Temporal coherence in multiphoton absorption. Far off-resonance intermediate states

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Abstract
We develop a consistent formalism for the treatment of temporal atomic or molecular coherence in multiphoton absorption. The formalism is fully quantum mechanical under the assumption that the exciting laser fields are well described by coherent states. We make use of the language and methodology of resonance physics to the extent possible, but deliberately avoid the rotating‐wave approximation, and do not restrict the allowed atomic states to be finite in number or the electric field strengths to be small in magnitude. For compactness in the presentation only electric dipole transitions are considered. As all of the transitions, both stimulated and spontaneous, are due to the activation of quantum mechanical dipoles, it is most efficient to construct the formalism so that it emphasizes the role of dipole operators, and we do this. The one strong restriction imposed here, but avoided in a following paper, is to consider only multiphoton transitions that have one resonance between initial and final states and no intermediate resonance. We describe, in effect, the time dependences associated with the early multiphoton absorption calculations of Bebb and Gold.