Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities

Experiments have demonstrated that the strong light-matter coupling in polaritonic microcavities significantly enhances transport. Motivated by these experiments, we have solved the disordered multimode Tavis-Cummings model in the thermodynamic limit and used this solution to analyze its dispersion and localization properties. The solution implies that wave-vector-resolved spectroscopic quantities can be described by single-mode models, but spatially resolved quantities require the multimode solution. Nondiagonal elements of the Green's function decay exponentially with distance, which defines the coherence length. The coherence length is strongly correlated with the photon weight and exhibits inverse scaling with respect to the Rabi frequency and an unusual dependence on disorder. For energies away from the average molecular energy $E_{\text{M}}$ and above the confinement energy $E_C$, the coherence length rapidly diverges such that it exceeds the photon resonance wavelength $\lambda_0$. The rapid divergence allows us to differentiate the localized and delocalized regimes and identify the transition from diffusive to ballistic transport.