Limits to the fundamental measurement accuracy in Josephson junction array voltage intercomparisons

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 ΔV from two hysteretic Josephson junctions driven in series opposition is proportional to the difference in their driving frequencies Δω if the junctions are each biased to the nth voltage step. It is shown here, however, that ΔV is systematically smaller than the voltage difference ΔV0 predicted by the ideal junction relation ΔV0=(nℏ/2e)Δω. If the loop inductance approaches zero, the smallest detectable voltage difference ΔV0 between two junctions is limited by the intrinsic Josephson inductance. For arrays of more than one junction, however, ΔV0 remains proportional to the loop inductance.