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The Journal of Chemical Physics

Adapting optimal control theory and using learning loops to provide experimentally feasible shaping mask patterns

Thomas Hornung, Marcus Motzkus, Regina de Vivie‐Riedle

Published Aug 15, 2001• 65 citations
Publisher

Abstract

In this article we present two algorithms that provide optimal control pulses directly applicable in experiment. These are, namely, the optimal control algorithm, in which we incorporated spectral pressure during optimization, and complementarily a theoretical variant of the learning loop based on an evolutionary algorithm. With these tools a productive dialog between theory and experiments on optimal control is imaginable. The implementation of these pulses is assured by calculating the optimal mask pattern, that serves as an interface between theory and experiment.

DOI
10.1063/1.1378817

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In this article we present two algorithms that provide optimal control pulses directly applicable in experiment. These are, namely, the optimal control algorithm, in which we incorporated spectral pressure during optimization, and complementarily a theoretical variant of the learning loop based on an evolutionary algorithm. With these tools a productive dialog between theory and experiments on optimal control is imaginable. The implementation of these pulses is assured by calculating the optimal mask pattern, that serves as an interface between theory and experiment.
We report a good agreement between the shapes of tailored pulses obtained theoretically and experimentally by using the optimal-control theory and the closed-loop learning technique to maximize the ionization yield in NaK. The theoretical pulse shapes are found to be robust regarding the choice of the initial guess. We assign the leading features of the pulse shapes to processes underlying the optimal control and reveal the mechanism which involves an electronic transition followed by a direct two-photon process and sequential one-photon processes at later times. We show that the optimal control not only serves for maximizing the desired yield but also as a tool for the analysis and the identification of the responsible processes.
Optimal control of complex quantum systems in theory and experiment is the focus of this thesis. The theoretical aspect of our work was concerned with the development of algorithms that are capable of precisely tailoring the shapes of control pulses to meet various control goals while respecting all physical constraints, both fundamental and problem specific. Having these effective tools at hand, we computed control inputs for a range of physical systems using simulation-based time propagation. We extended the dressed chopped random basis (dCRAB) optimization method, previously developed in our group, such that boundary conditions and other constraints that arise from experimental setups of quantum systems can be regarded. Therefore, we wrote a software suite that enables experimentalists to improve their control pulses by directly interfacing the lab with our control algorithm.
Optimization of quantum systems by closed-loop adaptive pulse shaping offers a rich domain for the development and application of specialized evolutionary algorithms. Derandomized evolution strategies (DESs) are presented here as a robust class of optimizers for experimental quantum control. The combination of stochastic and quasi-local search embodied by these algorithms is especially amenable to the inherent topology of quantum control landscapes. Implementation of DES in the laboratory results in efficiency gains of up to $\ensuremath{\sim}9$ times that of the standard genetic algorithm, and thus is a promising tool for optimization of unstable or fragile systems. The statistical learning upon which these algorithms are predicated also provide the means for obtaining a control problem's Hessian matrix with no additional experimental overhead. The forced optimal covariance adaptive learning (FOCAL) method is introduced to enable retrieval of the Hessian matrix, which can reveal information about the landscape's local structure and dynamic mechanism. Exploitation of such algorithms in quantum control experiments should enhance their efficiency and provide additional fundamental insights.
The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse-shaping experiments allow us to coherently control product ratios of chemical reactions. The theoretical design of the laser pulse to transfer an initial state to a given final state can be achieved with the help of quantum optimal control theory (QOCT). This tutorial provides an introduction to QOCT. It shows how the control equations defining such an optimal pulse follow from the variation of a properly defined functional. We explain the most successful schemes to solve these control equations and show how to incorporate additional constraints in the pulse design. The algorithms are then applied to simple quantum systems and the obtained pulses are analysed. Besides the traditional final-time control methods, the tutorial also presents an algorithm and an example to handle time-dependent control targets.
Optimal control theory (OCT) has wide applicability in the quest for seeking optimal laser pulses in coherent control of quantum phenomena. We have revised OCT making it possible to distill robust electric fields realizable via femtosecond pulse-shaping technology. The simple pulse structures offer direct physical insight into the control mechanism and selectively isolate the most stable pathways involving only few frequencies. Moreover, a generalized functional makes a vital extension in including the laser system used in control experiments.