Numerical mapping of ultrafast electron motion

in the hydrogen molecular ion


S. Barmaki*, K. Guessaf, S. Laulan

Laboratoire de Physique Computationnelle et Photonique

Secteur des Sciences, Université de Moncton-campus de Shippagan,

Shippagan, New-Brunswick, E8S 1P6, Canada

** Corresponding author. E-mail:

Received: 10 January 2013; revised version accepted: 12 April 2013



     We numerically simulate a pump-probe experiment to image the attosecond electron motion in the hydrogen molecular ion at short internuclear distances. In the pump step, we create a coherent electronic wavepacket, which is a combination of the fundamental and the first excited electronic states. We let the electronic wavepacket oscillate for a time delay , and then we ionize the ion with an intense attosecond x-ray laser pulse. Results of the ionized electron angular distribution are obtained by exact numerical solution of the 3D time-dependent Schrödinger equation in the Born-Oppenheimer approximation. We show that the asymmetry in the electron momentum distribution, obtained at different time delay  between the pump and the probe pulses, allows for the mapping of the attosecond electron motion in .


Keywords : Pump-probe experiment; Time-dependent Schrödinger equation; B-spline functions; Attosecond x-ray laser pulse; Ionization; Electron momentum distribution.

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