Theory of high-power excitation spectra of rf-SQUID

TL;DR

This paper develops a theoretical framework for understanding the non-linear excitation spectra of an rf-SQUID coupled to a Josephson spectrometer, explaining experimental observations through bifurcation analysis and load-line feedback effects.

Contribution

It introduces a model mapping the rf-SQUID dynamics to a generalized Duffing oscillator, incorporating load-line feedback to accurately reproduce experimental data.

Findings

Identification of a bifurcation transition in the absorption lineshape

Demonstration of the importance of load-line feedback for quantitative agreement

Qualitative understanding of phase-dependent spectral features

Abstract

We discuss the theory of linear and non-linear spectroscopy of an rf-SQUID coupled to a Josephson spectrometer. Recent experimental measurements on this system have shown a strongly non-linear absorption lineshape, 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 non-linearity, undergoing a bifurcation. Finally we show that in order to quantitatively reproduce the experimental data reported in arXiv:2106.02632, it is crucial to include the feedback from the load-line, leading to an additional source of non-linearity.