Symmetric excitation and de-excitation of a cavity QED system

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.