Influence of microwave fields on the electron tunneling through a quantum dot

We consider a quantum dot coupled to two leads in the presence of external microwave (MW) fields which are applied to the dot and two leads, respectively. The amplitudes, phases, and frequencies of the MW fields are taken arbitrarily. Under the adiabatic approximation, the formula for the time-dependent current $j(t)$ and the average current $〈j(t)〉$ are obtained. Some analytical results for several special cases are presented and studied numerically. When the MW field is applied only to one lead, the detailed structure of the main resonant peak in the average current vs gate voltage is in good agreement with the experiment of Kouwenhoven et al. [Phys. Rev. Lett. 73, 3443 (1994)]. For the case with different frequencies of MW fields in different regions, some interesting effects occur, including multiple-photon-assisted tunneling, the combination of sidebands and the electron-photon pump effect, and the coherent effect.