Line Profiles of Two-Photon Transitions

The linewidth depends on the relative orientation of the two wave vectors k and j 2. In the experimental arrangement of Fig. 10,49 the two vectors are either parallel (k = 1 2 photons come from the same wave) or anti- 

Here the first term describes the cases where the two photons come from different waves, in the second they both come from the incident wave, and in the third term, from the reflected wave. Integration over all velocities yields the Lorentzian Doppler-free profile from the first term and the Doppler-broadened background from the second and third terms. 

When both waves have the same polarization, the probability that the two photons come from different waves, is just twice as large as the probability that both come from the same wave. This can be understood as follows In the 

6o)p = 1000 MHz this factor becomes 200 The background can be often completely eliminated by choosing the right kind of polarization (see below). In most cases we can therefore regard the first term in (10.63) to be the dominant one and can neglect the two other contributions. For the resonance case 0) = 2o) the first term is equal to 1 and we obtain for the total two-photon transition probability. 

For two-photon transitions with aM = 0 the Doppler-broadened background can be eliminated by a proper choice of the laser polarization. If the incident laser wave has a circular polarization, the wave reflected at M2 in Fig.10.49 has a polarization. Transitions with aM = 0 (e.g., s s transitions) 

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The line profile of two-photon transitions can be deduced from the following consideration assume the reflected beam in Fig. 2.32 to have the same intensity as the incident beam. In this case the two terms in the second factor of (2.66) become identical, while the first factor, which describes the line profile, differs for the case when both photons are absorbed out of the same beam from the case when they come from different beams. The probability for the latter case is twice as large as for the former case. This can be seen as follows Let (a, a) be the probability for the... 

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