Photoelectron spectra with Qprop and t-SURFF

Abstract

Calculating strong-field, momentum-resolved photoelectron spectra (PES) from numerical solutions of the time-dependent Schrödinger equation (TDSE) is a very demanding task due to the large spatial excursions and drifts of electrons in intense laser fields. The time-dependent surface flux (t-SURFF) method for the calculation of PES [Tao and Scrinzi (2012)] allows to keep the numerical grid much smaller than the space over which the wavefunction would be spread at the end of the laser pulse. We present an implementation of the t-SURFF method in the well established TDSE-solver Qprop [Bauer and Koval (2006)]. Qprop efficiently propagates wavefunctions for single-active electron systems with spherically symmetric binding potentials in classical, linearly (along z) or elliptically (in the xy-plane) polarized laser fields in dipole approximation. Its combination with t-SURFF makes the simulation of PES feasible in cases where it is just too expensive to keep the entire wavefunction on the numerical grid, e.g., in the long-wavelength or long-pulse regime. Program summaryProgram title: QpropCatalogue identifier: ADXB_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXB_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 12458No. of bytes in distributed program, including test data, etc.: 86258Distribution format: at.gzProgramming language: C++.Computer: x86_64.Operating system: Linux.RAM: The memory requirements for calculating PES are determined by the maximum ℓ in the spherical harmonics expansion of the wave function and the number of momentum (or energy) values for which the PES are to be calculated. The example with the largest memory demand (large-clubs) uses approximately 6GB of RAM. The size of the numerical representation of a wavefunction during propagation is modest for the examples included (53 MB for the large-club example).Number of processors used: The evaluation of the PES can be distributed over up to Nk MPI processes (Nk is the number of momentum values).Catalogue identifier of previous version: ADXB_v1_0Journal reference of previous version: Comput. Phys. Comm. 174(2006)396Classification: 2.5.External routines: GNU Scientific Library, Open MPI (optional), BOOST (optional)Does the new version supersede the previous version?: For TDDFT calculations the previous version should be used.Nature of problem:When atoms are ionized by intense laser fields electrons may escape with large momenta (especially when rescattering is involved). This translates to a rapidly spreading wavefunction in numerical simulations of these systems thus rendering the calculation of PES very costly for increasing wave lengths and peak intensities.Solution method:The TDSE is solved by propagating the wavefunction using a Crank–Nicolson propagator. The wavefunction is represented by an expansion in spherical harmonics. In order to reduce the requirements with respect to the grid size the t-SURFF method is used to calculate PES.Reasons for new version:Using the window operator method to calculate PES is increasingly costly with increasing ponderomotive energies and pulse durations. The new version of Qprop provides an implementation of the t-SURFF method which allows the use of much smaller numerical grids.Summary of revisions:An implementation of the t-SURFF method and examples for calculating PES are provided in the new release.Restrictions:The dipole approximation for the laser interaction has to be applicable. t-SURFF is only implemented for velocity gauge. Furthermore a finite cutoff for long range binding potentials has to be used in the implemented t-SURFF method.Additional comments:For additional information see www.qprop.deRunning time:Depends strongly on the laser interaction studied. The examples given in this paper have run times from a few minutes to 12.5 hours.