Simulating topological phases with atom arrays in an optical waveguide

In this paper, we employ the atomic arrays in one-dimensional optical waveguides to simulate topological phases, where the waveguide is modeled as a one-dimensional infinitely long coupled cavity array. Under the Markov approximation, the coherent and dissipative coupling between atoms is established by eliminating waveguide modes. When the detuning between atoms and cavity fields lies in the band gap, the dynamics of the system is completely dominated by the coherent interaction. Under this condition, we designed three atomic arrays with different geometries and show that the topologically trivial and non-trivial phases of atomic arrays can be simulated. Furthermore, by introducing periodic atomic driving, the topological phase transition can be induced by adjusting the driving parameters. Finally, we investigate the effect of next-nearest neighbor interactions on topological state transfer and find that the next-nearest neighbor interactions break the degenerated bandgap state and establish a topological state transfer channel.