In this paper, we review our recent progress in theoretical studies of quantum control of chemical reactions. Coherent interaction between the reaction system and applied laser fields is utilized to maximize the yield of a desired product (a target state). We have developed several kinds of effective theoretical methods for designing optimized ultrashort pulses for a desired reaction. One kind of control method is based on the control theory of a linearly time-invariant (LTI) system, by which the total population of the nontarget states and the total energies of the laser fields are minimized. This procedure is carried out at each successive short stage (local optimization theory), in which the time-dependent Schrödinger equation can be approximated to the equation of motion of the LTI system. Another control method is based on a tracking problem. A given trace in the tracking problem is introduced in an objective function of the quantum control. We have also developed a method using classical mechanics that provides a guiding principle for the control of a multidimensional molecular system. These methods based on local optimization theory can generate a wide variety of pulses ranging from weak field cases to strong field cases. In our treatment, π- and chirped pulses are obtained a priori as examples of optimized pulses. These methods have been applied to control of nuclear motions on adiabatic or diabatic potential surfaces. In addition to quantum control of typical unimolecular reactions such as isomerization, predissociation of NaI and enantiomer selective preparation, we present applications to orientation of molecules and population transfer to dark states (i.e., control of intramolecular vibrational energy redistribution). Control of orientation of molecules is a prerequisite for enantiomer selective preparation. Electronic dynamics of molecules in intense laser fields such as intramolecular electron transfer on an attosecond time scale is next discussed in order to extend our methods to novel control scenarios of chemical reactions by ultrafast manipulation of electronic motions. We have developed an efficient grid point method for accurately solving the time-dependent Schrödinger equation for the electronic degrees of freedom of a molecule. This fundamental numerical tool which extends the molecular orbital description enables us to clarify the mechanisms of intense-field-electronic dynamics such as tunnel ionization and Coulomb explosions of molecules. We present applications of this method to H 2 + and H 2 in high-intensity and electronically nonresonant low-frequency fields (I > 10 13 W cm -2 and λ > 700 nm). For H 2, it has been revealed for the first time that the two localized ionic states, H -H + and H +H -, are alternately created according to the laser cycle. Such an intramolecular electronic motion induces nuclear motions (e.g., bond stretching). Possible new control schemes of electronic and nuclear dynamics utilizing electron-electron and electron-nucleus correlations are finally proposed.
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