Understanding the Energy Gap Law under Vibrational Strong Coupling

The rate of non-radiative decay between two molecular electronic states is succinctly described by the energy gap law, which suggests an approximately-exponential dependence of the rate on the electronic energy gap. Here, we inquire whether this rate is modified under vibrational strong coupling, a regime whereby the molecular vibrations are strongly coupled to an infrared cavity. We show that, under most conditions, the collective light-matter coupling strength is not large enough to counter the entropic penalty involved with using the polariton modes, so the energy gap law remains unchanged. This effect (or the lack thereof) may be reversed with deep strong light-matter couplings or large detunings, both of which increase the upper polariton frequency. Finally, we demonstrate how vibrational polariton condensates mitigate the entropy problem by providing large occupation numbers in the polariton modes.