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Journal of Experimental and Theoretical Physics Letters

Atom in an elliptically polarized resonance field: Exact stationary solution

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

Published Jul 1, 1996• 2 citations
Publisher

Abstract

An analytical method is developed for finding the exact stationary solution for the density matrix of atoms in a monochromatic resonance field of arbitrary ellipticity and intensity. A solution for the transitions F g = F → F e = F +1 ( F g and F e are the angular momenta of the ground and excited states) is obtained in an analytical invariant form. The properties of this solution are investigated.

DOI
10.1134/1.567162

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An analytical method is developed for finding the exact stationary solution for the density matrix of atoms in a monochromatic resonance field of arbitrary ellipticity and intensity. A solution for the transitions F g = F → F e = F +1 ( F g and F e are the angular momenta of the ground and excited states) is obtained in an analytical invariant form. The properties of this solution are investigated.
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.
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.