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KHADZHI, Peter; KOROVAY, Olesya V.; NADKIN, L.. Dispersion laws of a highly excited three-level atom with an equidistant energy spectrum. In: Materials Science and Condensed Matter Physics. Ediția 9, 25-28 septembrie 2018, Chișinău. Chișinău, Republica Moldova: Institutul de Fizică Aplicată, 2018, p. 73.
|Materials Science and Condensed Matter Physics
Ediția 9, 2018
Conferința "International Conference on Materials Science and Condensed Matter Physics" |
Chișinău, Moldova, 25-28 septembrie 2018
Increased attention is currently focused on the study of processes of the interaction of laser radiation with matter in size-limited media. Bose–Einstein condensation and superfluidity in exciton-polariton 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 one-photon transitions between successive pairs of neighboring levels. At the same time, direct two-photon transitions between the first and third levels are optically allowed in three-level 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 one-photon 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 two-photon 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 three-level 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, one-photon and two-photon transitions in the dynamics of three-level atoms have not been taken into account simultaneously. We report below studies of the dispersion law of three-level 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 one-photon transition between them is optically forbidden. However, a direct two-photon transition between these levels is optically allowed. For this reason, we take into account one photon transitions between levels and and two-photon 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 three-level 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 three-level 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 two-level atom is split into two equations and . The former equation, the well-known polariton equation and the latter equation is the dispersion ratio for ―bare‖ photons not interacting with the medium. Both polariton-like 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 one-photon transitions and an optically allowed two-photon transition. The repulsion and attraction of the branches of the dispersion law, their intersection, self-consistent variation of the coupling strength of photons with atoms, and a strong dependence on the phase difference between the coupling constants are predicted.