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The Journal of Chemical Physics

On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system

Samuel H. Tersigni, Pierre Gaspard, Stuart A. Rice

Published Aug 1, 1990• 120 citations
Publisher

Abstract

A previously reported method for shaping electromagnetic field pulses to achieve chemical selectivity is extended and applied to a simple multiple level model system. The pulse shaping approach is based on optimal control theory, where both the time-dependent Schrödinger equation and the constant pulse energy are used as constraints on the variational scheme. A conjugate gradient direction method is used to direct the convergence of the iterative process used to calculate the optimum pulse shape. The method is applied to a five-level system interacting with an optical (laser) field. Results demonstrating selectivity and stability are compared to those of other recent related investigations.

DOI
10.1063/1.459680

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A previously reported method for shaping electromagnetic field pulses to achieve chemical selectivity is extended and applied to a simple multiple level model system. The pulse shaping approach is based on optimal control theory, where both the time-dependent Schrödinger equation and the constant pulse energy are used as constraints on the variational scheme. A conjugate gradient direction method is used to direct the convergence of the iterative process used to calculate the optimum pulse shape. The method is applied to a five-level system interacting with an optical (laser) field. Results demonstrating selectivity and stability are compared to those of other recent related investigations.
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.
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We theoretically investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose, a perturbative model for light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85 Rb 2 molecules in a magneto-optical trap. We find that optimized pulse shapes may maximize the formation of ground state molecules in a specific vibrational state at a pump-dump delay time for which unshaped pulses lead to a minimum of the formation rate. Compared to the maximum formation rate obtained for unshaped pulses at the optimum pump-dump delay, the optimized pulses lead to a significant improvement of about 40% for the target level population. Since our model yields the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments.
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