Photon sidebands of the ground state and the excited state of a quantum dot: A nonequilibrium Green-function approach

The electron tunneling through an ultrasmall quantum dot in the presence of time-dependent microwave (MW) fields is studied. In the investigation, two single electronic states (the ground state and the excited state) and the intradot Coulomb interaction are considered. Assuming the tunneling through the system as a coherent process, the time-dependent current and the average current are derived using the nonequilibrium Green-function method. Then we consider two special cases with $ħ\omega >\Delta \epsilon$ and $ħ\omega <\Delta \epsilon ,$ respectively, where ω is the frequency of MW fields and Δε is the energy difference between two electronic states. Both the sidebands of the photon-assisted tunneling originated from the ground state, and, in particular, from the excited state are obtained, which is in good agreement with the recent experiment by Oosterkamp et al. [Phys. Rev. Lett. 78, 1536 (1997)]. Moreover, the dependence of the integrated average current on the intensity of MW fields is also discussed, and attributed to the many-body effect of the quantum dot.