The differences between the virtual and zero photon cases can be rationalized as follows. With the choice of the initial cavity state as in eq. 9 and η = 0.06, the initial average total energy ⟨H⟩ is always less than the classical barrier height (∼ 2030 cm -1 ) for the range of cavity frequencies shown. Therefore, quantum tunneling through the potential barrier contributes significantly to the isomerization process. More importantly, since there are initially no photons in the cavity mode, the cavity can not transfer its energy to the reactive mode initially to boost the isomerization process. Thus, quantum mechanically, we see a suppression of ⟨P iso ⟩ compared to the off-cavity value near ω c ≡ ω 10 = 1039 cm -1 . In this frequency region, Fig. ) implies that the reactive mode initially transfers significant energy to the cavity mode, and thereafter system and cavity exchange energy coher- ently. Furthermore, note that in this case the quantumclassical correspondence in Fig. (a) is not good when compared to the virtual photon case. Such disagreement between quantum and classical dynamics is perhaps expected in this highly quantum regime where the cavity mode has initially no photons. Nevertheless, note that the classical ⟨P iso ⟩ tends to decrease in the vicinity of ω c ≈ ω 10 . This observation again points to large scale changes in the classical phase space structure.