In the usual Su-Schrieffer-Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here we study the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice system modelled as a SSH chain. We find that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied with the appearance of a nontopological edge state in the whole parameter region, and the novel phase transition leads to the inversion of odd-even effect in the system directly. Furthermore, we also study the topological properties as well as phase transitions when two unbalanced coupling potentials are injected into both the ends of the circuit QED lattice system, and find that the system exhibits three distinguishing phases in the process of multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential, which is reflected by the existence of a pair of nontopological edge states under strong coupling potential regime. Our scheme provides a feasible and visible method to induce a variety of different kinds of topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice system both in experiment and theory.
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