Pump/probe state space

An investigation of the diffraction signatures of specific vibronic states with the vibrations of the same symmetry reveals that even those vibrations have characteristic diffraction signatures. While the overall appearances of these diffraction patterns are similar, they show characteristic spacings and modulation amplitudes. We therefore conclude that different vibrational states have characteristic diffraction signatures, which can be observed using pump-probe electron diffraction. 

Figure 2. Franck-Condon windows lVpc(Gi, r, v5) for the Na3(X) - N83(B) and for the Na3(B) Na3+ (X) + e transitions, X = 621 nm. The FC windows are evaluated as rather small areas of the lobes of vibrational wavefunctions that are transferred from one electronic state to the other. The vertical arrows indicate these regions in statu nascendi subsequently, the nascent lobes of the wavepackets move coherently to other domains of the potential-energy surfaces, yielding, e.g., the situation at t = 653 fs, which is illustrated in the figure. The snapshots of three-dimensional (3d) ab initio densities are superimposed on equicontours of the ab initio potential-energy surfaces of Na3(X), Na3(B), and Na3+ (X), adapted from Ref. 5 and projected in the pseudorotational coordinate space Qx r cos

It must be emphasized that such phenomena are to be expected for a statistical system only in the regime of low level densities. Theories like RRKM and phase space theory (PST) (Pechukas and Light 1965) are applicable when such quantum fluctuations are absent for example, due to a large density of states and/or averaging over experimental parameter such as parent rotational levels in the case of incomplete expansion-cooling and/or the laser linewidth in ultrafast experiments. However, in the present case, it is unlikely that such phenomena can be invoked to explain why different rates are obtained when using ultrafast pump-probe methods that differ only in experimental detail. 

It has to be emphasized that only an ultrashort laserpulse can create a localized wave packet as displayed in the figure. The longer the pulse, the more the prepared state will be delocalized in coordinate space and thus resemble a single stationary scattering state of the molecule. The time evolution of such a state is given by a phase factor and thus the whole idea of pump/probe spectroscopy is lost. 

The electric field envelope of the femtosecond pump pulse which is short compared to the period of the oscillations in Fig. 15.3 (b) covers a frequency range much broader than the energy spacing of individual levels of the low-frequency mode. In other words, the pump spectrum overlaps with several lines of the vibrational progression depicted in Fig. 15.1 (b). As a result, impulsive dipole excitation from the Vqd = 0 to 1 state creates a nonstationary superposition of the wavefunc-tions of low-frequency levels in the Vqd = 1 tate with a well-defined mutual phase. This quantum-coherent wavepacket oscillates in the Vqd = 1 state with the frequency Q of the low-frequency mode and leads to a modulation of O-H stretching absorption which is measured by the probe pulses. In addition to the wavepacket in the Vqd = 1 state, impulsive Raman excitation within the spectral envelope of... 

In a femtosecond pump-and-probe experiment the pump pulse excites the vibrational levels v = 10-12 in the A X y state of Na2 coherently. The vibrational spacings are 109 cm and 108 cm . The probe laser pulse excites the molecules only from the inner turning point into a higher Rydberg state. If the fluorescence /pKAr) from this state is observed as function of the delay time At between the pump and probe pulses, calculate the period ATi of the oscillating signal and the period AT2 of its modulated envelope. 

---