Tuning the collective decay of two entangled emitters by means of a nearby surface

We consider the radiative properties of a system of two identical correlated atoms interacting with the electromagnetic field in its vacuum state in the presence of a generic dielectric environment. We suppose that the two emitters are prepared in a symmetric or antisymmetric superposition of one ground state and one excited state and we evaluate the transition rate to the collective ground state, showing distinctive cooperative radiative features. Using a macroscopic quantum electrodynamics approach to describe the electromagnetic field, we first obtain an analytical expression for the decay rate of the two entangled two-level atoms in terms of the Green's tensor of the generic external environment. We then investigate the emission process when both atoms are in free space and, subsequently, when a perfectly reflecting mirror is present, showing how the boundary affects the physical features of the superradiant and subradiant emission by the two coupled emitters. The possibility to control and tailor radiative processes is also discussed. (paper)