Quantum control of reaction dynamics in multi-dimensional systems

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Recently there have been considerable efforts in quantum control of chemical reaction dynamics. Various theoretical treatments based on optimal or local control theory and on perturbative or nonperturbative methods have been developed for designing laser pulses to manipulate nuclear wave packets to the desired target under consideration. Most of the existing theoretical treatments cannot treat multi-dimensional reaction systems. The purpose in this project was to develop control theory applicable to such a multi-dimensional system.From the general viewpoint of chemical reaction dynamics, the process of a reaction is described in terms of a representative point that moves from a reactant to a product over a transition region. It is natural to consider a reaction in quantum control in a similar way ; i.e., quantum control is viewed as a representative point moving on the reaction coordinate in nonstationary laser fields. In this research project, we developed a classical, local control theory for controlling reaction dynamics. The theory is based on a classical mechanical, feedback control method within a local optimization treatment. The classical treatment was extended to control wave packet dynamics by replacing the classical momentum by a quantum mechanically averaged momentum. That is, the controlled field is derived from Hamilton's equation of motion under the constraint of a smaller amount of laser energy. The dynamics, on the other hand, is evaluated by solving the time-dependent Schrodinger equation. We applyed the theory to two-dimensional reaction dynamics of HCN isomerization. We showed that the present control method can design pulses for the isomerization with a high quantum yield.