Noise and disorder effects in a series of birhythmic Josephson junctions coupled to a resonator

TL;DR

This study investigates how uncorrelated white noise and parameter disorder affect the dynamics and stability of a series of birhythmic Josephson junctions coupled to a resonator, revealing that disorder can suppress birhythmicity and alter the energy landscape.

Contribution

It provides new insights into the impact of disorder on birhythmic Josephson junction arrays coupled to resonators, highlighting the conditions under which birhythmicity persists or is lost.

Findings

Disorder reduces the array's effective energy response to noise.

Birhythmicity is preserved at low disorder levels but lost at high variance.

Disorder complicates the energy landscape, affecting stability and separatrix detection.

Abstract

This paper deal the effects of uncorrelated white noise, in a serie of Josephson Junctions coupled to a linear $RLC$ resonator. The junction are hysteretic, and hence can be considered birhythmic, that is capable to oscillate at different frequencies for the same set of parameters. Both Josephson Junctions with identical and disordered parameters are considered. With the uniform parameters, the array behaves similarly to single Josephson junctions, also in the presence of noise. The magnitude of the effective energy that characterizes the response to noise becomes smaller as the number of elements of the array increases, making the resonator less stable. Disorder in the parameters drastically changes the physics of the array. The disordered array of Josephson junctions misses the birhythmicity properties for large values of the variance of the disorder parameter. Nevertheless, the system remains birhythmic for low values of the disorder parameter. Finally, disorder makes it difficult to locate the separatrix, hinting to a more complex structure of the effective energy landscape.