Modeling of the dynamics of selective resonant fluorescence of two interacting nanoparticles
Morozov V. A. 1
1Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Moscow, Russia
Email: morozov@mail.ioc.ac.ru
A system of self-consistent differential equations of the first order in time is presented, which reflects the dynamics of resonant fluorescence of two interacting two-level particles when one of them is irradiated with a long rectangular pulse of light. This system of equations is obtained based on the analysis of equations describing the dynamics of the states of a common composite system of a marked pair of particles and a quantized radiation field, taking into account the continuous absorption of a fluorescence photon by the macroscopic environment of particles, which is attributed to the radiation of one or another of the interacting particles when its ground state is populated ("selective" fluorescence). Along with the dynamics of the population of the initial collective state of the general system, the dynamics of the population and coherence of the main and excited collective states of particles when they absorb one of the irradiation photons, the resulting system describes the dynamics of the population of each particle in its ground state, recorded with the absorption of a resonant fluorescence photon noted above. This description of the dynamics of the population of the ground state of each of the particles distinguishes the above system of equations from systems that, in relation to the fluorescence of this pair of particles, describe the dynamics of their collective ground state, such as, for example, the system of optical Bloch equations. Accordingly, the characteristic features of the dynamics of selective resonant fluorescence under consideration differ significantly from the characteristic features of the dynamics of resonant fluorescence described by the system of optical Bloch equations. These differences are illustrated by figures reflecting the results of numerical solutions of the reduced system of equations and solutions of the corresponding system of optical Bloch equations. Keywords: mathematical modeling, interacting two-level nanoparticles, dynamics of resonant fluorescence.
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