Mathematical modeling of resonance fluorescence spectra of two two-level interacting nanoparticles

The mathematical modeling of the resonance fluorescence spectra associated with the dynamic interaction of two two-level nanoparticles is carried out. The cases of weak and strong pumping of a single particle by a long pulse of monochromatic light with a carrier frequency equal to or close to the frequency of its own transition are considered. Expressions for the contours of the spectra of collective and two components of selective resonant fluorescence are obtained – as a function of the frequency of the recorded photon of fluorescence – as a result of using solutions of the Schrodinger equation system for the amplitudes of states of a composite system of particles, a quantized irradiation field and a resonant fluorescence field. Based on the analysis of graphical images of the obtained functions, the characteristic features of the shape and position of the maxima of the contours of the spectra at different values of the parameters of the structure and interaction of particles and the irradiation field are determined.