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 E0 is near the position VL + 1 2m1ω = VR + 1 2m2ω (e = ~ = 1), where m1 and m2 are integers, ω is the frequency of microwave, VL and VR the chemical potentials of the superconducting leads. Analytical result is derived in the limit ∆ → ∞, based on which new features of ac Josephson effect are revealed. PACS numbers: 74.50.+r, 73.63.Kv, 73.23.Ad