Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis-Cummings model

We consider molecules confined to a microcavity of dimensions such that an excitation of the molecule is nearly resonant with a cavity mode. The molecular excitation energies are assumed to be Gaussianly distributed with mean ϵ_a and variance σ. We find an asymptotically exact solution for large number density N. Conditions for the existence of the polaritonic states and expressions for their energies are obtained. Polaritonic states are found to be quite stable against disorder. Our results are verified by comparison with simulations. When ϵ_a is equal to energy of the cavity state ϵ_c, the Rabi splitting is found to increase by 2σ²N|Ṽ|, where Ṽ is the coupling of a molecular excitation to the cavity state. An analytic expression is found for the disorder-induced width of the polaritonic peak. Results for various densities of states and the absorption spectrum are presented. The dark states turn "gray" in the presence of disorder with their contribution to the absorption increasing with σ. Lifetimes of the cavity and molecular states are found to be important, and for sufficiently large Rabi splitting, the width of the polaritonic peaks is dominated by them. We also give analytical results for the case where the molecular levels follow a uniform distribution. We conclude that the study of the width of the polaritonic peaks as a function of the Rabi splitting can give information on the distribution of molecular energy levels. Finally, the effects of (a) orientational disorder and (b) spatial variation on the cavity field are presented.