Statistics of voltage fluctuations in resistively shunted Josephson junctions

TL;DR

This paper investigates the statistical properties of voltage fluctuations in resistively shunted Josephson junctions, revealing Gaussian behavior at high bias currents and Poissonian at low currents, with complex non-Gaussian features near the critical current.

Contribution

It provides exact numerical and analytical results for the cumulants of voltage fluctuations, including effects of colored noise, advancing understanding of noise behavior in Josephson junctions.

Findings

Voltage fluctuations are Gaussian at high bias currents.

Voltage fluctuations are Poissonian at low bias currents.

Near the critical current, higher-order cumulants oscillate and noise becomes non-Gaussian.

Abstract

The intrinsic nonlinearity of Josephson junctions converts Gaussian current noise in the input into non-Gaussian voltage noise in the output. For a resistively shunted Josephson junction with white input noise we determine numerically exactly the properties of the few lowest cumulants of the voltage fluctuations, and we derive analytical expressions for these cumulants in several important limits. The statistics of the voltage fluctuations is found to be Gaussian at bias currents well above the Josephson critical current, but Poissonian at currents below the critical value. In the transition region close to the critical current the higher-order cumulants oscillate and the voltage noise is strongly non-Gaussian. For coloured input noise we determine the third cumulant of the voltage.