Semiclassical theory of two-photon polarization-dependent fractional optical collisions: Application to the Mg-He(3s²¹S₀→3p¹P₁→5s¹S₀, 4d¹D₂) optical collision

We have analyzed by perturbation theory technique two-photon polarization-dependent fractional optical collisions. In its general form the cross section of the collision is expressed as the overlap integral of its spectral profile with the spectrum of the second order correlation function of the electromagnetic field. Based on the semiclassical expansion of radial wave functions and of a retarded Green function we have expressed the spectral profile of the cross section in terms of well understood semiclassical characteristics of the process such as the rotational transformations of the transition dipole moments and the transition amplitudes describing the adiabatic or nonadiabatic dynamics of the electronic subsystem along classical trajectories. As a practical example, we have calculated the Mg-He (3s²¹S₀→3p¹P₁→5s¹S₀,4d¹D₂) fractional optical collision cross section. The partial wave analysis for excitation up to the 5s¹S₀ state has shown the nonvalidity of quasistatic approximation based on successive single-photon transitions for some frequency detunings. For example, for the positive detuning from two-photon atomic resonance we have obtained the dominant contribution coming from the direct two-photon Franck-Condon transitions. Such a contribution gives the magnitude of the polarization ratio, characterizing the dependence of the cross section on mutual laser polarizations at the first and at the second steps of the photoexcitation, different than for successive single-photon Franck-Condon transitions. In the more complicated case of excitation up to the 4d¹D₂ state of magnesium the role of the interference between different photoexcitation channels becomes important. The polarization ratio has a stable value close to 1/7 in a broad spectral range in the blue wing of the second frequency detuning. There is a strong dependence of the polarization ratio in the red wing of the second detuning. Such spectral behavior can be explained by the partial selection in the red wing of the atomic resonance line, perturbed by the collisions of those Zeeman transitions in which contributions in the polarization ratio have different orders and different signs.