Photodissociation from a Superposition State

Assuming that em 1 =0, (e.g., the two states belong to different electronic states), it follows from Eq. (3.2) that in the long-time limit 

It follows from Eq. (2.3) (extended to continuum states) and Eq. (2,10) that we can write, in complete generality, that 

the branching ratios at a fixed energy E are independent of the laser power and pulse shape. This result, which coincides with that of perturbation theory, holds true -aslong as there is only one initial state IE)) that is excited to the continuum. 

This argument motivates the idea that the way to control photodissociation is to eii e more than one initial state, or in greater generality, to use multiple excitation pathways. In this chapter we demonstrate that such a strategy allows us to actively /rtipijence and control which photodissociation product is formed. These ideas, which firbduce the notion of coherent control, will be later shown to hold true for any lical process, not just for photodissociation. 

Of particular interest is the probability of being in a complete subspace of state denoted by the label q that is, all m associated with a fixed q, where n = (m, q). greatest concern in chemistry is the case where q labels the chemical identity (i the arrangement channel) of the product of a chemical reaction hence below often explicitly refer to q in this manner. However, it should be clear that the th applies to any other q chosen from the set of n quantum numbers. 

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We have elucidated the nature of pulsed-shaping control of photodissociation from the viewpoint of energy-resolved coherent control theory. Clearly, when excitation is from a superposition of states, as in the vast majority of control scenarios, the role of the pulse shaping is to enhance a different set of interfering pathways for each control objective. 

Control over the a, and production of the desired superposition states can be achieved by several routes. One nice way is to utilize the reactants from an earlier photodissociation step, altering the af by any of a number of coherent control scenarios [2] for this piereactive step. Consider then preparing n, 0) via a prereactive stage in which an adduct AB, made up of a structureless atom A and the molecular fragment B, is photodissociated. The AB is assumed to be initially in a pure state of energy Eg and the photodissociation is carried out with a coherent source. Under these circumstances photodissociation produces B in a linear combination of internal states. For... 

Figure 5.3 Contour plot of I yield [I /(I + I )] for two color photodissociation of a fi CH3I superposition state composed of bound states with vibrational and rotational qua numbers (v, J) — (0, 2) and (1,2) excited with frequencies a>1 = 41,579 cm-1 and 1 41,163 cm-1. Contours increase, in increments of 0.04 from the center well . (Taken Fig. 1, Ref [175].)...

Figure 4 Contour plot of the yield of a quantum state of the products m me photodissociation of CH3 I from a linear superposition of lEj > and IE3 >, to yield I + a) v=3, or b) v=4. The labelling of the abscissa and ordinate is as i Fig. 3...

Easy availability of ultrafast high intensity lasers has fuelled the dream of their use as molecular scissors to cleave selected bonds (1-3). Theoretical approaches to laser assisted control of chemical reactions have kept pace and demonstrated remarkable success (4,5) with experimental results (6-9) buttressing the theoretical claims. The different tablished theoretical approaches to control have been reviewed recently (10). While the focus of these theoretical approaches has been on field design, the photodissociation yield has also been found to be extremely sensitive to the initial vibrational state from which photolysis is induced and results for (11), HI (12,13), HCl (14) and HOD (2,3,15,16) reveal a crucial role for the initial state of the system in product selectivity and enhancement. This critical dependence on initial vibrational state indicates that a suitably optimized linear superposition of the field free vibrational states may be another route to selective control of photodissociation. 

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