Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong to the deep strong coupling regime

We report on spectra of circuit quantum electrodynamics (QED) systems in an intermediate regime that lies between the ultrastrong and deep strong coupling regimes, which have been reported previously in the literature. Our experimental results, along with numerical simulations, demonstrate that as the coupling strength increases, the spectrum of a circuit-QED system undergoes multiple qualitative transformations, such that several ranges are identified, each with its own unique spectral features. These results allow us to define characteristic features that distinguish several different regimes of coupling in circuit-QED systems.