Steady-state photoluminescence and nanoscopy of two near-identical emitters with dipole-dipole coupling

Abstract: We report progress in the theory of photoluminescence and light scattering by two closely spaced particles. This study is based on our original method to derive the master equation for a system of coupled quantum emitters driven by a cw laser. We emphasise on the case when the emitters are two-level systems but notably different in their transition frequencies and transition moments. The master equation is shown to describe the dipole-dipole coupling and the cooperative entanglement between the particles naturally. It is provided by the use of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchies for reduced density matrices and correlation operators of the material and photonic subsystems. Tackling the hierarchies has also provided us with an elegant way to calculate the photoluminescence excitation spectra subject to the arrangement of the excitation and the position of the detector against the emitters. Our findings may be important for developing novel possibilities for the all-optical nanoscopy and may help construction of entangled systems to be implemented in quantum technologies.