Optical response of a binary atomic system with incoherent gain

We study the optical response of a binary system of identical atoms in which one of them is excited by an incoherent pump. Applying the diagrammatic formalism developed by Donaire [Phys. Rev. A 104, 043704 (2021)], we show how scattering, absorption, stimulated emission, spontaneous emission, and resonant energy transfer can be tailored by varying (1) the interatomic distance, which governs the interference effects of the emitted radiation, and (2) the pump rate, which determines the population of the atomic levels. It is found that, for sufficiently strong pumping, the collective component of the extinction cross section becomes negligible, regardless of the interatomic distance, as optical gains compensate for losses, and the total extinction cross section is reduced to less than half of its value in the absence of pumping. In contrast, at weak pumping and short interatomic distances, interference effects lead to a significant suppression of the extinction cross section relative to that of two noninteracting atoms.