ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions

We investigate ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions. In the presence of microwave irradiation, we show that the trajectory of multiple Andreev reflections can be closed by emitting or absorbing photons. Consequently, photon-assisted Andreev states are formed and play the role of carrying supercurrent. On the Shapiro steps, dc component appears when the resonant level is near a series of positions with spacing of half of the microwave frequency. Analytical result is derived in the limit of infinite superconducting gap, based on which new features of ac Josephson effect are revealed.