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Until very recently, two-photon interaction processes have been consideredonly as arising from second- or higher-order effects in driven systems, and solimited to extremely small coupling strengths. However, a variety of novelphysical phenomena emerges in the strong and ultrastrong coupling regimes.Strikingly, for a critical value of the coupling strength the discrete spectrumcollapses into a continuous band. In this extended abstract, we discuss recentproposals to implement genuine two-photon interactions in an undrivensolid-state system, in the framework of circuit QED. In particular, we reviewcounterintuitive spectral features of two-photon interaction models and we showhow the onset of the spectral collapse can be observed in feasible scatteringexperiments.

Observing the Spectral Collapse of Two-Photon Interaction Models