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Wigner time delay - does it correctly describe the dynamics of the center of an electron wave packet in photo ionization?

September 23, 2015

This paper is addressing the recent progress in understanding single-photon ionization dynamics of the outermost valence electrons in noble gases. The Wigner time delay, which is a measure for the spectral variation of the scattering phase, is generally supposed to apply well to the mechanism of single-photon ionization because this process can be interpreted as a half-scattering event. However, in this work we demonstrate that the Wigner time delay (related to the electron wave packet group delay) can correctly explain the “classical trajectory” of the center of an electron wave packet only up to a certain level.

We are able to show experimentally that the Wigner time delay can reproduce correctly the general trend of the measured delays but it does not capture all the observed features. This is in analogy to the tunnel ionization case (see Fig. 1), where the group delay concept gives the wrong explanation for the measured delay [1] due to the energy dependent transmission filter imposed by the tunnelling barrier to the electron wave packet. In the case of single-photon ionization, resonances in the continuum introduce a filtering effect on the propagating electron wave packet similar to a tunnel barrier. This results into a strong variation of the Wigner delay that can no longer be translated into the classical delay of the center of the electron wave packet.

[1] A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, Optica 1, 343 (2014).



Figure 1. (a) Potential barrier of height Eb (black solid line) and transmission probability (blue dotted line) as a function of the ratio between the kinetic energy of the wave packet E and the barrier height Eb. (b) Tunneling case: if the average kinetic energy of the wave packet is smaller than the barrier height, propagation proceeds by tunneling. After propagation through the barrier, the wave packet disperses and its peak would be found at a time given by the dashed line. However, the transmission probability [blue dotted line in (a)] acts as an energy-dependent high-pass filter, which induces an additional temporal shift [solid line in lower part of panel (b)] not related to the time spent within the barrier. (c) Single-photon ionization case: the energy of the wave packet is significantly larger than Eb and therefore a meaningful relation between the wave packet peaks before and after the filter persists. However, resonances in the continuum can act as filters also in the case of (c) inducing strong variation of the Wigner delay, which cannot be translated into the classical delay of the center of the electron wave packet.

Sabbar, M., Heuser, S., Boge, R., Lucchini, M., Carette, T., Lindroth, E., Gallmann, L., Cirelli, C., and Keller, U. (2015) Resonance Effects in Photoemission Time Delays. Phys Rev Lett  115,  133001 (10.1103/PhysRevLett.115.133001)

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