Potential energy surface pulse sequence

Figure 8. (a) Pulse sequence resulting from optimization of the control field to generate H in the same reaction as studied in Fig. 6. (6) The Husimi transform of the pulse sequence shown in (a). (c) Time dependence of the norms of the ground-state and excited-state populations as a result of application of the pulse sequence shown in (a). Absolute value of the ground-state wave function at 1500 au (37.5 fs) propagated under the pulse sequence shown in (a), shown superposed on a contour diagram of the ground-state potential energy surface. (From D. J. Tannor and Y. Jin, in Mode Selective Chemistry, B. Pullman, J. Jortner, and R. D. Levine, Eds. Kluwer, Dordrecht, 1991.)...

An additional result that emerges from our study concerns the extent to which wavepacket control is possible using coherent pulse sequences. In a two-level system one can exchange the phases of the two levels with a 7t pulse and, in effect, achieve time reversal of the state of the system. In a multilevel system the extent of control is much more restricted. The center of the wavepacket evolves according to the Franck-Condon principle and Hamilton s equations of motion, which in turn are dictated by nature s potential energy surfaces. What can be controlled by the experimenter is the instant at which the wavepacket changes surfaces. This concept forms the basis for a scheme for controlling the selectivity of a reaction,24,25 which we discuss in the next section. 

Figures 33a-33c show the swarm on the excited-state potential energy surface, for the same pulse sequence as Fig. 29 (second pulse at 610 a.u.). The swarm mimics closely the quantum wavepacket, including the sequence of contraction and spreading. Figures 33d-33/ shows the swarm on the ground-state potential energy surface, after the second pulse. Those trajectories that do exit do so from channel 2.

Ultrafast spectroscopies have opened the door not only to understand early time dynamics of the intrinsically fast processes but also to control the outcome of the reaction in real time [59, 60]. Quantum control necessarily relies on very detailed a priori knowledge of the potential energy surface and dynamics of the system for designing pulse shapes and pulse sequences that wiU ultimately promote the molecules into the desired reaction path with minimal energy losses. 

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