  Until very recently, two-photon interaction processes have been considered
only as arising from second- or higher-order effects in driven systems, and so
limited to extremely small coupling strengths. However, a variety of novel
physical phenomena emerges in the strong and ultrastrong coupling regimes.
Strikingly, for a critical value of the coupling strength the discrete spectrum
collapses into a continuous band. In this extended abstract, we discuss recent
proposals to implement genuine two-photon interactions in an undriven
solid-state system, in the framework of circuit QED. In particular, we review
counterintuitive spectral features of two-photon interaction models and we show
how the onset of the spectral collapse can be observed in feasible scattering
experiments.
