Wavepacket spreading

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

B. Kohler Prof. Fleming, your experimental results clearly indicate that in the case of I2 in hexane the vibrational coherence of an initially prepared wavepacket persists for unexpectedly long times. However, quantum dynamical calculations show that wavepacket spreading due to anharmonicity can be very substantial even for isolated molecules... 

G. R. Fleming Sure the wavepacket spreads, but not as much as you would think on this time scale. What can be done experimentally to get precise data is to do wavelet analysis to see what shape it had. That is a realistic goal for a simple system using solid-state lasers. 

Figure 5 shows a plot of the magnitude of the overlap for / = 0, K0/ (f)> sl. versus time. The magnitude of the overlap decreases as the wavepacket spreads out. There is no recurrence. The steeper the inverted potential (i.e., the higher coj), the faster the wavepacket spreads out and the faster the overlap decreases. Because the inverted harmonic potential surface can model only a small area around the Frank-Condon region, this model can only be applied to short time dynamics. 

Both the energy gap and the vibronic spacing in the electronic spectra of the [PtClJ ion are explained by an excited state distortion in a nontotally symmetric mode. The 315 cm MIME frequency results from the distortion in the 329cm Aj, mode and the 304cm Bj, mode. The low intensity in the energy gap is a result of slow wavepacket spreading along the Bj, coordinate. 

Figure 25. Magnitude of the excited-state wavefunction before the second pulse (a) t = 200 a.u. (b) t = 600 a.u. (c) t = 800 a.u. Note the extensive wavepacket spreading because the surface is so flat. This spreading will undermine the selectivity of products, (d) Ground-state wavefunction at t = 1200 a.u., after the second pulse. The poor selectivity of products is apparent. 

We have applied these ideas to the case described in Figs. 24 and 25, where wavepacket spreading on the broad, anharmonic, excited-state potential energy surface destroys the selectivity. A square pulse was used for... 

Figures 37a and 37b show the wavefunction on the excited state potential surface at t = 200 a.u. and 400 a.u without the locking pulse. Figures 37c and lid show the wavefunction at the corresponding times with the locking pulse. The motion of the center of the wavepacket is greatly reduced. More important, with respect to selectivity, there is almost no wavepacket spreading. This example suggests that strong fields may be used in conjunction with the carefully tailored waveforms we have described above to achieve selectivity of reaction.

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