Measurement accuracy of macroscopic quantum circuits with RF-biased Josephson junction arrays

The DC voltage output from a hysteretic Josephson junction which is locked to an AC frequency source differs from the ideal Josephson relation if the junction drives a current about a closed superconducting circuit. The difference in voltage Delta V from two hysteretic Josephson junctions driven in series opposition is proportional to the difference in their driving frequencies Delta omega if the junctions are each biased to the nth voltage step. It is shown here, however, that Delta V is systematically smaller than the voltage difference Delta V₀ predicted by the ideal Josephson relation Delta V₀=(nh(cross)/2e) Delta omega . If the loop inductance approaches zero, the smallest detectable voltage difference Delta V₀ between two junctions is limited by the intrinsic Josephson inductance. For arrays of more than one junction, however, Delta V₀ remains proportional to the loop inductance.