The transient transmission through a quantum dot under the influence of oscillating external fields

We consider a quantum dot coupled to two leads in the presence of oscillating external fields applied to the dot and the two leads. Using the nonequilibrium-Green-function method, the formula for the transient transmission probability (TTP) T-epsilon f,T-epsilon i (t', t) is derived. The numerical studies reveal the following facts. When t' - t similar to 1/Gamma (Gamma is the full width of the resonant state), no visible resonant tunnelling behaviour occurs, and T-epsilon f,T-epsilon i(t', t) strongly depends on the time at which the electron enters the dot, t, and that at which it exits from it, t'; when t'-t much greater than 1/Gamma, the resonant tunnelling becomes striking, and T-epsilon f,T-epsilon i (t', t) depends only weakly on t and t'. The conventional transmission probability T-epsilon f,T-epsilon i, defined as the limit as t --> -infinity and t' -->+infinity, has a very rich spectrum and exhibits a simultaneous quenching of some channels. On the basis of the properties of T-epsilon f,T-epsilon i, the condition for the occurrence of an electron-photon pump has also been discussed.