Exploring the Delocalization of Dark States in a Multimode Optical Cavity

TL;DR

This study investigates how dark states in a multimode optical cavity delocalize in three dimensions, revealing that their delocalization scales with the number of molecules and depends on disorder and cavity length, which is crucial for understanding polariton chemistry.

Contribution

It provides a three-dimensional analysis of dark state delocalization in multimode cavities, extending beyond simplified one-dimensional models and highlighting the importance of multimode effects in polariton phenomena.

Findings

Dark state delocalization scales linearly with the number of molecules in the plane.

Adding layers along the cavity axis increases delocalization less significantly.

Delocalization is enhanced by lower energetic disorder and longer cavity length.

Abstract

The strong coupling between molecules and photonic modes in a Fabry-P\'{e}rot optical cavity, which forms hybrid light-matter states called polaritons, has been demonstrated as a promising route to control the rates of chemical reactions. However, theoretical studies, which largely employ models with a single cavity mode, cannot explain the experimentally observed kinetic changes. While simplified multimode models with one spatial dimension can capture experimental features involving the polariton states, it is unclear whether they can also describe the dark states. Here, we study the delocalization of dark states for molecules in a multimode cavity, accounting for the three-dimensional nature of experimental setups. Accounting for energetic and orientational disorder, but fixing Rabi splitting and intermolecular distances (i.e., no positional disorder), we find that the delocalization of the dark states scales linearly with the number of molecules in the plane parallel to the cavity mirrors, in contrast to one-dimensional multimode models. Adding layers of molecules along the axis normal to the mirrors increases the delocalization much less. Similar to the one-dimensional models, the dark-state delocalization is enhanced for smaller values of molecular energetic disorder, relative to the light-matter coupling, and cavities with longer longitudinal length. Our work indicates that for certain phenomena, understanding the dark states under strong light-matter coupling might require a proper multimode description of the optical cavity.