Permanent dipole moments and two-color multiphoton resonances in the two-level molecule: The rotating wave approximation versus exact results

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Abstract
The interaction of two continuous wave electric fields (lasers) with a two-level molecule, that has a nonzero difference d, between the permanent dipoles of the two states involved in a multiphoton two-color transition, is studied in the rotating wave approximation and by using exact methods. Analytical rotating wave approximation results for the time-dependent populations of the molecular states and for the resonance profiles are derived and used to help discuss the effects of permanent dipole moments in the two-color absorption problem. Several examples of multiphoton, two-color, two-level resonance profiles calculated in the rotating wave approximation and by using exact techniques, are employed for illustrative purposes. They are used to help quantify the conditions for the validity of the two-color rotating wave approximation, which are considerably more restrictive than the analogous conditions for the one-color rotating wave approximation with d≠0, and to illustrate the interpretive and predictive nature of the rotating wave approximation results. For example, there are many multiphoton, two-color transitions that are available if a molecule possesses permanent dipoles (d≠0). The analytic rotating wave approximation expression for the molecule-two laser coupling can often be used to reliably estimate the field parameters of the two lasers that are required to optimize a given transition relative to others.

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