Multi-level Purcell effect and the impact of vibrational modes in molecular quantum optics

The increased decay rate of a two-level system weakly coupled to an optical cavity, known as the Purcell effect, is a cornerstone of cavity QED. However, the effect of cavity coupling is not well understood if the two-level system is replaced by a multi-level interacting system. Motivated by experiments looking to characterise molecular systems via exploiting a cavity interaction, we study a manifestation of the Purcell effect in a bio-inspired photosynthetic dimer. We focus in particular on how molecular vibrational modes, thought to play an important role in photosynthetic exciton transport, impact the system-cavity behaviour in the Purcell regime. We provide a theoretical picture in terms of an effective non-Hermitian Hamiltonian, which extends the simple picture of a Jaynes-Cummings model to the description of a `multi-level' Purcell effect, where different levels have differing Purcell factors, with effective cooperativities mediated by coherent vibrational interactions.