Overlap populations field theory

A field like Eq. (4.3) with separate and overlapping pulses is capable of giving an almost 100% population transfer. This above-the-barrier mechanism is also obtained when using the more sophisticated optimal control theory. Here the laser pulse form is obtained from maximizing the functional (see, e.g.. Ref [48])... 

In the first mechanism, a population transfer from LO phonon to acoustical phonons with half the frequency of the optical phonon and opposite wave vectors takes place. The problem is similar to the decay of a local mode. Thus, the lifetime of the optical mode should be similar to the lifetime of a local mode of the same frequency, because the strain field of a local mode has a similar character like the local mode. Estimations of this process can be made from second-order perturbation theory. In the case of population transfer, cubic terms are dominating in the vibrational potential. For the population transfer, energy and momentum conservation has to be fulfilled, which is the case for bulk material because of the overlap of the density of states of two acoustical phonons with that of the LO phonon. For pure population transfer, a linear increase of the LO half-width with the number n of the LO phonons is expected. 

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