Phase space perspective on a model for isomerization in an optical cavity

Explanation for the modification of rates and mechanism of reactions carried out in optical cavities still eludes us. Several studies indicate that the cavity-mediated changes in the nature of vibrational energy flow within a molecule may play a significant role. Here we study a model polaritonic system, proposed and analyzed earlier by Fischer, Anders, and Saalfrank[1], comprising of a one dimensional isomerization mode coupled to a single photon mode in a lossless cavity. We show that the isomerization probability in presence of virtual photons, for specific cavity-system coupling strengths and cavity frequencies, can exhibit suppression or enhancement for different choices of the initial reactant vibropolariton wavepacket. We observe qualitative agreement between the classical and quantum average isomerization probabilities in the virtual photon case. A significant part of the effects due to coupling to the cavity can be rationalized in terms of a “chaos-order-chaos” transition of the classical phase space and the phase space localization nature of the polariton states that dominantly participate in the quantum isomerization dynamics. On the other hand, for initial states with zero photons (i.e., a “dark cavity”) the isomerization probability is suppressed when the cavity frequency is tuned near to the fundamental frequency of the reactive mode. The classical-quantum correspondence in the zero photon case is unsatisfactory. In this simple model we find that the suppression or enhancement of isomerization arises due to the interplay between cavity-system energy flow dynamics and quantum tunnelling.