Tannor-Rice control scheme

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. 

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 ... 

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. 

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. 

Other prominent examples are theoretical proposals for different optical control schemes using laser field parameters for the manipulation of ultrafast process pioneered by Rice and Tannor, Shapiro and Brumer, and Peirce, Dahleh, and Rabitz [2, 56-61]. They stimulated control experiments that were carried out first on simple systems such as metallic dimers and trimers [62-84], and later on more complex systems [23-25, 43, 85-89], confirming theoretically proposed concepts. Since tailored laser pulses have the ability to select pathways that optimally lead to the chosen target, their analysis should allow one to determine the mechanism of the processes and to provide the information about the selected pathways (inversion problem). Therefore, theoretical approaches are needed, which are capable of designing interpretable optimal laser pulses for complex systems (e.g., clusters or biomolecules) by establishing the connection between the underlying dynamical processes and their shapes. In this case, the optimal control can be used as a tool for the analysis. 

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

In this chapter we review our recent applications of a local control scheme to various problems in chemical physics. The approach we follow is called Local Control Theory (LCT). The idea first appeared in the formulation of Optimal Control Theory introduced by Kosloff, Rice, and Tannor [42] and has been... 

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. 

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. 

Experimentally, 50 femtosecond pulses may not be easily obtainable. Table X therefore gives the results of quantum mechanical wavepacket calculations for pulses of various temporal widths, but with a constant pulse energy. Note that as the pulse width increases, the yield in the dissociation window only decreases slightly. However, the yield in the nondissociation window increases dramatically, resulting in a reduced contrast ratio. For 120 femtosecond pulses, the contrast has dropped to 17, which probably represents the limit of detection for the window pattern. Our net conclusion, then, is that pulses shorter than 120 femtoseconds should be adequate to resolve the windows, and thereby demonstrate the principle underlying the Tannor-Rice scheme for controlling the product formation in a photoinduced reaction. 

The second example is the quadratically chirped pump-dump scheme. Since the pioneering work by Tannor and Rice [119], the pump-dump method has been widely used to control various processes. However, since it is not possible to transfer a wave packet from one potential energy surface to another nearly completely by using the ordinary transform limited or linear chirped pulses, the... 

A beautiful experiment demonstrating coherent control in the sense of the Tannor-Kosloff-Rice scheme was carried out by Baumert et al. [17] using resonant three-photon ionization and fragmentation of Na2. 

For a three-photon and a two-photon process we have shown that vibrational wavepacket propagation excited by an ultrashort laser pulse can be used to drive a molecule to a nuclear configuration where the desired product formation by a second probe pulse is favored (Tannor-Kosloff-Rice scheme). In both cases the relative fragmentation and ionization yield of Na2 was controlled as a function of pump-probe delay. By varying the delay between pump and probe pulses very slowly and therefore controlling the phase relation between the two pulses, additional interference effects could be detected. 

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