Perturbative formulation of optimal control for two-photon transitions: Reduction to an eigenvalue problem

An alternative perturbative formulation is introduced to reduce the task of designing optimal controls of molecular motion. The method provides multiple optimal control fields as eigenvectors corresponding to the positive eigenvalues of a matrix {A(mn)}. Analytical equations for the matrix elements A(mn) are derived. Numerical examples are given for simple three- and four-state molecular systems. The method is shown to be computationally simple and efficient in providing good quality control results.