Breathing modes of long Josephson junctions with phase-shifts

TL;DR

This paper analyzes how microwave drives interact with long Josephson junctions with phase-shifts, revealing that small-amplitude microwaves cannot induce resistive switching near eigenfrequencies due to excitation of higher harmonics, confirmed analytically and numerically.

Contribution

It demonstrates analytically and numerically that small microwave amplitudes cannot switch long Josephson junctions to resistive states near eigenfrequencies, clarifying experimental observations.

Findings

Small microwave amplitudes do not induce resistive switching near eigenfrequencies.

Higher harmonics in the continuous spectrum are excited, preventing resonance.

A stable breather mode oscillation is created by the microwave field.

Abstract

We consider a spatially inhomogeneous sine-Gordon equation with a time-periodic drive, modeling a microwave driven long Josephson junction with phase-shifts. Under appropriate conditions, Josephson junctions with phase-shifts can have a spatially nonuniform ground state. In recent reports, it is experimentally shown that a microwave drive can be used to measure the eigenfrequency of a junction's ground state. Such a microwave spectroscopy is based on the observation that when the frequency of the applied microwave is in the vicinity of the natural frequency of the ground state, the junction can switch to a resistive state, characterized by a non-zero junction voltage. It was conjectured that the process is analogous to the resonant phenomenon in a simple pendulum motion driven by a time periodic external force. In the case of long junctions with phase-shifts, it would be a resonance between the internal breathing mode of the ground state and the microwave field. Nonetheless, it was also reported that the microwave power needed to switch the junction into a resistive state depends on the magnitude of the eigenfrequency to be measured. Using multiple scale expansions, we show here that an infinitely long Josephson junction with phase-shifts cannot be switched to a resistive state by microwave field with frequency close to the system's eigenfrequency, provided that the applied microwave amplitude is small enough, which confirms the experimental observations. It is because higher harmonics with frequencies in the continuous spectrum are excited, in the form of continuous wave radiation. The presence of applied microwaves balances the nonlinear damping, creating a stable breather mode oscillation. We confirm our analytical results numerically.