Abstract
We introduce a perturbation technique based upon a graph representation of the density matrix equations describing strong field optical interactions in a multilevel system. The method is applied to the determination of cubic and quartic AC Stark shifts, both for the first time. The cubic result, which occurs when two strong fields are present in a three wave parametric interaction linkage diagram, is unique in that the shift depends on the absolute phase of the waves as well as their amplitudes.
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