Stochastic dynamics of a Josephson junction threshold detector

TL;DR

This paper extends the stochastic path integral formalism to Hamiltonian systems with Markovian noise, applying it to analyze a Josephson junction detector's escape dynamics and measurement back-action effects.

Contribution

It introduces a generalized formalism for stochastic dynamics with non-Gaussian noise and applies it to Josephson junctions, revealing new effects of measurement back-action.

Findings

Activation rate depends on third current cumulant

Back-action of measurement circuit influences escape dynamics

Formalism applicable to non-Gaussian noise in Hamiltonian systems

Abstract

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. Activation rate dependence on the third current cumulant includes an additional term originating from the back-action of the measurement circuit.