Tore Birkeland

Numerical study of two-photon ionization of helium using an ab initio numerical framework

Few-photon-induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold ({approx} 54.4 eV) versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process caused by the bandwidth of the applied field.

A master equation approach to double ionization of helium

It is demonstrated how a numerical approach based on absorbing boundaries may be used to describe the process of non-sequential two-photon double ionization of helium. Contrary to any method based on solving the Schrodinger equation alone, this numerical scheme is able to reconstruct the remaining particles as one particle is absorbed. This may be used to distinguish between single and double ionization. A model of reduced dimensionality, which describes the process at a qualitative level, has been used. The results have been compared with a more conventional method in which the time-dependent Schrodinger equation is solved and the final wavefunction is analysed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e. with no electron–electron interaction included in the final states. It is found that the two methods indeed produce the same total cross sections for the process.

Dynamics of H(2p) ionization in ultrashort strong laser pulses

The ionization dynamics of an initially excited aligned H(2p, m = 0) atom exposed to short intense laser pulses is studied in the non-perturbative regime based on a three-dimensional numerical solution of the time-dependent Schrodinger equation on a spherical grid. The laser pulse is given a linear polarization vector which defines an angle θ with the symmetry axis of the initial 2p state. Strong orientation effects for ionization are found as a function of polarization direction for high laser frequencies. The angular distribution of the photo-electron spectrum shows two characteristic features related to ionization dynamics and interference of parallel versus perpendicular states with respect to the polarization direction of the field. For high enough field intensities, the ionization probability saturates below unity. In this limit, the angular electronic distribution is insensitive to the laser polarization direction. Another characteristic feature is a complete suppression of multiphoton peaks which results in kinetic emission spectra dominated by slow electrons.

Parallel Pseudo-Spectral Methods for the Time-Dependent Schrödinger Equation

Simulations in quantum mechanics can easily become extremely computationally demanding, making parallel computing a necessity. In this chapter we outline a computational technique of the time-dependent Schrodinger equation (TDSE) using pseudo-spectral methods. The split-step propagator method with dimensional splitting enables efficient parallelization; each fractional step can be perfectly parallelized, while redistribution is necessary between steps. It is showed that the scalability of the split-step method can be greatly increased by applying an improved data distribution scheme. The software framework PyProp is also introduced, implementing the methods described in this chapter. PyProp tries to combine the flexibility of object-oriented programming (C++), the convenience of high-level scripting language (Python) and high-performance computational libraries (blitz++, FFTW, LAPACK) to create a flexible framework for solving the TDSE.

Full 3D ab initio studies of interference effects in high-energy ion-molecule collisions

We present an investigation of the interference effects which have been observed experimentally and predicted for ionizing collisions between highly charged projectiles and molecular hydrogen targets. The present data have been obtained from a non perturbative treatment of the collision system, using the semiclassical impact parameter method and solving the time-dependent Schrodinger equation fully numerically, the scattering wavefunction being discretized in the electron position space and, for detailed analysis, on spaces of reduced dimensionality. We discuss the oscillatory structures observed in differential cross sections as function of outgoing electron energy and angle in Kr34+ – H2 collisions. Emphasis is placed on the discussion on Young-type interference pattern as well as extra high frequency oscillations which have been observed experimentally but not confirmed by theoretical calculations.

Full three-dimensional ab initio studies of interference effects in high-energy ion-molecule collisions

Following ab initio 1D and 2D calculations by Sisourat et. al. [1] we here report full three dimensional calculations of the single ionization of an H2-molecule by a highly charged Kr+34 ion at high velocity impact (60 MeV/u). Prior theoretical investigations have all failed to account for any second order interference effects. Final results will be presented at the conference.

Two-electron stabilization in helium

A recently developed framework for solving the time-dependent Schrodinger equation for one- and two-electron systems has allowed us to investigate stabilization of the helium atom exposed to strong laser fields. In our calculations, we fully account for the electron-electron interaction and include all electronic degrees of freedom. Preliminary results suggests that single- and double ionization stabilizes at different intensities.