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

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