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

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.