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_n=n(hf/2e), within an error of 10 ppm. The experimental observation agreed with the theoretical relation to subnanovolt accuracy under irradiation by frequency-modulated millimeter waves. Phase locking of order parameters is thus observed in the array of mesoscopic SNS weak links in the HTS film.