The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Abstract

Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta J _i and J _f. The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of J _i and J _f and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼lξ holds and dichroism occurs only when the photons are elliptically polarized, with 0<|ξ|<1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons.