Transition Probability of Two-Photon Transitions

The probability A - for a two-photon transition between the ground state E. and an excited state of a molecule, induced by photons and ho)2 from two light waves with wave vectors ky k polarization vectors e 2, and intensities l2 can be written as a product of two factors [8.93] 

The first factor gives the spectral line profile of the two-photon transition. It corresponds exactly to that of a single-photon transition of a moving molecule at a center frequency = o) + 0J2 + v(k2 i2) homogen- 

This Doppler-free two-photon spectroscopy will be discussed in Sect.10.6. 

The second factor describes the transition probability for the two-photon transition. It can be derived quantum mechanically by second-order perturbation theory (see for example [8.94]). This factor contains a sum of products of matrix elements transitions between the initial state i and 

Often a fictitious virtual level is introduced to describe the two-photon transition by a symbolic two-step transition E. - (Fig.8.40). 

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