological phase transitions and topological quantum states modulated by the counter-rotating wave terms in a one-dimensional superconducting microwave cavity lattice

We propose a one-dimensional lattice theory scheme based on superconducting microwave cavities, which includes two different types of microwave cavity unit cells. The coupling between unit cells is controlled by flux qubits to simulate and study their topological insulator characteristics. Specifically, a one-dimensional superconducting microwave cavity lattice scheme with a p-wave superconducting pairing term is achieved by mapping the counter-rotating wave terms to the p-wave superconducting pairing term. We found that the p-wave superconducting pairing term can modulate the topological quantum state of the system, allowing for the creation of topological quantum information transmission channels with four edge states. In addition, when the p-wave superconducting pairing term and the nearest-neighbor interaction exist, we find that the energy band undergoes fluctuations, inducing the generation of new energy bands, but the degeneracy of the edge states remains stable, which can achieve multiple topological quantum state transmission paths. However, when its regulatory value exceeds the threshold, the energy gap of the system will close, causing the edge states to annihilate in new energy bands. Furthermore, when considering the existence of defects in the system, we found that when the strength of the defects are small, the edge state produces small fluctuations, but it can be clearly distinguished, indicating its robustness. When the strength of the defect exceeds the threshold, the edge state and energy band cause irregular fluctuations, allowing the edge state to integrate into the energy band. Our research results have important theoretical value and practical significance, and can be applied in quantum optics and quantum information processing in the future.