  Based on exactly mapping of a many-body electron-phonon interaction problem
onto a one-body problem, we apply the well-established nonequilibrium Green
function technique to solve the time-dependent phonon-assisted tunneling at low
temperature through a single-molecular quantum dot connected to two leads,
which is subject to a microwave irradiation field. It is found that in the
presence of the electron-phonon interaction and the microwave irradiation
field, the time-average transmission and the nonlinear differential conductance
display additional peaks due to pure photon absorption or emission processes
and photon-absorption-assisted phonon emission processes. The variation of the
time-average current with frequency of the microwave irradiation field is also
studied.
