Fractional Shapiro steps and superstructure in revivals of supercurrent inmesoscopic Josephson junction

Dynamic behavior of supercurrent in mesoscopic Josephson junction interacti ng with even coherent state (CS) and odd CS of nonclassical microwave with frequency omega(1) and classical radiation with frequency omega(2) is inves tigated. It is shown that the supercurrent through the junction has a de co mponent only for all rational values of omega(1)/omega(2) (fractional Shapi ro steps). It is also shown that the dynamic behavior of the supercurrent e xhibits collapse and revival phenomenon and the revivals are dominated by t he periodical superstructure. Dynamic behavior of supercurrent fluctuation is also studied and it is found that generally when the fluctuation is larg e, the supercurrent exhibits collapses and when the fluctuation is small, t he supercurrent exhibits revivals.