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

Feynman's path integral approach is to sum over all possible spatiotemporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in the classical view. However, the complete characterization of the 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 a deep-learning-performed strong-field Feynman's formulation with a preclassification scheme that 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 a bridge between deep learning and strong-field physics through 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 new light on the quantum-classical correspondence.

Attosecond Time Delay of Retrapped Resonant Ionization.

A recent ultrafast pump-probe technique has allowed measurement of time delays during photoemission in a variety of systems ranging from atoms and molecules to solids with unprecedented temporal resolution. However, identifying the underlying physics is still a challenge especially in complicated multichannel above-threshold ionization (ATI) experiments. Here we demonstrate that the time delays of different ionization pathways in ATI can be clearly resolved and extracted with a semiclassical statistical method. The remarkable phase shift of near threshold photoelectrons can be attributed to a temporary retrapping of a photoelectron by the atomic potential in a quasibound state after emerging in the continuum state. This continuum-bound-continuum scattering manifests as a new resonant effect in strong-field photoemission. Our results unify the seemingly opposing quantum Eisenbud-Wigner-Smith time delay and classical Coulomb-induced time delay by highlighting the same physical picture, which holds promise for an intuitive interpretation of time-resolved fundamental electronic processes in strong-field experiments and epistemological reexamination of the quantum-classical correspondence.