Simultaneous saturation of two atomic transitions sharing a common level

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Abstract
A dressed-atom approach is generalised for studying several effects which could be observed on an atomic beam interacting with two monochromatic resonant laser beams saturating two atomic transitions sharing a common level, a situation which occurs frequently in stepwise excitation experiments. The problem of the optimisation of the population of the upper state is investigated. Analytical expressions are derived for the positions, the widths and the weights of the various components of the fluorescence and absorption spectra. The results obtained at the limit where one of the two lasers has a much weaker intensity than the other one are interpreted perturbatively by treating to lowest orders the scattering of the weak laser beam by the atom dressed by the intense one.