Quantum electrodynamics of bimolecular multiphoton processes in the condensed phase

Bimolecular photophysics is an area that accommodates a wide range of pairwise interactions of molecules with radiation, including cooperative absorption and emission, and bimolecular scattering. In this paper a QED theory is developed to deal with bimolecular multiphoton processes without recourse to the usual dilute medium approximation. The theory is fully microscopic, taking explicit account of effects due to any surrounding molecular medium. To this end, the concept of medium-dressed photons (bath polaritons) has been adopted, extending both to the real incoming and outgoing photons and also to the virtual photons that carry an energy mismatch between participating molecules. Modifications of the bimolecular rates resulting from the influence of the medium originate in two ways. One, associated with the real photons, brings in the refractive indexes at the appropriate photon frequencies. All terms constituting the transition matrix element are subject to introduction of the same refractive factor for each absorbed or emitted photon. Another medium effect, due to the virtual photons, appears through the electromagnetic coupling tensor which experiences, inter alia, changes due to screening and local field factors. Here the refractive effects in each term relate to the appropriate mismatch frequencies. These frequencies generally lie in a different spectral region to the real photons, and may equally be situated in either transparent or absorbing areas. In the latter absorbing case, an exponential decay factor emerges in the coupling tensor, regularising the long-range R−2 contribution. That solves the problem of potentially infinite ensemble rates which arises in the dilute medium approximation.