Mapping of coherent nuclear wavepacket dynamics in D₂⁺ with ultrashort laser pulses

Bernold Feuerstein^1,2, Uwe Thumm¹

¹James R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506-2604, USA
²Permanent Address: Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany

Fast ionization of D₂ leads to the coherent population of many vibrational states of D₂⁺. Usually, only the squared absolute values of the vibrational state amplitudes, known as Franck- Condon factors, are observed since insufficient experimental time resolution averages out all coherence effects. We propose a Coulomb explosion imaging method to visualize the coherent motion of bound wavepackets using ultrashort (5 fs), intense pump-probe laser pulses. With this type of experiment, decoherence times in the fs to ps range could be directly measured, providing essential information for coherent control.

In order to simulate such a type of experiment, we solve the time-dependent Schrodinger equation in a 2D collinear model (along the laser polarization axis) for D₂⁺ with one dimension for the electronic and the nuclear coordinate, respectively. For the time propagation of the wavepackets, we use the Crank-Nicholson splitoperator technique. Momentum distributions are derived using the "virtual detector" method [1].

We demonstrate the Coulomb explosion imaging of both dissociating and bound nuclear wavepackets. For dissociation, we consider the v=0 ground state of D₂⁺ interacting with two 25 fs pulses of 0.3 PW/cm² intensity and variable delay. Our calculation reproduces qualitatively results of a previous pump-probe experiment [2]. The reconstructed bound wavepackets from a simulation of a pump-probe study with D₂ (v=0) as initial state using intense ultrashort pulses are shown in Figure 1.

Figure 1: Snapshots of the coherent nuclear motion in D₂⁺ following
ionization of D₂ (v=0) in a 5 fs, 1 PW/cm2 laser pulse for various delays
τ of the probe pulse. Solid curves: original density |Φ(R,τ)|². Dashed curves:
reconstructed probability density. The time-independent Franck-Condon
distribution is given by the dotted curve.

References:

[1] B. Feuerstein and U. Thumm, J. Phys. B 36, 707 (2003).
[2] C. Trump, H. Rottke, and W. Sandner, Phys. Rev. A 59, 2858 (1999).

This work was supported by the Chemical Sciences, Geosciences and Biosciences Division,
Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy.
B.F. acknowledges the financial support in form of a Research Scholarship from the Deutsche Forschungsgemeinschaft.

Submitted to ISIAC 2003, July 2003 in Stockholm, Sweden.

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