Topological phase transition of the generalized Su-Schrieffer-Heeger model based on a frequency-modulated circuit quantum electrodynamics lattice

We propose a scheme to investigate the topological phase transition in the generalized one-dimensional Su-Schrieffer-Heeger (SSH) model based on a circuit quantum electrodynamics (QED) lattice with frequency modulation. We find that, if we keep the resonant counter rotating wave terms to map the p-wave superconducting pairing terms in the topological superconductor by dint of frequency modulation, the circuit QED lattice can be equivalent to the SSH model with p-wave superconducting pairing terms. The numerical results show that the existence of the superconducting pairing terms cannot close the energy gap of the SSH model within the feasible range of parameters, which means that the superconducting pairing terms cannot induce the topological phase transition. To induce the topological phase transition, we add the next-nearest-neighboring (NNN) interaction into the circuit QED-based SSH model simultaneously. We find that, for a given superconducting pairing strength, the appropriate selection of the NNN interaction can induce closing of the energy gap. It indicates that a new topological phase transition between the topologically nontrivial SSH phase and the topologically trivial SSH phase occurs in the SSH model. Our scheme provides a means to explore the topological SSH phase transition based on a circuit QED lattice with frequency modulation.