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Journal of Modern Optics

Multi-objective optimization on alkali dimers

Stefan M. Weber, Franziska Sauer, Mateusz Plewicki, A. Merli, Ludger H. Wöste, Albrecht Lindinger

Published Nov 10, 2007• 6 citations
Publisher

Abstract

We present experimental results of a multi-objective evolutionary algorithm that controls the ionization of the NaK molecule and the fragmentation/ionization of potassium dimers. The two physically contradictive goals are dimer ionization and fragmentation into the atomic isotopes. In the NaK case, we use an approach to simplify the usually complex results of feedback-loop coherent control experiments and implement the ‘pulse cleaning’ method. It defines the objective function in a way that unnecessary spectral features are reduced and the most important vibronic transitions are enhanced. This method will be developed in terms of a classical multi-objective optimization and we present some corresponding Pareto-optimal solutions.

DOI
10.1080/09500340701553022

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•May 22, 2018•1 citation
We present experimental results of a multi-objective evolutionary algorithm that controls the ionization of the NaK molecule and the fragmentation/ionization of potassium dimers. The two physically contradictive goals are dimer ionization and fragmentation into the atomic isotopes. In the NaK case, we use an approach to simplify the usually complex results of feedback-loop coherent control experiments and implement the ‘pulse cleaning’ method. It defines the objective function in a way that unnecessary spectral features are reduced and the most important vibronic transitions are enhanced. This method will be developed in terms of a classical multi-objective optimization and we present some corresponding Pareto-optimal solutions.
We have performed transient multi-photon ionization experiments on small alkali clusters of different size in order to probe their wave packet dynamics, structural reorientations, charge transfers and dissociative events in different vibrationally excited electronic states including their ground state. The observed processes were highly dependent on the irradiated pulse parameters like wavelength range or its phase and amplitude; an emphasis to employ a feedback control system for generating the optimum pulse shapes. Their spectral and temporal behavior reflects interesting properties about the investigated system and the irradiated photo-chemical process. First, we present the vibrational dynamics of bound electronically excited states of alkali dimers and trimers. The scheme for observing the wave packet dynamics in the electronic ground state using stimulated Raman-pumping is shown. Since the employed pulse parameters significantly influence the efficiency of the irradiated dynamic pathways photo-induced ioniziation experiments were carried out. The controllability of 3-photon ionization pathways is investigated on the model-like systems NaK and K2. A closed learning loop for adaptive feedback control is used to find the optimal fs pulse shape. Sinusoidal parameterizations of the spectral phase modulation are investigated in regard to the obtained optimal field. By reducing the number of parameters and thereby the complexity of the phase moduation, optimal pulse shapes can be generated that carry fingerprints of the molecule's dynamical properties. This enables to find "understandable" optimal pulse forms and offers the possiblity to gain insight into the photo-induced control process. Characteristic motions of the involved wave packets are proposed to explain the optimized dynamic dissociation pathways.
Selective optimization of the 39,39K2 and 39,41K2 isotopomers in a three-photon ionization process is presented by applying evolution strategies on shaped fs pulses in a feedback loop. The optimizations at different center wavelengths show considerably large enhancements of one isotope compared to the other and reversed. We compare the acquired optimized pulse shapes for combined phase and amplitude with pure amplitude modulation. Particularly from their spectra we are able to extract information about the optimally chosen differing ionization paths via the involved vibrational states. Furthermore, a comparison of the temporal shape of the optimized pulse forms for combined phase and amplitude with pure phase optimization is given. The presented pulse form analysis demonstrates the potential of restricted optimization to gain insight into the underlying dynamical processes. Our approach reveals how the optimization algorithm precisely addresses the vibrational wave functions both spectrally and temporally.
We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.
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.
We report on selective optimization of different isotopes in an ionization process by means of spectrally broad shaped fs-laser pulses. This is demonstrated for (39,39)K2 and (39,41)K2 by applying evolution strategies in a feedback loop, whereby a surprisingly high enhancement of one isotope versus the other and vice versa is achieved (total factor approximately 140). Information about the dynamics on the involved vibrational states is extracted from the optimal pulse shapes, which provides a new spectroscopical approach of yielding distinct frequency pattern on fs-time scales. The method should, in principle, be feasible for all molecules.
How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objective optimization, and the differential evolution genetic algorithm. The goal is to find out how a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process. We work on a simple one-dimensional model of hydrogen-like atoms (the Pöschl-Teller potential) that allows to tune the number of bound states that play a role in the ionization dynamics. We show how the detailed shape of the pulse accelerates the ionization, and how the presence or absence of bound states influences the velocity of the process.