MP-CITDSE: A set of ab-initio programs for the simulation of hydrogenic and helium-like atom-laser interactions

Abstract

MP-CITDSE is a package of programs which solves the time-dependent Schrödinger equation for hydrogenic and helium-like atomic systems interacting with an ultra-short laser pulse (of attosecond or femtosecond duration). The output of the computations – with some minimal processing – may be used to calculate excited populations, single and double ionisation yields, kinetic, angular and radial electron distributions, and harmonic yields. For the Helium atom, a full account of the inter-electronic correlation effects is included via a configuration interaction approach; for the time propagation of the wavefunction a spectral basis expansion on the eigenstates of the field-free Hamiltonian is used; for this reason post-processing of the expansion coefficients just after the pulse lead to simple formulas for quantities of experimental interest. Program summaryProgram Title: MP-CITDSECPC Library link to program files:https://doi.org/10.17632/gv4zxmfdx3.1Developer's repository link:https://github.com/aforembs/MP-CITDSELicensing provisions: GPLv3Programming language: C++Nature of problem: The ultra-fast high-intensity laser pulses of modern experimental sources require an ab-initio theoretical treatment, as the characteristics of such pulses are generally incompatible with the established Lowest-order Perturbation Theory (LOPT) approximation. Such a treatment can be quite cumbersome to not only implement, but also describe in a clear, intuitive manner. Its inherent complexity ensures that even in its simplest form, an ab-initio TDSE solver can easily consist of several thousand lines of code. As with any project of such scope a significant amount of effort is required to keep the code up to date, running on several platforms, compilers and operating systems. As such, while the numerical problem tackled by MP-CITDSE is that of the simulation of hydrogenic and helium-like atom-laser interactions on a single node computer/workstation; its main challenges are longevity and expandability. By doing away with unnecessary abstractions within the code, using a modern standard of a widely used and performant language (C++ 17) and hosting the source code on a publicly available GitHub repository we hope that the programs provided herein prove themselves useful to many current and future AMO Physicists.Solution method: The atomic systems are considered confined in a spherical box of finite size. In the one-electron case (hydrogen) the eigenstates are calculated in a spherical coordinate system by the direct diagonalisation of the field-free Hamiltonian matrix representation on a B-splines piecewise polynomial basis expansion of the radial part of the eigenfunctions; for the two-electron case (helium) the numerically calculated one-electron eigenstates are angularly coupled to form a zero-order (uncorrelated) two-electron numerical basis; then the latter basis is further coupled via a configuration-interaction approach to eventually calculate the helium's two-electron eigenstates.Following these steps, for both systems (hydrogen and helium) the computation proceeds by expanding the time-dependent wavefunction on the corresponding field-free eigenstate basis; thus, we end up to a system of first-order ordinary differential equations (ODEs) in time for the expansion (time-dependent) coefficients; the dynamical parameters for the ODEs time propagation, namely the eigenenergies and dipole matrix elements are calculated only once prior to the ODEs propagation [2]. The structure of the propagating matrix is block tridiagonal.Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the MP-CITDSE code. In this version we solve the ODEs using a Runge-Kutta-Felnberg (RKF) algorithm. Also we have restricted the code to treat hydrogen and helium but with very little effort (non-relativistic) hydrogenic and helium-like atomic systems can also be simulated. The programs are supplied with two methods of compilation, via make and cmake to ensure greater portability.