  We calculate the time evolution of a cavity-QED system subject to a time
dependent sinusoidal drive. The drive is modulated by an envelope function with
the shape of a pulse. The system consists of electrons embedded in a
semiconductor nanostructure which is coupled to a single mode quantized
electromagnetic field. The electron-electron as well as photon-electron
interaction is treated exactly using "exact numerical diagonalization" and the
time evolution is calculated by numerically solving the equation of motion for
the system's density matrix. We find that the drive causes symmetric excitation
and de-excitation where the system climbs up the Jaynes-Cummings ladder and
descends back down symmetrically into its original state. This effect persists
even in the ultra-strong coupling regime where the Jaynes-Cummings model is
invalid. We investigate the robustness of this symmetric behavior with respect
to the drive de-tuning and pulse duration.
