Theory of high-power excitation spectra of rf-SQUID

We discuss the theory of linear and nonlinear spectroscopy of an rf superconducting quantum interference device (rf-SQUID) coupled to a Josephson spectrometer. Recent experimental measurements on this system have shown a strongly nonlinear absorption line shape, whose current peak maximum undergoes a forward-backward bending transition depending on the value of the rf-SQUID phase. We show that this transition can be qualitatively understood by mapping the dynamics of the driven rf-SQUID onto a generalized Duffing oscillator, with tunable drive and nonlinearity, undergoing a bifurcation. Finally we show that in order to quantitatively reproduce the experimental data reported by Griesmar et al. [Phys. Rev. Research 3, 043078 (2021)10.1103/PhysRevResearch.3.043078], it is crucial to include the feedback from the load line, leading to an additional source of nonlinearity.