Abstract
Photoelectron spectra obtained with intense pulses generated by free-electron lasers through self-amplified spontaneous emission are intrinsically noisy and vary from shot to shot. We extract the purified spectrum, corresponding to a Fourier-limited pulse, with the help of a deep neural network. It is trained on a huge number of spectra, which was made possible by an extremely efficient propagation of the Schrödinger equation with synthetic Hamilton matrices and random realizations of fluctuating pulses. We show that the trained network is sufficiently generic such that it can purify atomic or molecular spectra, dominated by resonant two- or three-photon ionization, nonlinear processes which are particularly sensitive to pulse fluctuations. This is possible without training on those systems.
Highlights
Recent years have seen an avalanchelike increase of machine-learning applications in physics [1,2,3], which roughly fall into three categories: (a) applications within theory, e.g., for quantum information [1] or to elucidate intricate many-body properties [4], (b) within experiment to optimize experimental conditions, e.g., to characterize a free-electron laser (FEL) pulse [5], and (c) applications that condition learning algorithms theoretically with the goal to apply the trained model to experimental data
In principle far more general, we choose to be specific and apply the approach we develop to the purification of noisy photoelectron spectra as routinely obtained with self-amplified spontaneous emission (SASE) FELs operating in the desired frequency range
We introduce synthetic Hamilton matrices (SHMs)
Summary
Recent years have seen an avalanchelike increase of machine-learning applications in physics [1,2,3], which roughly fall into three categories: (a) applications within theory, e.g., for quantum information [1] or to elucidate intricate many-body properties [4], (b) within experiment to optimize experimental conditions, e.g., to characterize a free-electron laser (FEL) pulse [5], and (c) applications that condition learning algorithms theoretically with the goal to apply the trained model to experimental data. The new element, formulated for the present context, is the generation of nmat Hamilton matrices with random energies Ekα, coupling matrix elements Vkαβ, and field strengths Ak, corresponding to intensities (referring to the Fourier-limited pulse) in the range of 5 × 1015; ...; 5 × 1016 W=cm2.
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