Transient current through a quantum dot with two time-dependent barriers

We investigate the transient-current characteristics of a quantum dot coupled to two leads through two time-dependent barriers. A general formula for the time-dependent current j(t) is derived by using the nonequilibrium-Green-function technique. Two particular cases, those of rectangular-pulse modulations and harmonic modulations imposed on the two barriers, are studied in detail. For the rectangular-pulse modulations, a turnstile effect is obtained if the full width of the resonant state (Gamma) is much larger than the frequency (omega), i.e. Gamma much less than omega; and the special behaviour of the transient current j(t) is attributed to the phase coherence due to the time variation of the barriers. For the harmonic modulations, we find that a new energy scale Aw emerges if Gamma < omega, and the main resonant peak is split into two peaks.