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Cavity quantum electrodynamics (CQED) and its extensions are widely used forthe description of exciton-polariton systems. However, the exciton-polaritonmodels based on CQED vary greatly within different contexts. One of the mostsignificant discrepancies among these CQED models is whether one should includedirect intermolecular interactions in the CQED Hamiltonian. To answer thisquestion, in this article, we derive an effective dissipative CQED modelincluding free-space dipole-dipole interactions (CQED-DDI) from a microscopicHamiltonian based on macroscopic quantum electrodynamics. Dissipative CQED-DDIsuccessfully captures the nature of vacuum fluctuations in dielectric media andseparates it into the free-space effects and the dielectric-induced effects.The former include spontaneous emissions, dephasings and dipole-dipoleinteractions in free space; the latter include exciton-polariton interactionsand photonic losses due to dielectric media. We apply dissipative CQED-DDI toinvestigate the exciton-polariton dynamics (the population dynamics ofmolecules above a plasmonic surface) and compare the results with those basedon the methods proposed by several previous studies. We find that directintermolecular interactions are a crucial element when employing CQED-likemodels to study exciton-polariton systems involving multiple molecules.

Microscopic theory of exciton-polariton model involving multiple  molecules: Macroscopic quantum electrodynamics formulation and essence of  direct intermolecular interactions