Accurate Josephson voltage-frequency relation in a granular array of mesoscopic SNS weak links

Electron transport in short superconducting weak links is described in terms of multiple Andreev reflections (MAR). According to a recent theory, the current carried by the quasiparticles bound in the N region of a mesoscopic superconductor-normal-superconductor (SNS) weak link consists of dc and cosine components instead of a sinusoidal component. The presence of the dc pair-current component locks the phase relation of the wave function between superconducting grains throughout the series-parallel array of the SNS weak links. We have made a precise measurement of I-V characteristics at 63 K using a constriction in a YBCO polycrystalline film, in which networks of grain boundary Josephson weak links are naturally formed. The measured values of voltage between microwave-induced-current-steps are equal to the theoretical values for a single Josephson element, V/sub n/=n(hf/2e), within an error of 10 ppm. The experimental observation agreed with the theoretical relation to subnanovolt accuracy under irradiation by frequencymodulated millimeter waves. Phase locking of order parameters is thus observed in the array of mesoscopic SNS weak links in the HTS film.