Interplay between static and dynamic disorder: Contrasting effects on dark state population inside a cavity

Strong light-matter interactions between molecules and quantized electromagnetic fields inside an optical cavity open up novel possibilities, although inevitably influenced by disorder, an inherent attribute of realistic molecular systems. Here, we explore the steady-state optical response of molecular emitters within a lossy cavity, with a focus on the combined effects of static and dynamic disorders, as frequently observed in solution-phase experiments. By analyzing the transmission spectra, molecular energy change, and dark state population, we uncover the contrasting effects of static and dynamic disorders on the dark state population and its interplay with polariton states. We find that the Rabi splitting exhibits an inversion with increasing disorder strength, where the maximum splitting is determined by the interplay of static and dynamic disorders. Furthermore, we identify a dark state-induced polariton linewidth narrowing, revealing a mechanism distinct from motional narrowing induced by frequency fluctuations. These mechanistic insights highlight the critical role of dark states, establishing a foundation for future developments in the fields of polariton chemistry and strong coupling spectroscopy.