Quantum control of reaction dynamics in multi-dimensional systems

近年来，人们在化学反应动力学的量子控制方面做了大量的工作。各种基于最优或局部控制理论和微扰或非微扰方法的理论处理已经发展用于设计激光脉冲以操纵核波包达到所考虑的期望目标。现有的理论处理大多不能处理多维反应体系。这个项目的目的是发展适用于这种多维系统的控制理论。从化学反应动力学的一般观点来看，反应过程是用一个代表性的点来描述的，这个点经过一个过渡区从反应物转移到生成物。以类似的方式考虑量子控制中的反应是很自然的；也就是说，量子控制被看作是在非定常激光场的反应坐标上运动的一个代表性点。在这个研究项目中，我们发展了一个经典的局部控制理论来控制反应动力学。该理论是基于经典的机械，反馈控制方法在局部优化处理。将经典处理扩展到用量子力学平均动量代替经典动量来控制波包动力学。也就是说，受控场是在较小的激光能量约束下由汉密尔顿运动方程导出的。另一方面，动力学是通过求解时变薛定谔方程来评估的。我们将该理论应用于HCN异构化的二维反应动力学。结果表明，该控制方法可以设计出高量子产率的异构化脉冲。

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.