Intermolecular forces, spontaneous emission, and superradiance in a dielectric medium: Polariton-mediated interactions

Abstract

A reduced equation of motion that describes the excited-state dynamics of interacting two-level impurity molecules in a dielectric host crystal is derived starting from a microscopic model for the total system. Our theory generalizes the derivation of the conventional superradiance master equation for molecules in vacuum; the role of photons in the conventional theory is played by polaritons (mixed crystal-radiation excitations) in our approach. Our final equation thus contains dispersive and superradiant polariton-mediated intermolecular interactions. The effect of the dielectric host is completely contained within a rescaling of these interactions with the transverse dielectric function ε(ω) of the crystal taken at the impurity’s transition frequency. Our theory yields all local field and screening factors for both the dispersive and the dissipative couplings from a single, unified starting point. Known scaling laws for the spontaneous-emission rate and the instantaneous dipole-dipole interaction are extended to the frequency region where the dispersion of ε(ω) is important.