Resonantly enhanced two-photon association

The significance of resonantly enhanced two-photon association stems from the visibility of using it to form ultracold molecules, a topic of considerable interest. fSr cooling schemes that work for atoms [338-340] tend to fail for molecules, ily due to the presence of many near-resonance lines and the presence of other ges, of freedom, in addition to translation (rotations, vibrations, etc.), that must 

Rather than attempting to cool warm molecules one can try to synthesize cold molecules by associating cold atoms. The molecules thus formed are expected to maintain the translational temperature of the recombining atoms because the center-of-mass motion remains unchanged in the association process (save for the little. momentum imparted by the photon). This idea was first proposed by Julienne and j co-workers [343, 344] who envisioned a multistep association, first involving the continuum-to-bound excitation of translational continuum states of cold trapped. atoms to an excited vibrational level in an excited electronic molecular state. This step was followed by bound-bound spontaneous emission to the ground electronic state. (I 

An undesirable feature of this scheme is that the spontaneous nature of the seconiS step allows the molecules to end up in a large range of vibrational levels. As aJ consequence, the use of stimulated emission [308, 345-351], discussed below, is preferable insofar as it allows population transfer to a particular final molecular state., of interest. M 

---

If fset of equations used in Section 11.1 for two-photon dissociation problems can ilfqsed to address another significant problem—that of resonantly enhanced two-t mpfon association, depicted schematically in Figure 10.1c. 

Frequently, values of P for wavelengths where experimental data do not exist are estimated by extrapolation using a two-level model description of the resonance enhancement of P (see Appendix). Levine and co-workers [170] have also shown how to estimate the wavelength (frequency) dispersion of two-photon contributions to p. Because of the potential of significant errors associated with each measurement method, it is important to compare results from different measurement techniques. Perhaps the ultimate test of the characterization of the product of pP is the slope of electro-optic coefficient versus chromophore number density at low chromophore loading. It is, after all, optimization of the electro-optic coefficient of the macroscopic material that is our ultimate objective. 

Further features are evident when the relative magnitudes of the dipole difference d and the transition dipole p ° are considered. One immediately striking feature is the observation that the second, fourth, sixth, and eighth terms all disappear if d = 0, leaving only terms associated with virtual excitation routes. [Note that no such routes were manifest in the second-harmonic result. If d = 0 then the entire expression Eq. (85) becomes zero—any process involving an odd number of photons has to entail at least one 00 or uu segment in the interaction sequence.] In the third-harmonic case, in particular, both terms associated with two-photon resonances disappear—in other words, there can be no two-photon resonance enhancement of third-harmonic generation under such circumstances. If, however, d p °, then the even terms of Eq. (90)... 

---