[Show abstract][Hide abstract] ABSTRACT: 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 Schrödinger 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 Schrödinger 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.
Journal of Physics B Atomic Molecular and Optical Physics 10/2011; 44(21):215003. DOI:10.1088/0953-4075/44/21/215003 · 1.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The process of nonsequential two-photon double ionization of helium is studied by two complementary numerical approaches. First, the time-dependent Schr{\"o}dinger equation is solved and the final wave function is analyzed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e., with no electron-electron interaction included in the final states. Then, the double ionization probability is found by means of a recently developed approach in which the concept of absorbing boundaries has been generalized to apply to systems consisting of more than one particle. This generalization is achieved through the Lindblad equation. A model of reduced dimensionality, which describes the process at a qualitative level, has been used. The agreement between the methods provides a strong indication that procedures using projections onto uncorrelated continuum states are adequate when extracting total cross sections for the direct double ionization process. Comment: 8 pages, 4 figures
[Show abstract][Hide abstract] ABSTRACT: Few-photon-induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schrödinger 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 (~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.
Physical Review A 06/2010; 81(6). DOI:10.1103/PhysRevA.81.063402 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the impact of electron-electron correlation on the ionization dynamics of helium in intense, high-frequency laser fields by solving the time-dependent Schrödinger equation from first principles. Although we observe a decrease in the total ionization yield at high field strengths, the hallmark of atomic stabilization, the repulsion between the electrons has a detrimental effect on the degree of stabilization, in particular for short pulses. Investigation of the ion channel yields reveals that the double ionization process is less prone to two-electron effects, and consequently exhibits the most distinct signature of stabilization. We also find that commonly used one-dimensional models tend to overestimate the effect of correlation.
[Show abstract][Hide abstract] ABSTRACT: We present a detailed analysis of the interference effects observed for ionization in collisions of fast highly charged projectiles with molecular hydrogen. We propose a nonperturbative semiclassical approach to describe the process under consideration by solving the time-dependent Schrödinger equation fully numerically on a 3D spatial grid. We present results for Kr34+-H2 collisions at 63 MeV/u impact energy and discuss different structures observed experimentally in doubly differential cross sections. The presence of Young-type minima and the absence of high-frequency oscillations are especially addressed. We also report unexpected interference patterns which can be observed for fixed-in-space molecular targets.
Physical Review A 02/2010; 81(2). DOI:10.1103/PhysRevA.81.022718 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 Schrödinger 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.
Journal of Physics Conference Series 12/2009; 194(1):012045. DOI:10.1088/1742-6596/194/1/012045
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Physics Conference Series 12/2009; 194(10):102040. DOI:10.1088/1742-6596/194/10/102040
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Physics Conference Series 11/2009; 194(3). DOI:10.1088/1742-6596/194/3/032025
[Show abstract][Hide abstract] ABSTRACT: 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 Schrödinger 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.
[Show abstract][Hide abstract] ABSTRACT: The capability of intense ultrashort laser pulses to initiate, control and image vibrational wavepacket dynamics in the deuterium molecular ion has been simulated with a view to inform and direct future femtosecond pump–control–probe experiments. The intense-field coherent control of the vibrational superposition has been studied as a function of pulse intensity and delay time, to provide an indication of key constraints for experimental studies. For selected cases of the control mechanism, probing of the subsequent vibrational wavepacket dynamics has been simulated via the photodissociation (PD) channel. Such PD probing is shown to elucidate the modified wavepacket dynamics where the position of the quantum revival is sensitive to the control process. Through Fourier transform analysis the PD yield is also shown to provide a characterisation of the vibrational distribution. It has been shown that a simple ‘critical R cut-off’ approximation can be used to reproduce the effect of a probe pulse interaction, providing a convenient and efficient alternative to intensive computer simulations of the PD mechanism in the deuterium molecular ion.
