Purcell-induced suppression of superradiance for molecular overlayers on noble atom surfaces

We study the impact of an environment on the electromagnetic responses of a molecule in the presence of a dielectric medium. By applying the dipole-dipole coupling between the molecule's and the environment's degrees of freedom, we can reduce the complex system into its components and predict excitation lifetimes of single and few molecules attached to a dielectric surface by knowing the entire quantum-mechanical properties of the molecules, such as transition energies and dipole moments. The derived theory allows for the description of superradiance between two molecules depending on the geometric arrangement between both concerning their separation and orientation with respect to each other. We analyze the possibility of superradiance between two molecules bound to a dielectric sphere and determine a change in the relevant length scale where the usually considered wavelength in free space is replaced with the binding distance, drastically reducing the length scales at which collective effects can take place.