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SM ISO690:2012 KHADZHI, Peter; KOROVAY, Olesya V.; NADKIN, L.. Dispersion laws of a highly excited threelevel atom with an equidistant energy spectrum. In: Materials Science and Condensed Matter Physics. Ediția 9, 2528 septembrie 2018, Chișinău. Chișinău, Republica Moldova: Institutul de Fizică Aplicată, 2018, p. 73. 
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Materials Science and Condensed Matter Physics Ediția 9, 2018 

Conferința "International Conference on Materials Science and Condensed Matter Physics" Chișinău, Moldova, 2528 septembrie 2018  


CZU: 539.2  
Pag. 7373  


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Increased attention is currently focused on the study of processes of the interaction of laser radiation with matter in sizelimited media. Bose–Einstein condensation and superfluidity in excitonpolariton systems in microcavities were studied. Studies of phenomena caused by the strong coupling of photons to atomic systems are of particular interest. Nonlinear optical phenomena in three and multilevel atomic systems were studied taking into account optically induced onephoton transitions between successive pairs of neighboring levels. At the same time, direct twophoton transitions between the first and third levels are optically allowed in threelevel atomic systems. Within this model, a number of active levels, e.g., three levels, which are in resonance with the incident laser radiation, are ―cut‖ from the system. Optically induced onephoton transitions from the ground state of a crystal to an exciton state and from the exciton state to a biexciton state, as well as a direct twophoton transition from the ground state of the crystal to the biexciton level, occur in the exciton region of the spectrum. In semiconductors of type CdS and CdSe, where the binding energy of a biexciton is vanishingly low, this model of matter is in essence an equidistant threelevel model. Equidistant multilevel systems are often used in the theory of cascade lasers. It is noteworthy that the model of quantum oscillator is also equidistant. As far as we know, onephoton and twophoton transitions in the dynamics of threelevel atoms have not been taken into account simultaneously. We report below studies of the dispersion law of threelevel atoms with an equidistant energy spectrum interacting with photons of an ultrashort pulse of resonant laser radiation. States 1 and 3 have the same parity; therefore, a onephoton transition between them is optically forbidden. However, a direct twophoton transition between these levels is optically allowed. For this reason, we take into account one photon transitions between levels and and twophoton transitions induced by photons of a single pulse between levels 1 and 3. Although the used scheme of equidistant energy spectrum seems specific, the Λ, V, and Σ models of threelevel atoms are widely used in atomic optics. The dispersion law of atomic polaritons has the form: We now consider in more detail the features of the dispersion law for the threelevel atom with the equidistant energy spectrum. The eigenfrequencies of the second and third (excited) levels are and , respectively. Photons of a single pulse with the frequency are incident on the atom. In the limit of twolevel atom is split into two equations and . The former equation, the wellknown polariton equation and the latter equation is the dispersion ratio for ―bare‖ photons not interacting with the medium. Both polaritonlike branches of the dispersion law intersect the straight line at two points. If, e.g., but , i.e., if the photon interacts with the atom through the transition, is not split into two independent equations. In view of the interaction, the branches of the dispersion law intersect at the points of energy degeneracy. As a result, the dispersion law is split into three separate branches, upper, middle, and lower. The upper and middle branches have extrema near the point, whereas the middle and lower branches have extrema. With an increase in , splittings increase and positions of extrema are shifted. It has been shown that the dispersion law of atomic polaritons consists of three branches whose position and shape are determined by the Rabi frequencies of optically allowed onephoton transitions and an optically allowed twophoton transition. The repulsion and attraction of the branches of the dispersion law, their intersection, selfconsistent variation of the coupling strength of photons with atoms, and a strong dependence on the phase difference between the coupling constants are predicted. 

