Reduced semiclassical electrodynamics approach for molecular polaritons

Recent experiments demonstrate that polariton formation may provide a novel strategy to modify local molecular processes when a large ensemble of molecules is confined within an optical cavity. Inspired by these intriguing experimental findings, various theoretical frameworks have been developed over the years for modeling molecular polaritons. Notably, there has been a recent push to generalize single-molecule strong coupling models to describe collective strong coupling in the large N limit. Here, we examine a numerical strategy based on coupled Maxwell-Schrödinger equations for modeling local molecular processes under collective strong coupling. In this approach, only a few molecules, known as quantum impurities, are treated quantum mechanically, while the remaining molecules forming strong coupling and the cavity structure are modeled by dielectric functions. By solving the coupled Maxwell-Schrödinger equations for a model system, we observe a polariton-induced Purcell effect: the radiative decay rate of a quantum impurity is significantly enhanced when the impurity frequency matches the polariton frequency, while the radiative decay rate is greatly suppressed when the impurity is near resonance with the bulk molecular frequency forming strong coupling. However, our simulations also reveal that this approach is unable to properly model the polariton dephasing rate, as the dark-mode degrees of freedom are not explicitly included when most molecules are represented by dielectric functions.