Non-Markovian theory of nonlinear-optical phenomena associated with the extremely fast relaxation in condensed matter

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Abstract
The transient nonlinear-optical phenomena associated with the extremely fast relaxation processes in condensed matter are investigated from a microscopic viewpoint, taking into account the non-Markovian nature of the system. It is found that, in the ultrashort time region comparable to the thermal-reservoir correlation time, the transient nonlinear-optical response exhibits the characteristic time variation inherent in the non-Markovian nature of the matter system. This result cannot be explained by the conventional phenomenological theory based on the relaxation time description. The general formula obtained is applied, as an example, to the transient four-photon parametric coupling generated by the two-pulse excitation of the localized-electron-phonon system. It is found that not only the time variation of the signal intensity, but also the dependence of the time-integrated intensity of the pulse interval exhibits the characteristic feature which reflects the dynamics of the relaxation of the phonon system. It is emphasized that this result provides us the most practical tool to observe the extremely fast relaxation processes in condensed matter.