Topological phase transition and detectable edge state in a quasi-three-dimensional circuit quantum electrodynamic lattice

Abstract

We investigate the topological phase transition and the edge states in a quasi-three-dimensional topological system mapped by a circuit quantum electrodynamic lattice via introducing two periodic spatial parameters. It is found that with the increasing of the periodically modulated on-site potential strength, the system undergoes a topological phase transition, corresponding to the change of the number of Weyl points under the periodic boundary condition. Under the open boundary condition, the phase transition is reflected by the energy band separation and the appearance of new edge states. Interestingly, the system holds two pairs of crossed edge states in the energy gaps when the periodic parameters take certain values. Furthermore, we show that, benefiting from the Bose statistical properties of the circuit quantum electrodynamic, the edge states of the system can be directly detected by measuring the average photon number of the cavity field in the steady state.