  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.
