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In this work, we investigated the nonadiabatic transport properties of theone-dimensional time-dependent superconductor-normal metal-superconductor (SNS)Josephson junction biased by a current source and driven by ahigh-frequency-ac-gate-potential applied to the normal-metal layer. BCSsuperconductors are considered and treated with the time-dependentBogoliubov-de Gennes equation. Using Floquet theory, we compute thetransmission coefficients and the Wigner-Smith delay times as a function of theincident energy and find that they display resonances when one of the electronor hole Floquet wavevectors coincides with the bound quasiparticle state withinthe superconducting energy gap. The resonance varies with the phase differencebetween the two superconductors as a result of the bound quasiparticle leveldisplacement. The supercurrent flowing through the SNS junction is dramaticallyenhanced by the resonances.

Resonance in the nonadiabatic quantum pumping of the time-dependent Josephson junction