Superconducting coplanar waveguide resonators (SCPWR) are scalable devices with applications mainly as photon detectors and in the field of experimental quantum information. When used in the context of quantum information they are treated as linear resonators, hence, characterization of their nonlinear properties in the single-photon regime is required.

In this work coupled SCPWR are measured and characterized, focusing on their nonlinear properties. We observe that at low powers the nonlinear behavior of the resonators can be explained as resulting from interacting two-level systems (TLS) loss, while at higher powers the dominant nonlinear mechanism is kinetic inductance. In the intermediate power regime our results are best fit by a noninteracting TLS loss mechanism, familiar in the literature.

A method for nonlinear characterization using pump-and-probe measurements on the pair of coupled resonators is implemented. Using this method and an appropriate model, the Kerr coefficient is estimated to be at the order of  K ≈ -1.2×10^-2  Hz per photon.  Additional frequency shifts observed in the pump-probe experiments and not in single resonance spectroscopy are explained by asymmetric saturation effects.