where k 1 and k 3 are dominated by the phonon or photonmediated population transfer, and k 2 is dominated by excited state tunneling splitting 0 . Here, we explicitly ignored other high-lying vibrational states |⌫ 4 i and |⌫ 5 i due to their negligible population (see Fig. ), as well as the vibrational ground state tunneling pathway 77 |⌫ L i ! |⌫ R i due to the small tunneling splitting . Based on the observation of the population dynamics in Fig. , it seems that both populations of |⌫ 0 L i and |⌫ 0 R i reach steady states. As such, the dynamics of our model systems (both inside and outside the cavity) are classic textbook examples of steady-state kinetics. This means that the product population under the steady-state limit can be approximated as (see details in Appendix B)