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

In this work, we investigated the nonadiabatic transport properties of the one-dimensional time-dependent superconductor-normal metal-superconductor (SNS) Josephson junction biased by a current source and driven by a high-frequency-ac-gate-potential applied to the normal-metal layer. BCS superconductors are considered and treated with the time-dependent Bogoliubov-de Gennes equation. Using Floquet theory, we compute the transmission coefficients and the Wigner-Smith delay times as a function of the incident energy and find that they display resonances when one of the electron or hole Floquet wavevectors coincides with the bound quasiparticle state within the superconducting energy gap. The resonance varies with the phase difference between the two superconductors as a result of the bound quasiparticle level displacement. The supercurrent flowing through the SNS junction is dramatically enhanced by the resonances