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We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states. 

Abstract The circular dichroism (CD) of photoelectrons generated by near-infrared (NIR) laser pulses using multiphoton ionization of excited He⁺ions in the 3p(m= +1) state is investigated. The ions were prepared by circularly polarized extreme ultraviolet (XUV) pulses. For circularly polarized NIR pulses co- and counter-rotating relative to the polarization of the XUV pulse, a complex variation of the CD is observed as a result of intensity- and polarization-dependent Freeman resonances, with and without additional dichroic AC-Stark shifts. The experimental results are compared with numerical solutions of the time-dependent Schrödinger equation to identify and interpret the pronounced variation of the experimentally observed CD. 

Free-electron lasers (FELs) are the world's most brilliant light sources with rapidly evolving technological capabilities in terms of ultrabright and ultrashort pulses over a large range of photon energies. Their revolutionary and innovative developments have opened new fields of science regarding nonlinear light-matter interaction, the investigation of ultrafast processes from specific observer sites, and approaches to imaging matter with atomic resolution. A core aspect of FEL science is the study of isolated and prototypical systems in the gas phase with the possibility of addressing well-defined electronic transitions or particular atomic sites in molecules. Notably for polarization-controlled short-wavelength FELs, the gas phase offers new avenues for investigations of nonlinear and ultrafast phenomena in spin-orientated systems, for decoding the function of the chiral building blocks of life as well as steering reactions and particle emission dynamics in otherwise inaccessible ways. This roadmap comprises descriptions of technological capabilities of facilities worldwide, innovative diagnostics and instrumentation, as well as recent scientific highlights, novel methodology, and mathematical modeling. The experimental and theoretical landscape of using polarization controllable FELs for dichroic light-matter interaction in the gas phase will be discussed and comprehensively outlined to stimulate and strengthen global collaborative efforts of all disciplines. Published by the American Physical Society2025 

Half-cycle oscillation is observed in transient absorption spectra of N₂O at NKedge (400 eV) irradiated by intense IR pulses, which is attributed to tunneling ionization of core excited states by intensive TDSE-based simulation.