Principle of Coherent Control

Note that the entire theory needs to be modified only slightly to accommodate control of scattering into different angles, that is, the differential cross section, into channel q. A specific example of this type of control is discussed in Section 3.4 where we apply this approach to manipulating electric currents in semiconductors. 

Control of the type discussed above, in which quantum interference effects are used to constructively or destructively alter product properties, is called coherent control (CC). Photodissociation of a superposition state, the scenario described above, will be seen to be just one particular implementation of a general principle of coherent control Coherently driving a state with phase coherence through multiple, coherent, 

Rlfcifial lities on the control parameters can be easily generated experimentally jjlpipiig the molecular terms are determined from a fit of the control expression to small number of experimentally determined yields. 

Another important example of coherent control introduces the possibility of quan- turn interference that arises through competitive optical routes in the excitation of a single bound state to an energy E. Specifically, we consider the photodissociation of a single state via two simultaneous pathways, an TV-photon and an M-photon disso- ciation route. As will become evident in our discussion of selection rules (Section 3,3.2), the N vs. M scenarios are of two types, N and M of the same parity (e.g., both N and M odd or both even) or of opposite parity (one of N, M being odd and ] the other being even). The latter allows for control over the photodissociation differ- ] 

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The essential principle of coherent control in the continuum is to create a linear superposition of degenerate continuum eigenstates out of which the desired process (e.g., dissociation) occurs. If one can alter the coefficients a of the superposition at will, then the probabilities of processes, which derive from squares of amplitudes, will display an interference term whose magnitude depends upon the a,. Thus, varying the coefficients a, allows control over the product properties via quantum interference. This strategy forms the basis for coherent control scenarios in which multiple optical excitation routes are used to dissociate a molecule. It is important to emphasize that interference effects relevant for control over product distributions arise only from energetically degenerate states [7], a feature that is central to the discussion below. 

Chapter 3 provided an introduction to the principles of coherent control and included a number of examples of scenarios that embody that principle. In this chapter we consider several other scenarios that both shed further light on these principles and that suggest a number of useful experimental scenarios. 

The general principle of coherent control based on quantum interference between various photoexcitation pathways, including CW-laser weak excitation, is illustrated in Fig. 12.4. This quantum interference can be constructive or destructive, which allows control of the final state, that is, the control of a given reaction product. As an explicit example, Brumer and Shapiro (1986) have considered the process of photodissociation of methyl iodide, where the following two product channels are possible at an excitation energy of E ... 

The concept of coherent control, which we have developed with isolated molecules in the gas phase, is universal and should apply to condensed matter as well. We anticipate that the coherent control of wave functions delocalized over many particles in solids or liquids will be a useful tool to track the temporal evolution of the delocalized wave function modulated by many-body interactions with other particles surrounding itself. We may find a clue to better understand the quantum-classical boundary by observing such dynamical evolution of wave functions of condensed matter. In the condensed phase, however, the coherence lifetime is in principle much shorter than in the gas phase, and the coherent control is more difficult accordingly. In this section, we show our recent efforts to develop the coherent control of condensed matter. 

In this article we approach the topic of coherent control from the perspective of a chemist who wishes to maximize the yield of a particular product of a chemical reaction. The traditional approach to this problem is to utilize the principles of thermodynamics and kinetics to shift the equilibrium and increase the speed of a reaction, perhaps using a catalyst to increase the yield. Powerful as these methods are, however, they have inherent limitations. They are not useful, for example, if one wishes to produce molecules in a single quantum state or aligned along some spatial axis. Even for bulk samples averaged over many quantum states, conventional methods may be ineffective in maximizing the yield of a minor side product. 

The underlying principle of coherent phase control is that the probability of an event occurring is given by the square of the sum of the quantum mechanical amplitudes... 

A whole chapter is devoted to time-resolved spectroscopy including the generation and detection of ultrashort light pulses. The principles of coherent spectroscopy, which have found widespread applications, are covered in a separate chapter. The combination of laser spectroscopy and collision physics, which has given new impetus to the study and control of chemical reactions, has deserved an extra chapter. In addition, more space has been given to optical cooling and trapping of atoms and ions. 

Only much later it was realized that the excellent coherence of laser light offers another, maybe much more powerful control parameter, which allows us to make use of quantum mechanical interference. This principle forms the basis of what is today generally referred to as coherent control. 

Despite the expectations raised with any new scheme for coherent control, their experimental realizations have so far (like the theoretical models) been widely limited to simple molecules or even atoms. Nevertheless, the feasibility of most schemes could be demonstrated in the laboratory. The picture that presents itself is therefore encouraging in principle even though for practical applications a lot of work remains to be done. It is the inten-... 

In principle, the coherent background can be supplied as shown in Fig. 2a, where the reference beam is directed along the diffracted beam. The phase of the reference is directly controlled by means of a piezo-mounted mirror. 

The numerator and denominator of Eq. (3.54) each display the canonical form for coherent control, that is, a form similar to Eq. (3.19) in which there are independent contributions from more than one route, modulated by an interference term. Since the interference term is controllable through variation of the (x and 3 — 3 < />,) laboratory parameters, so too is the branching ratio Rqq,(E). Thus, the principle upon which this control scenario is based is the same as that in Section 3.1, but the interference is introduced in an entirely different way. 

In Chapter 1 we introduce the concept of SHE (safety, health and environment) information systems. It will provide a frame of reference in our subsequent analysis of the different tools and methods used in accident control through experience feedback. We make a comparison with the human information processes and identify basic similarities and differences. Chapter 2 gives an overview of different boundary conditions of a SHE information system, both inside and outside a company. Chapter 3 introduces four different approaches in safety practice and describes how these will contribute in subsequent parts of the book to our understanding of how to prevent accidents. In Chapter 4 we will look into a case from the environmental field. It demonstrates a successful application of basic principles of experience feedback in the reduction of emissions from a fertiliser plant. We use this example to present some of the issues dealt with in later parts of the book and demonstrate how they form a coherent whole. 

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