Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics

Abstract

Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view. However, the complete characterization of quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose deep-learning-performed strong-field Feynman's formulation with pre-classification scheme which can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build up a bridge between deep learning and strong-field physics through the Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science, and shed a new light on the quantum-classical correspondence.The wave function and the temporal evolution contain all information of quantum physics. However, they might be possibly the hardest to grasp in the classical world. Seventy years ago, Feynman proposed a path integral approach which has been viewed as the "sum over paths or histories" version of quantum mechanics, i.e. the wave function can be represented as a coherent superposition of contributions of all possible spatio-temporal paths [1,2]. Even though the Feynman's path integral (FPI) has been considered as the most fundamental way to interpret the quantum mechanics and answer what is the nature of measurements, the complete characterization of quantum wavepacket with all possible paths is formidable due to track ergodicity. Typically, only a very limited amount of paths could be accessed, and therefore only a reduced amount of information of quantum wavepacket could be obtained in different approximation methods so far.The development history of semiclassical methods based on FPI in strong-field physics, from the strong-field approximation (SFA) to the Coulomb corrected strongfield approximation (CCSFA) and quantum trajectory Monte Carlo methods, also proves that the more trajectories have been adopted, the more information could be extracted . As a result, despite of the notable success of these methods, there still exist a large number of unexplored regimes, including the open question about whether one could truly achieve the quantumclassical correspondence. Actually, with increasingly so-phisticated experiments, the limitation of existing semiclassical methods based on FPI for reproducing and explaining some quantum phenomena has been becoming increasingly evident due to the limited amount of paths, especially for the new attosecond measurements where a series of high-resolution photoelectron spectra with different pump-probe delays are needed to obtain attosecond time-resolved movies of electrons [25][26][27][...

Perspectives for analyzing non-linear photo-ionization spectra with deep neural networks trained with synthetic Hamilton matrices

“…They do not exhibit detailed structure, mostly a single peak with different form of the shoulders and reconstruction seems to work well with the exception of large positive chirp, where the position of the spectral peak is systematically red shifted in the predicted spectrum consistent with the largest error (see 6.4 × 10 16 Fig. 4 Prediction of 3D helium spectra (black, solid) for chirped pulses (10). The reference 3D helium spectra are shown with blue dashed lines.…”

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“…Other recent applications of the machine learning in strong-field physics are discussed in, e.g., Refs. [110,111].…”

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