The Quantum Theory of Transient Resonance Raman Scattering and Its Application to a Strongly Coupled Localized Electron-Phonon System
The quantum mechanical description of the transient resonance Raman scattering including both the excitation and observation processes is presented. To obtain the general formula for the actually observable transient emission spectrum, the following way of observation is proposed; the use of a spectroscope for wave transformation and a photon-counter behind it for particle transformation. On its basis, the transient emission spectrum and its average over the duration time of photon-counting are explicitly defined especially for systems small compared with the spacial extent of an incident pulse. It will be shown that the transient emission spectrum conforms to the minimal case of the Heisenberg uncertainty relation through the restriction for the emission time coming from the Fourier transform of the transfer function of the spectroscope. The theory is applied to a strongly coupled localized electron-phonon system. It will be shown that what aspects of the correlation between absorption and emission are disclosed depends strongly on both the ways of excitation and observation.