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 ∆ . Here, we explicitly ignored other high-lying vibrational states |ν 4 and |ν 5 due to their negligible population (see Fig. ), as well as the vibrational ground state tunneling pathway |ν L → |ν R due to the small tunneling splitting ∆. Based on the observation of the population dynamics in Fig. , it seems that both populations of |ν L and |ν R 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)