Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

TL;DR

This paper investigates the classical dynamics of a voltage-biased Josephson junction coupled to a resonator, revealing the transition from linear response to nonlinear oscillations through analysis of steady states, bifurcations, and power spectra.

Contribution

It provides a comprehensive analysis of the nonlinear dynamics in Josephson junction-resonator systems, including steady states and bifurcation phenomena, under various driving conditions.

Findings

Identification of steady states in different regimes

Observation of bifurcations and irregular motion

Analysis of microwave power and Josephson current behavior

Abstract

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.