Accurate determination of the Josephson critical current by lock-in measurements

TL;DR

This paper demonstrates that lock-in measurement techniques, specifically first and third harmonic measurements, enable highly accurate determination of the Josephson critical current by reducing noise effects, validated through theoretical derivations and experiments.

Contribution

It introduces a method to accurately extract the Josephson critical current using harmonic lock-in measurements, improving noise resilience over traditional methods.

Findings

Lock-in measurements suppress 1/f noise in critical current determination.

Analytic expressions for resistance harmonics are derived and validated.

Experimental verification on nano-scale Josephson junctions confirms the method's accuracy.

Abstract

Operation of Josephson electronics usually requires determination of the Josephson critical current $I_c$, which is affected both by fluctuations and measurement noise. Lock-in measurements allow obviation of $1/f$ noise and, therefore, provide a major advantage in terms of noise and accuracy with respect to conventional dc-measurements. In this work we show both theoretically and experimentally that the $I_c$ can be accurately extracted using first and third harmonic lock-in measurements of junction resistance. We derive analytic expressions and verify them experimentally on nano-scale Nb-PtNi-Nb and Nb-CuNi-Nb Josephson junctions.