Journal of Modern Optics 05/2009; 56(9):1060-1069. DOI:10.1080/09500340902919444 · 1.01 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a numerical solution of the multi-dimensional time dependent Schrödinger equation using a split-operator technique for time stepping and a spectral approximation in the spatial coordinates. We are particularly interested in systems with near spherical symmetries. One expects these problems to be most efficiently computed in spherical coordinates as a coarse grain discretization should be sufficient in the angular directions. However, in this coordinate system the standard Fourier basis does not provide a good basis set in the radial direction. Here, we suggest an alternative basis set based on Chebyshev polynomials and a variable transformation.Furthermore, it is shown how the use of operator splitting produces a splitting error which introduces high frequency modes in the numerical solution in the case of the singular Coulomb potential. Incorporating the Coulomb potential into the radial Laplacian provides a much better splitting. Fortunately our new basis set allows this in some cases.Numerical experiments are presented which demonstrate the advantages and limitations of our technique. Details are demonstrated by 1D toy examples, while the superior efficiency is demonstrated by a 3D example.
Journal of Computational and Applied Mathematics 03/2009; 225(1):56–67. DOI:10.1016/j.cam.2008.06.015 · 1.27 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a new algorithm for vibrational control in deuterium molecules that is feasible with current experimental technology. A pump mechanism is used to create a coherent superposition of the D2+ vibrations. A short, intense infrared control pulse is applied after a chosen delay time to create selective interferences. A `chessboard' pattern of states can be realized in which a set of even- or odd-numbered vibrational states can be selectively annihilated or enhanced. A technique is proposed for experimental realization and observation of this effect using 5 fs pulses of 790 nm radiation, with intermediate intensity (5e13 W/cm2) Comment: 12 pages, 5 figures
Journal of Physics B Atomic Molecular and Optical Physics 06/2008; 41(20). DOI:10.1088/0953-4075/41/20/205504 · 1.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A quantum-mechanical approach is employed to study the binding of two bare nuclei of equal charge in strong laser fields beyond the dipole approximation [ Smirnova et al. Phys. Rev. Lett. 90 243001 (2003)]. The role of nondipole effects in the binding mechanism is investigated, and it is found that, in spite of a significant contribution to the dynamics, the nondipole effects do not alter the characteristic lifetime of the system. The results are supported by classical calculations addressing the question of decoupling of the center-of-mass and relative motions.
Physical Review A 07/2007; 76(1). DOI:10.1103/PhysRevA.76.013415 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The energy levels of laterally coupled parabolic double quantum dots are calculated for varying interdot distances. Electron-electron interaction is shown to dominate the spectra: In the diatomic molecule limit of large interdot separation, the two nearly degenerate singlet and triplet ground states are followed by a narrow band of four singlet and four triplet states. The energy spacing between the ground state and the first band of excited states scales directly with the confinement strength of the quantum wells. Similar level separation and band structure are found when the double dot is exposed to a perpendicular magnetic field. Conversely, an electric field parallel to the interdot direction results in a strong level mixing and a narrow transition from a localized state to a covalent diatomic molecular state.
Physical Review B 07/2007; 76(3). DOI:10.1103/PhysRevB.76.035303 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: On a parallel computer with distributed memory, multidimensional arrays are usually mapped onto the nodes such that only one or more of the indexes becomes distributed. Global computa- tion on data associated with the reminding indexes may then be done without communication. However, when global communication is needed on all indexes a complete redistribution of the data is needed. In higher dimension (d > 2) different mappings and subsequent redistribution techniques are possible. In this paper we present a general redistribution algorithm for data of dimensiond mapped on to a processor array of dimensionr < d. We show by a complexity analysis and numerical experiments that while using a 1D processor grid is the most efficient for modest number of processors, using 2D processor grid has better scalability and hence work best for higher number of processors.
Parallel Computing: Architectures, Algorithms and Applications, ParCo 2007, Forschungszentrum Jülich and RWTH Aachen University, Germany, 4-7 September 2007; 01/2007
[Show abstract][Hide abstract] ABSTRACT: 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 Schrödinger 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.
Journal of Physics B Atomic Molecular and Optical Physics 10/2004; 37(20):4205. DOI:10.1088/0953-4075/37/20/014 · 1.98 Impact Factor