Coherent Control of Chemical Reactions

Abstract

The traditional goals of chemical kinetics are to measure the rates of chemical reactions and to understand their mechanisms on a molecular level. With the advent of lasers and molecular beams, it has become possible to study the reactions of molecules in individual quantum states and to explain their behavior in terms of single collisions governed by well-defined potential energy surfaces. Likewise, numerical methods have been refined to the point that it is possible to predict diverse properties of elementary reactions from first principles. In recent years, the challenge has shifted from measuring and calculating rates of reactions to devising methods of controlling their outcome. The idea of controlling the yield and product distribution of a reaction is, of course, a very old one. The field of catalysis, for example, is devoted to finding means of enhancing the natural yield of a reaction. Similarly, temperature and pressure have been used for decades in the chemical industry to alter reaction rates. With the development of narrow-band lasers, it has become possible to excite selectively a single molecular mode. Provided energy transfer is slow as compared to reaction, such mode-selective preparation of a molecule can be used to alter the outcome of its reaction.1-3 For example, if the OH bond in HOD is vibrationally excited, that bond becomes more reactive, and collisions with Cl atoms preferentially yield HCl rather than DCl.4 A more general, photochemical method for altering reaction pathways exploits the phase property of lasers and has become known as coherent control, or phase control.5 Two main schemes of coherently controlling physical and chemical processes have been developed over the past decade, based on similar concepts but differing in the properties of the electromagnetic fields that are used. The first, introduced by Tannor and Rice,6 uses an ultrashort pulse of laser light to create a coherent superposition of energy-resolved eigenstates, namely, a wave packet. Such carefully phased superposition states are, in general, nonstationary. By altering the amplitudes and phases of the light pulses, it is possible to modify the content of the superposition state and thus control the motion of the wave packet. Typically, a vibrational or electronic wave packet is generated at time t ) 0 by a short laser pulse. At some later time, when the wave packet has evolved to a desired configuration, a second pulse triggers the reaction. An experimental example of this method is control of the electronic branching ratio of Na atoms in the photodissociation of NaI, which was achieved by varying the timing between two transform-limited ultrashort pulses.7 Optimal control theory, introduced by Rabitz and co-workers8 and subsequently developed by several groups,5 employs a feedback loop to optimize the spectral content and temporal shape of a pulse in order to maximize the yield of a given product. Experimental demonstrations of the control of branching ratios by means of optimally tailored laser pulses were reported by Bardeen et al.9 and by Assion et al.10 The use of the intensity property of short pulses to control reactions was also reported.11 A second method was introduced by Brumer and Shapiro12 and is the subject of the present paper. In this approach, two long laser pulses (in principle, they could be continuous beams) excite an atom or a molecule from an initial state to a final state. The frequencies of the lasers are chosen so that the target absorbs either m photons from the first laser or n photons from the second laser to reach the same final state.13 That is, the laser frequencies satisfy the relation mωm ) nωn. An important property of the laser beams is that they have a well-defined phase relation; that is, the phases of the two electromagnetic fields differ by a controllable amount, φ. As we will show, by varying the relative phase of the two beams, it is possible to control the branching ratio of the reaction. It is useful to think of the latter method as an analog of Young’s two-slit experiment.14 In that experiment, particles emerging from two slits create a pattern on a screen. If only one slit is open, the result is a diffraction pattern produced by that slit. If both slits are open, Robert J. Gordon obtained his doctorate from Dudley Herschbach at Harvard University in 1970. After postdoctoral studies at Caltech and the Naval Research Laboratory, he came to the University of Illinois at Chicago, where he is a professor of chemistry. Prof. Gordon’s research interests include experimental studies of the spectroscopy and reaction dynamics of small molecules.