Time-dependent Surface Flux Method Research Articles

Strong-field nonsequential double photoionization using virtual-detector theory with path summation

We present an ab initio study of the nonsequential strong-field ionization dynamics of a model two-electron atom with helium character. Single- and double-ionization events are characterized and displayed using detector signals extracted at different points in the two-electron two-dimensional space. The double photoelectron momentum distribution is calculated via coherent path-summation over virtual-particle trajectories. A comparison is made between the momentum distributions obtained with the virtual-detector method, the Schr\"odinger wave function, and the time-dependent surface flux method developed by Tao and Scrinzi [New J. Phys. 14, 013021 (2012)]. Insights into different ionization and electron recollision pathways are gained from detailed virtual-particle tracking and energy-time readouts. This study demonstrates the extension of virtual-detector theory to strong-field multielectron quantum dynamics and highlights the importance of the evolving quantum phase in quasiclassical electron propagation.

TRecX — An environment for solving time-dependent Schrödinger-like problems

tRecX is a C++ code for solving generalized inhomogeneous time-dependent Schrödinger-type equations idΨ/dt=H[t,Ψ]+Φ in arbitrary dimensions and in a variety of coordinate systems. The operator H[t,Ψ] may have simple non-linearities, as in Gross-Pitaevskii and Hartree(-Fock) problems. Primary application of tRecX has been non-perturbative strong-field single and double photo-electron emission in atomic and molecular physics. The code is designed for large-scale ab initio calculations, for exploring models, and for advanced teaching in computational physics. Distinctive numerical methods are the time-dependent surface flux method for the computation of single and double emission spectra and exterior complex scaling for absorption. Wave functions and operators are handled by tree-structures with the systematic use of recursion on the coarse-grain level. Numerical, analytic, and grid-based discretizations can be combined and are treated on the same abstract level. Operators are specified in the input using a script language including symbolic algebra. User-friendly in- and output, error safety, and documentation are integrated by design. Program summaryProgram title: tRecX — time-dependent Recursive indeXing (tRecX=tSurff+irECS)CPC Library link to program files:https://doi.org/10.17632/zdjbnjxzrn.1Developer's repository link:https://gitlab.physik.uni-muenchen.de/AG-Scrinzi/tRecXCode Ocean capsule:https://codeocean.com/capsule/5391166Licensing provisions: GNU General Public License 2Programming language: C++Nature of problem: tRecX is a general solver for time-dependent Schrödinger-like problems, with applications mostly in strong field and attosecond physics. There are no technical restrictions on the spatial dimension of the problem with up to 6 spatial dimensions realized in the strong-field double ionization of Helium. A selection of coordinate systems is available and any Hamiltonian involving up to second derivatives and arbitrary up to three dimensional potentials can be defined on input by simple scripts.Solution method: The method of lines is used with spatial discretization by a flexible combination of one dimensional basis sets, DVR representations, discrete vectors, expansions into higher-dimensional eigenfunctions of user-defined operators and multi-center basis sets. Photo-emission spectra are calculated using the time-dependent surface flux method (tSurff) in combination with infinite range exterior complex scaling (irECS) for absorption. The code is object oriented and makes extensive use of tree-structures and recursive algorithms. Parallelization is by MPI. Code design and performance allow use in production as well as for graduate level training.

Quantum simulation of dissociative ionization of H2+ in full dimensionality with a time-dependent surface-flux method

The dissociative ionization of $H_2^+$ in a linearly polarized, 400 nm laser pulse is simulated by solving a three-particle time-dependent Schr\"odinger equation in full dimensionality without using any data from quantum chemistry computation. The joint energy spectrum (JES) is computed using a time-dependent surface flux (tSurff) method, the details of which are given. The calculated ground energy is -0.597 atomic units and internuclear distance is 1.997 atomic units if the kinetic energy term of protons is excluded, consistent with the reported precise values from quantum chemistry computation. If the kinetic term of the protons is included, the ground energy is -0.592 atomic units with an internuclear distance 2.05 atomic units. Energy sharing is observed in JES and we find peak of the JES with respect to nuclear kinetic energy release (KER) is within $2\sim4$ eV, which is different from the previous two dimensional computations (over 10 eV), but is close to the reported experimental values. The projected energy distribution on azimuth angles shows that the electron and the protons tend to dissociate in the direction of polarization of the laser pulse.

Application of the time-dependent surface flux method to the time-dependent multiconfiguration self-consistent-field method

We present a numerical implementation of the time-dependent surface flux (tSURFF) method [New J. Phys. 14, 013021 (2012)], an efficient computational scheme to extract photoelectron energy spectra, to the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method. Extending the original tSURFF method developed for single particle systems, we formulate the equations of motion for the spectral amplitude of orbital functions constutiting the TD-MCSCF wave function, from which the angle-resolved photoelectron energy spectrum, and more generally, photoelectron reduced density matrices (RDMs) are readiliy obtained. The tSURFF method applied to the TD-MCSCF wave function, in combination with an efficient absorbing boundary offered by the infinite-range exterior complex scaling, enables accurate {\it ab initio} computations of photoelectron energy spectra from multielectron systems subject to an intense and ultrashort laser pulse with a computational cost significantly reduced compared to that required in projecting the total wave function onto scattering states. We apply the present implementation to the photoionization of Ne exposed to an attosecond extreme-ultraviolet (XUV) pulse and above-threshold ionization of Ar irradiated by an intense mid-infrared laser field, demonstrating both accuracy and efficiency of the present method.

Dissociation and dissociative ionization of H2+using the time-dependent surface flux method

The time-dependent surface flux method developed for the description of electronic spectra [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012); A. Scrinzi, New J. Phys. 14, 085008 (2012)] is extended to treat dissociation and dissociative ionization processes of H${}_{2}{}^{+}$ interacting with strong laser pulses. By dividing the simulation volume into proper spatial regions associated with the individual reaction channels and monitoring the probability flux, the joint energy spectrum for the dissociative ionization process and the energy spectrum for dissociation is obtained. The methodology is illustrated by solving the time-dependent Schr\"odinger equation for a collinear one-dimensional model of H${}_{2}{}^{+}$ with electronic and nuclear motions treated exactly and validated by comparison with published results for dissociative ionization. The results for dissociation are qualitatively explained by analysis based on dressed diabatic Floquet potential energy curves, and the method is used to investigate the breakdown of the two-surface model.

Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method

The time-dependent surface flux (t-SURFF) method is introduced for computing strong-field infrared (IR) photo-ionization spectra of atoms by numerically solving the time-dependent Schrödinger equation on minimal simulation volumes. The volumes only need to accommodate the electron quiver motion and the relevant range of the atomic binding potential. Spectra are computed from the electron flux through a surface, beyond which the outgoing flux is absorbed by infinite range exterior complex scaling (irECS). Highly accurate IR photo-electron spectra are calculated in single active electron approximation and compared to the literature results. Detailed numerical evidence for performance and accuracy is given. Extensions to multi-electron systems and double ionization are discussed.