Tannor-Rice

Figure Al.6.30. (a) Two pulse sequence used in the Tannor-Rice pump-dump scheme, (b) The Husuni time-frequency distribution corresponding to the two pump sequence in (a), constmcted by taking the overlap of the pulse sequence with a two-parameter family of Gaussians, characterized by different centres in time and carrier frequency, and plotting the overlap as a fiinction of these two parameters. Note that the Husimi distribution allows one to visualize both the time delay and the frequency offset of pump and dump simultaneously (after [52a]).

S. A. Rice My answer to Prof. Manz is that, as I indicated in my presentation, both the Brumer-Shapiro and the Tannor-Rice control schemes have been verified experimentally. To date, control of the branching ratio in a chemical reaction, or of any other process, by use of temporally and spectrally shaped laser fields has not been experimentally demonstrated. However, since all of the control schemes are based on the fundamental principles of quantum mechanics, it would be very strange (and disturbing) if they were not to be verified. This statement is not intended either to demean the experimental difficulties that must be overcome before any verification can be achieved or to imply that verification is unnecessary. Even though the principles of the several proposed control schemes are not in question, the implementation of the analysis of any particular case involves approximations, for example, the neglect of the influence of some states of the molecule on the reaction. Moreover, for lack of sufficient information, our understanding of the robustness of the proposed control schemes to the inevitable uncertainties introduced by, for example, fluctuations in the laser field, is very limited. Certainly, experimental verification of the various control schemes in a variety of cases will be very valuable. 

A more sophisticated version of the Tannor-Rice scheme exploits both amplitude and phase control by pump-dump pulse separation. In this case the second pulse of the sequence, whose phase is locked to that of the first one, creates amplitude in the excited electronic state that is in superposition with the initial, propagated amplitude. The intramolecular superposition of amplitudes is subject to interference whether the interference is constructive or destructive, giving rise to larger or smaller excited-state population for a given delay between pulses, depends on the optical phase difference between the two pulses and on the detailed nature of the evolution of the initial amplitude. Just as for the Brumer-Shapiro scheme, the situation described is analogous to a two-slit experiment. This more sophisticated Tannor-Rice method has been used by Scherer et al. [18] to control the population of a level of I2. The success of this experiment confirms that it is possible to control population flow with interference that is local in time. 

Because of the transparency of interpretation, it is convenient to start with the original Tannor-Rice perturbation theory treatment of control of molecular dynamics. We consider a molecule that can undergo fragmentation to produce two products ... 

In general, the results of the calculations establish that it is possible to guide the reaction to preferentially form one or the other product with high yield. Note that, unlike the original Tannor-Rice pump-dump scheme, in which the pulse sequences that favor the different products have different temporal separations, the complex optimal pulses occupy about the same time window. Indeed, the optimal pulse shape that generates one product is very crudely like a two-pulse sequence, which suggests that the mechanism of the enhancement of product formation in this case is that the time delay between the pulses is such that the wavepacket on the excited-state... 

We call the reader s attention to the similarity between Eqs. (4.17) and (4.5). The result obtained by Wilson and co-workers is more general that the Tannor-Rice result in that the latter calculates the field that maximizes the product yield for a pump pulse with given shape whereas the former makes no restriction concerning the shape of the pump pulse and does not assume that the pump and dump pulses can be distinguished from one another. 

My question to Prof. B. Kohler (as representative of the group of K. R. Wilson) is whether he would agree with S. A. Rice s classification that puts the technique of K. R. Wilson et al. [8] into strategy (ii) What are the fundamental analogies and what are the differences between their approach [8] and the Tannor-Rice-Kosloff-Rabitz approach (see Refs. 2 and 3 and current chapter) Finally, I should like to point to another strategy (iii) of laser control by vibrationally mediated chemistry that is achieved by IR + UV continuous-wave (CW) multiphoton transitions (see the pioneering papers by Letokhov [9] and sequel theoretical developments [10] and experimental applications [11]). 

Prof. S. A. Rice has pointed to another experimental verification of the Tannor-Rice-Kosloff scheme, carried out by Prof. G. R. Fleming. I would like to ask Prof. Fleming whether he could explain to us his experiment, that is, how are the two pump and control laser pulses used to control the branching ratio of competing chemical products ... 

D. J. Tannor I would like to point out that the Scherer-Fleming wavepacket interferometry experiment is very different from the Tannor-Rice pump-dump scheme, in that it exploits optical phase coherence of the laser light (optical phase coherence translates into electronic phase coherence between the wavepackets on different potential surfaces). However, there was a paragraph in the first paper of Tannor and Rice [7. Chem. Phys. 83, 5013 (1985), paragraph above Eq. (11)] that did in fact discuss the role of optical phase and suggested the possibility of experiments of the type performed by Scherer and Fleming. 

An intuitive method for controlling the motion of a wave packet is to use a pair of pump-probe laser pulses, as shown in Fig. 13. This method is called the pump-dump control scenario, in which the probe is a controlling pulse that is used to create a desired product of a chemical reaction. The controlling pulse is applied to the system just at the time when the wave packet on the excited state potential energy surface has propagated to the position of the desired reaction product on the ground state surface. In this scenario the control parameter is the delay time r. This type of control scheme is sometimes referred to as the Tannor-Rice model. 

PUMP-DUMP EXCITATION WITH MANY LEVELS TANNOR-RICE SCHEME... 

The initial experiment demonstrating control in accordance with the Tannor-Rice scenario is due to Gerber and co-workers [107, 108] in which control was demonstrated over the two-channel ionization ... 

Potential energy surfaces and excitation scheme involved in Tannor-Rice Oiled Na2 ionization. (Taken from Fig. 3, Ref. [108].)... 

A number of other early experiments confirming the Tannor-Rice scenario are discussed in detail in the monograph of Rice and Zhao [105], i... 

Figure 36 summarizes the relationship between the Tannor-Rice, Holme-Hutchinson, and Brumer-Shapiro schemes for control of photochemical products. 

Figure 36. Comparison of Tannor-Rice, Holme-Hutchinson. and Brumer-Shapiro selectivity schemes, (a) Tannor-Rice scheme uses two pulses, where each pulse is wide enough in frequency to excite a superposition of many vibrational levels, (h) Holme-Hutchinson scheme uses two monochromatic photons to prepare a superposition state on the excited-state surface (c) Brumer-Shapiro scheme uses one photon to prepare a superposition state on the ground-state surface then two additional photons to excite the superposition state to the excited state surface. 

An experiment on the Na2 molecule by Baumert and Gerber (1994) illustrates the Tannor-Rice scheme. A pair of ultrashort (70-110 fs) laser pulses is used to excite selectively either the... 

As the final topic in this paper we consider the use of a van der Waals molecule fragmentation reaction to test ideas concerning the active control of product formation. Specifically, we examine how the fundamental idea underlying the Tannor-Rice ° scheme can be tested. 

Once the conceptual features of the Tannor-Rice scheme are grasped, modifications of the methodology that enhance product selectivity are readily suggested. One such modification takes... 

Dr. Roger Carlson has suggested an approach to testing the key concepts of the the Tannor-Rice scheme which is simpler, both conceptually and experimentally, than the alteration of product yields in the photofragmentation of a triatomic molecule. In the experiment suggested,a diatomic molecule is subjected to a femtosecond duration pump-dump pulse sequence. Since there is only one reaction coordinate, product selectivity can not be achieved. However, the delay between pulses can still be used to control the kinetic energy of the final wavepacket one should be able to switch the dissociation on and off as a function of delay. 

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