Detecting charge noise with a Josephson junction: A problem of thermal escape in presence of non-Gaussian fluctuations

TL;DR

This paper investigates how a Josephson junction can detect charge noise from a mesoscopic conductor by analyzing thermal escape rates influenced by non-Gaussian current fluctuations, providing explicit formulas and experimental insights.

Contribution

It derives an effective Fokker-Planck equation for thermal escape in the presence of non-Gaussian noise and applies it to optimize charge noise detection with Josephson junctions.

Findings

Explicit expression for escape rate considering non-Gaussian noise

Analysis of rate asymmetry due to third moment of current noise

Guidelines for optimizing detection circuits

Abstract

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the fundamental problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyse experimental data and to optimize detection circuits.