Coherent control using quantum interference

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  

In order for these two chaimels to be coherent with respect to each other, that is, to be capable of interfering under CW-laser excitation conditions, it is necessary to use a coherent electromagnetic field of frequency a i2 to prepare a superposition state on the ground-state surface. Two additional laser fields of frequencies cui and o 2 are then used to raise the superposition state to the surfaces of the excited energetically degenerate state.  

Experiments with HCl (Park et al. 1991) have confirmed the predictions of coherent-control theory, particularly the sinusoidal dependence of the ionization rate on the relative phases of the two exciting lasers, as well as the dependence of the degree of sinusoidal modulation of the ionization cinrent on the relative laser field intensities. This technique was also used in experiments on controlfing the product ratio in the photodissociation of HI (Zhu et al. 1995) and the branching ratio in the photodissociation of Na2 (Shnitman et al. 1996). 

Although the demonstration of this technique was a success, its efficiency is limited because CW lasers interact only with a small part of the thermal distribution of the molecules. The decay of the coherence of the molecules and radiation limits the amount of energy that can be used effectively for control pm poses, because such coherence is a must for stable quantmn wave interference. In this regard, the two-femtosecond-pulse approach (Section 12.2) seems to be more effective, especially when used in combination with optimally shaped electromagnetic fields. Optimal control of the shape of the laser pulses used can provide effective excitation of the desired final quantum mechanical state. 

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Two main approaches to the control of molecules using wave interference in quantum systems have been proposed and developed in different languages . The first approach (Tannor and Rice 1985 Tannor et al. 1986) uses pairs of ultrashort coherent pulses to manipulate quantum mechanical wave packets in excited electronic states of molecules. These laser pulses are shorter than the coherence lifetime and the inverse rate of the vibrational-energy redistribution in molecules. An ultrashort pulse excites vibrational wave packets, which evolve freely until the desired spacing of the excited molecular bond is reached at some specified instant of time on a subpicosecond timescale. The second approach is based on the wave properties of molecules as quantum systems and uses quantum interference between various photoexcitation pathways (Brumer and Shapiro 1986). Shaped laser pulses can be used to control this interference with a view to achieving the necessary final quantum state of the molecule. The probability of production of the necessary excited quantum state and the required final product depends, for example, on the phase difference between two CW lasers. Both these methods are based on the existence of multiple interfering pathways from the initial... 

Other possible choices are to use two pairs of frequencies which together have the same energies. The key point is that quantum interference between the two pathways can be used to control the branching ratio. This coherent-control approach is very general and can be used in virtually any branch of molecular dynamics, including scattering and photo-dissociation. 

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. 

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. 

The research of Paul Brumer and his colleagues addresses several fundamental problems in theoretical chemical physics. These include studies of the control of molecular dynamics with lasers.98 In particular, the group has demonstrated that quantum interference effects can be used to control the motion of molecules, opening up a vast new area of research. For example, one can alter the rate and yield of production of desirable molecules in chemical reactions, alter the direction of motion of electrons in semiconductors, and change the refractive indices of materials etc. by creating and manipulating quantum interferences. In essence, this approach, called coherent control, provides a method for manipulating chemistry at its most fundamental level.99... 

Equation (7.75) defines what is meant by a so-called coherent sum of quantum states. The diagonal terms resemble the incoherent sum in Eq. (7.74) the values of the populations cn 2 are, however, determined by the laser pulse. The off-diagonal terms are called interference terms these terms are the key to quantum control. They are time dependent and we use the term coherent dynamics for the motion associated with the coherent excitation of quantum states. A particular simple form of Eq. (7.75) is obtained in the special case of two states. Then... 

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,... 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

The possibility to use laser radiations to achieve the so-called "coherent control" of molecular dissociation or of atomic photoionization has been predicted since the advent of laser sources in the early sixties. It was expected that, thanks to the coherence and monochromaticity properties of the laser light, one could selectively choose a dissociation channel and the spatial orientation of ejection of the fragments (either ions or electrons or even neutrals) in an elementary chemical process. However, earlier attempts, based on simple photoabsorption processes, have been unsuccessful and it is only recentiy that experiments have been shown to enable one to achieve such a goal in some selected systems. Amongst the various scenarios which have been explored, one of the most promising is based on the realization of quantum interferences in so-called "two-colour" photodissociation or... 

The first example is a three-level A-type system coupled by bichromatic coupling and probe fields, which opens two Raman transition channels [60]. The phase dependent interference between the resonant two-photon Raman transitions depends on the relative phases of the laser fields either constructive interference or destructive interference between the two Raman channels can be obtained by controlling the laser phases. The second example is a four-level system coupled by two coupling fields and two probe fields, in which a double-ElT configuration is created by the phase-dependent interference between the three-photon and one-photon excitation processes, or equivalently two independent Raman transition channels [58,62]. We will provide theoretical analyses of the phase dependent quantum interference in the two multi-level atomic systems and present experimental results obtained with cold Rb atoms. The two systems provide basic platforms to study coherent atom-photon interactions and quantum state manipulations, and to explore useful applications of the phase-dependent interference in the multi-level atomic systems. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

The conceptual framework underlying the control of the selectivity of product formation in a chemical reaction using ultrashort pulses rests on the proper choice of the time duration and the delay between the pump and the probe (or dump) step or/and their phase, which is based on the exploitation of the coherence properties of the laser radiation due to quantum mechanical interference effects [56, 57, 59, 60, 271]. During the genesis of this field. 

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