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Journal of Experimental and Theoretical Physics

Tensor structure of the stationary point of the radiative relaxation operator of an atom

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin, Gerard Nienhuis

Published Jul 1, 1998• 3 citations
Publisher

Abstract

We formulate the problem of the stationary point of the operator of radiative relaxation of an atom: the initial distribution among the sublevels of the excited state, whose nonzero eigenvalues (populations) coincide with the populations of the final distribution (after spontaneous decay) among the sublevels of the ground state. We show that these distributions can be expressed in terms of spherical functions of the complex direction. The results are then used to develop a compact analytical representation of the stationary density matrix of atoms interacting with an elliptically polarized monochromatic field.

DOI
10.1134/1.558627

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We formulate the problem of the stationary point of the operator of radiative relaxation of an atom: the initial distribution among the sublevels of the excited state, whose nonzero eigenvalues (populations) coincide with the populations of the final distribution (after spontaneous decay) among the sublevels of the ground state. We show that these distributions can be expressed in terms of spherical functions of the complex direction. The results are then used to develop a compact analytical representation of the stationary density matrix of atoms interacting with an elliptically polarized monochromatic field.
We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta Jg{J}_{g}Jg​ and Je{J}_{e}Je​ of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broadband radiation is given. We indicate various applications of these results.
The general nonstationary theory of propagation of an elliptically polarized pulse resonantly interacting with the 1/2–1/2 transition is presented. The theory that takes into account relaxation processes is developed in terms of irreducible tensor operator representation allowing diagonalization of the relaxation matrix and introduction of effective decay times governing relaxation of both population and coherence between magnetic sublevels of the resonant system. It is shown that interference of magnetic sublevels in the field of polarized radiation that optically pumps the atoms can result in inversionless amplification of radiation.