Optimal control of selectivity of unimolecular reactions via an excited electronic state with designed lasers

A molecular system is steered on the ground electronic surface from the initial state to a desired target state at time T via an excited electronic state by using optimally designed coherent laser fields. A new algorithm based on the SU(2) algebra is developed to solve the time-dependent Schrödinger equation for the systems involving two electronic states with time-dependent Hamiltonians. For the design of optimal fields with restricted functional forms the rotating wave approximation is introduced for significantly reducing the computational effort. As a model of unimolecular reactions, a double-well switching problem is studied. The objective is to move the system from one well to the other. It is found that the unrestricted optimal fields which successfully move the system from one well to the other at the target time T are complicated. The objective is achieved through the cooperative interaction between the system and the driving field. The optimal fields with restricted functional forms, such as a train of Gaussian pulses with a single carrier frequency, can also lead to the satisfactory achievement of the objective. However, except for some propitious cases a simple two-pulse pump-dump scheme does not achieve the control objective satisfactorily. Possible further potential applications are discussed briefly.