Evolutionary Methods make New Effective Laser Shapes

by Thomas Bäck and Joost N. Kok

Controlling the behaviour of atoms and molecules by very short laser pulses using so-called femtosecond lasers is a very active and challenging research field. In a collaboration between the Leiden Institute of Advanced Computer Science (LIACS) and the Institute for Atomic and Molecular Physics, Amsterdam (AMOLF), evolutionary algorithms are used to optimize the shape of such laser pulses, based on a reformulation of the task as a high-dimensional, nonlinear optimization problem. These optimization methods, gleaned from the model of organic evolution, turn out to be well suited for tackling this challenging task.

Traditionally, the advancement of physical understanding through experimental research involves the definition of controlled experiments in which a problem of interest is studied as a function of one or more relevant experimental parameters. The outcome of the experiment then provides insight into the specific role of these parameters. This approach dates back to the days of Galileo. In a famous series of experiments, he measured how far a ball rolls down a gradient as a function of the parameter time, and concluded that the distance travelled by the ball is proportional to the square of the time. This approach has led to an enormous wealth of accumulated knowledge. However, it fails when the number of parameters relevant to the problem of interest becomes very large. These days more and more of these situations are encountered.

In problems in physics that depend on a large number of parameters, great advances can be made using a new approach based on evolutionary algorithms. The large number of parameters limits the usefulness of experiments where only some of these parameters are varied in a prescribed manner. An evolutionary approach is a viable alternative in many of these situations. In this approach the system of interest is studied within a closed loop strategy, where in each iteration the set of system parameters is modified to some extent by means of specialized mutation and recombination operators. After doing an actual experiment on the system with these parameters, the best performing values for achieving a given objective (also called fitness in evolutionary algorithms) are selected for the next round.

The key advantage of this iterative optimization approach is that one does not need to know a priori the details of the working mechanism of the complex system. Instead, the goal is to learn about the underlying physics by interpreting the sets of parameters produced by the evolutionary algorithm. This is in contrast to performing experiments with controlled variations (ie knowledge-based or trial-and-error-based variations by human experts) of these parameters. Because of the generic nature of the evolutionary approach, this methodology can be applied to a wide variety of different situations.

Figure 1: The instrumental set-up for the laser pulse shaping experiment. The mask is controlled by a large number of continuous parameters, which affect the final form of the pulse in a highly nonlinear way.

For as long as efficient optical sources have been available, scientists have tried to use optical means to control the behaviour of atoms and molecules. Specifically, with the availability of easy-to-use tunable lasers, numerous efforts have been undertaken to control the dynamics (dissociation, ionization, reactivity) of chemically and biologically relevant species. In a joint Dutch 'Foundation for Fundamental Research on Matter' (FOM) project between LIACS (Professors Bäck and Kok) and AMOLF in Amsterdam (Professors Vrakking, Herek, Muller and Tans), interesting results have been obtained in the field of femtosecond laser pulse shaping using evolutionary algorithms. There is currently great interest in the atomic and molecular physics community in aligning molecules with laser pulses, since dealing with an aligned sample of molecules simplifies the interpretation of experimental data. To control the motion of atoms or molecules by irradiating them with laser light, one has to provide laser pulses with durations on the same time scale as the motion of the particles. The outline of an experimental setup for such an experiment is illustrated in Figure 1. By applying a self-learning loop using an evolutionary algorithm, the interaction between the system under study and the laser field can be steered, and optimal laser pulse shapes for a given optimization target can be found. The target function is the alignment of an ensemble of molecules after interaction with a shaped laser pulse. Using so-called niching methods, which make sure that an evolutionary algorithm yields several alternative solutions, new effective laser pulse shapes were detected.

Figure 2: Three different pulse shapes which have been obtained by evolutionary algorithms (left), and the corresponding course of the optimization process plotted as quality of the pulses over time (right). It is clear that, due to the niching technique employed, very different pulse shapes have been found which are nevertheless very similar in their final quality, thus confirming the high complexity of the underlying optimization problem.

Recent results (see Figure 2 for pulse shapes and the corresponding course of evolution) have shown how fruitful the cooperation between researchers from Evolutionary Algorithms and Molecular Physics can be, and clearly demonstrate advances in both fields (namely, optimized pulse shapes and new concepts in evolutionary algorithms). Moreover, as the project started just one year ago, a variety of additional results over the course of this collaboration are expected.

Link:
http://www.liacs.nl/research/Algorithms/

Please contact:
Thomas Bäck, LIACS, Leiden University, The Netherlands
Tel: +31 71 527 7108
E-mail: baeckliacs.nl