Quantum control of nuclear wave packets by locally designed optimal pulses

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Abstract
A new approach to locally design a control pulse is proposed. This locally optimized control pulse is explicitly derived, starting with optimal control formalism, and satisfies the necessary condition for a solution to the optimal control problem. Our method requires a known function, g(t), a priori, which gives one of the possible paths within the functional space of the objective functional. A special choice of g(t)≡0 reduces the expression of the control pulse to that derived by Kosloff et al. For numerical application, we restrict ourselves to this special case; however, by combining an appropriate choice of the target operator together with the backward time-propagation technique, we apply the local control method to population inversion and to wave packet shaping. As an illustrative example, we adopt a two-electronic-surface model with displaced harmonic potentials and that with displaced Morse potentials. It is shown that our scheme successfully controls the wave packet dynamics and that it can be a convenient alternative to the optimal control method for wave packet shaping.