Molecular spectroscopy in the dressed-state picture

It should be noted that instead of dressing the molecular states g and 5 by 1 and 0 photons, respectively, we could use any photon numbersp andp — The corresponding matrix elements are than proportional to p. In processes pertaining to linear spectroscopy it is convenient to stick with photon populations 1 and 0, keeping in mind that all observed fluxes should be proportional to the incident photon numberp or, more physically, to the incident field intensity o - With this in mind we will henceforth use the notation g, k) (or g, co) if the incident direction is not important for the discussion) as a substitute for g, lk - 

In Section 9.3 we have used this truncated dressed state picture to discuss photo-absorption and subsequent relaxation in a model described by a zero-order basis that includes the following states a molecular grovmd state with one photon of frequency a , 0) = g, co), an excited doorway state with no-photons, s, 0), and a continuous manifold of states /) that drives the relaxation. This model is useful for atomic spectroscopy, however, in molecular spectroscopy applications it has to be generalized in an essential way— by accounting also for molecular nuclear motions. In the following section we make this generalization before turning to consider effects due to interaction with the thermal environment. 

Because processes of interest to us take place in condensed phases, we can usually exclude rotational levels from our discussion gas phase rotational motions become in the condensed phase librations and intermolecular vibrations associated with the molecular motion in its solvent cage.  

We therefore envision the molecule as an entity characterized by its vibronic spectrum, interacting with a dissipative environment. As indicated above, a useful characteristic of the truncated dressed state approach is the simplification provided by considering only states that pertain to the process considered. In experiments involving a weak incident field of frequency co these states are found in the energy range about hco above the molecular ground state. For simplicity we assume that in this range there is only one excited electronic state. We therefore focus in what follows on a model characterized by two electronic states (See Fig. 18.1) and include also their associated vibrational manifolds. The lower molecular state g) 

In some cases involving diatomic hydrides HX embedded in solid low temperature matrices rotational motion is only slightly permrbed and expUcit consideration of this motion is useful, see Chapter 13. 

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