Learning from learning algorithms: Application to attosecond dynamics of high-harmonic generation

Abstract

Using experiment and modeling, we show that the data set generated when a learning algorithm is used to optimize a quantum system can help to uncover the physics behind the process being optimized. In particular, by optimizing the process of high-harmonic generation using shaped light pulses, we generate a large data set and analyze its statistical behavior. This behavior is then compared with theoretical predictions, verifying our understanding of the attosecond dynamics of high-harmonic generation and uncovering an anomalous region of parameter space. Experiments that study the dynamics of quantum systems, such as optical studies of atomic and molecular dynamics, often employ a "pump-probe" configuration where a pump pulse perturbs a system, and a probe pulse at varying time delay probes its evolution [1]. However, this technique corresponds to a simplified case of the more-general "stimuliresponse" experiment, where by observing the dynamical response of a system to varying stimulus, one can compare experiment with hypothesis. Often, in the case where the physics of a system is relatively simple, a pump-probe experiment can provide the most-readily interpretable data. However, pump-probe experiments can be difficult to interpret in the case of a complex quantum system, where the full dynamics are not already understood. Therefore devising new approaches to uncover and understand the dynamics of quantum systems is very important, in particular in the case of complex chemical and biological systems. Another area that requires a more sophisticated approach is the emerging field of "attosecond science" where subfemtosecond electron dynamics in atoms and molecules are observed. In this area, experimental constraints limit the applicability of a straightforward "pump-probe" experiment, and instead experiments infer various light source properties and electronic dynamics, using various comparisons of experimental observations with theoretical models [2][3][4][5].The more general case of a stimulus-response experiment was discussed by Rabitz [6] for the case of optically probed quantum (i.e., atomic, molecular, or electronic) systems. He suggested that the use of "learning algorithms" could both accomplish coherent control over a quantum system to obtain a desirable outcome [7][8][9][10][11][12], as well as provide information about the quantum system itself. In past work, we demonstrated the power of learning algorithms to selectively optimize the generation of coherent extreme-ultraviolet light using high-harmonic generation (HHG) [2]. By adjusting the phase of the laser field guided by a learning algorithm, we manipulated and optimized the quantum interferences that occur during the HHG process to achieve selective optimization of a single harmonic order. A comparison of theory with experiment was used to identify the mechanism behind the optimization: an optimally shaped light pulse allowed the phase of the radiating electron wave function to be adjusted on 10-20 attosecond time scales to selectively optimize a ...

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