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We present a simple, one-dimensional model of an atom exposed to a time-dependent intense, short-pulse EM field with the objective of teaching undergraduates how to apply various numerical methods to study the behavior of this system as it evolves in time using several time propagation schemes.In this model, the exact Coulomb potential is replaced by a soft-core interaction to avoid the singularity at the origin. While the model has some drawbacks, it has been shown to be a reasonable representation of what occurs in the fully three-dimensional hydrogen atom.The model can be used as a tool to train undergraduate physics majors in the art of computation and software development. PROGRAM SUMMARY: Program Title:: 1d hydrogen light interactionProgram Files doi:: http://dx.doi.org/10.17632/2275fmvdzc.1Code Ocean Capsule:: https://doi.org/10.24433/CO.1476487.v1Licensing provisions:: MIT licenseProgramming language:: FORTRAN90Nature of problem:: The one dimensional time dependent Schrödinger equation has been shown to be quite useful as a model to study the Hydrogen atom exposed to an intense, short pulse, electromagnetic field. We use a model potential that is cut-off near x = 0 and avoids the singularity of the true 1-D potential, but retains the characteristic Rydberg series and continuum to study excitation and ionization of the true H atom. The code employs a number of numerical methods to understand and compare the efficacy and accuracy when applied to this model problem.Solution method:: The program uses and contrasts a number of approaches; the Crank-Nicolson, Short Iterative Lanczos, various incarnations of the split-operator and the Chebychev method have been programmed. These methods have been compared using a 3-point finite difference (FD) discretization of the space coordinate. For completeness, some attention has also been given to using 5-9 FD formulas in order to show how higher order discretization affects the accuracy and efficiency of the methods but the primary focus of the method is the time propagation.Additional comments including restrictions and unusual features:: The main purpose of this code is as a teaching tool for undergraduates interested in acquiring knowledge of numerical methods and programming skills useful to a practicing computational physicist.
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We show that the correlation dynamics in coherently excited doubly excited resonances of helium can be followed in real time by two-photon interferometry. This approach promises to map the evolution of the two-electron wave packet onto experimentally easily accessible noncoincident single-electron spectra. We analyze the interferometric signal in terms of a semianalytical model which is validated by a numerical solution of the time-dependent two-electron Schrödinger equation in its full dimensionality.
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The complex Kohn variational method is extended to compute light-driven electronic transitions between continuum wave functions in atomic and molecular systems. This development enables the study of multiphoton processes in the perturbative regime for arbitrary light polarization. As a proof of principle, we apply the method to compute the photoelectron spectrum arising from the pump-probe two-photon ionization of helium induced by a sequence of extreme ultraviolet and infrared light pulses. We compare several two-photon ionization pump-probe spectra, resonant with the (2s2p) 1 P 1 o Feshbach resonance, with independent simulations based on the atomic B-spline close-coupling STOCK code, and find good agreement between the two approaches. This finite-pulse perturbative approach is a step towards the ab initio study of weak-field attosecond processes in polyelectronic molecules.
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Recent experimental developments of high-intensity, short-pulse extreme ultraviolet light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (variant Planck's over 2piomega > 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow us not only to probe but also to induce angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge breakup scenario and by postcollision interaction.