Robust optimal control of quantum molecular systems in the presence of disturbances and uncertainties

Recently, systematic optimal control theory has been successfully applied to design optical fields which act on a molecule to guide or transform it into a specifically prescribed state. Under realistic laboratory conditions and for real molecules, it is inevitable that there will exist disturbances and uncertainties in the control optical field, in the molecular Hamiltonian, and in the field-coupling coefficient (e.g., the dipole moment), etc. Therefore, it is important to design an optimal field which is robust to disturbances. In this paper, we provide a method through which the worst possible disturbance to the control process, under certain possible constraints, can be calculated and a corresponding optimal control field designed to be robust to the disturbances. Under disturbances of small amplitude, a perturbation solution to this problem can be applied. Illustrations are given for control of the wave-packet evolution of a diatomic molecule in the presence of disturbances.