Josephson Junctions as Threshold Detectors of the Full Counting Statistics: Open issues

TL;DR

This paper reviews the use of Josephson junctions as threshold detectors for electronic noise, identifies unresolved issues, and presents new analytical and numerical insights into their switching rates and full counting statistics measurement potential.

Contribution

It provides a new analytical correction for the rate due to the third cumulant and compares theoretical predictions with numerical and experimental data.

Findings

New analytical correction for non-Gaussian noise effects

Comparison of theoretical models with numerical simulations

Assessment of experimental data's consistency with theory

Abstract

I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristics is to be determined by the junction. This experimental setup has been proposed several years ago as a prospective scheme for determining the Full Counting Statistics of the electronic noise source. Despite of intensive theoretical as well as experimental research in this direction the promise has not been quite fulfilled yet and I will discuss what are the unsolved issues. First, I review a general theory for the calculation of the exponential part of the non-equilibrium switching rates of the junction and compare its predictions with previous results found in different limiting cases by several authors. I identify several possible weak points in the previous studies and I report a new analytical result for the linear correction to the rate due to the third cumulant of a non-Gaussian noise source in the limit of a very weak junction damping. The various analytical predictions are then compared with the results of the developed numerical method. Finally, I analyze the status of the so-far publicly available experimental data with respect to the theoretical predictions and discuss briefly the suitability of the present experimental schemes in view of their potential to measure the whole FCS of non-Gaussian noise sources as well as their relation to the available theories.