Nonideal Quantum Measurement Effects on the Switching Currents Distribution of Josephson Junctions

TL;DR

This paper investigates how nonideal quantum measurements affect the distribution of switching currents in Josephson junctions, revealing measurement backreaction effects and differences from traditional approximations.

Contribution

It introduces a simple measurement scheme modeling repeated voltage samplings and analyzes their impact on switching current distributions in Josephson junctions.

Findings

Distribution is unaffected by the quantum Zeno effect.

Distribution differs from WKB approximation, especially at fast ramp rates.

Quantum measurements induce backreaction effects on the switching currents.

Abstract

The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e. the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson junctions switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurements scheme. The measurements are modelled as repeated voltage samplings at discrete time intervals, that is with repeated projections of the time dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune of the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizeable in the asymptotic slow rate limit. This behaviour is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.