Nonadiabatic Strong Field Ionization of Atomic Hydrogen

D. Trabert, N. Anders, S. Brennecke, M. S. Schöffler, T. Jahnke, L. Ph. H. Schmidt, M. Kunitski, M. Lein, R. Dörner, and S. Eckart

Phys. Rev. Lett. 127, 273201 – Published 30 December 2021

Abstract

We present experimental data on the nonadiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schrödinger equation (TDSE). Experiment and TDSE show four above-threshold ionization peaks in the electron’s energy spectrum. The most probable emission angle (also known as “attoclock offset angle” or “streaking angle”) is found to increase with energy, a trend that is opposite to standard predictions based on Coulomb interaction with the ion. We show that this increase of deflection angle can be explained by a model that includes nonadiabatic corrections of the initial momentum distribution at the tunnel exit and nonadiabatic corrections of the tunnel exit position itself.

Received 29 July 2021
Accepted 7 December 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.273201

Physics Subject Headings (PhySH)

Light-matter interaction Multiphoton or tunneling ionization & excitation Ultrafast phenomena

Atoms

Atomic, Molecular & Optical

Authors & Affiliations

D. Trabert ¹, N. Anders ¹, S. Brennecke^2,*, M. S. Schöffler¹, T. Jahnke¹, L. Ph. H. Schmidt¹, M. Kunitski¹, M. Lein², R. Dörner ¹, and S. Eckart ^1,†

¹Institut für Kernphysik, Goethe-Universität, Max-von-Laue-Straße 1, 60438 Frankfurt, Germany
²Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany

^*simon.brennecke@itp.uni-hannover.de
^†eckart@atom.uni-frankfurt.de

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Vol. 127, Iss. 27 — 31 December 2021

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Images

Figure 1
(a) Measured electron momentum distribution projected onto the laser’s polarization plane for the ionization of atomic hydrogen by femtosecond laser pulses at a central wavelength of 390 nm, an ellipticity of $ε = 0.85$ , and a peak intensity of $1.4 \times 10^{14} W / {cm}^{2}$ . The light’s helicity and the orientation of the polarization ellipse are indicated by the inset in the lower right corner. (b) Focal-averaged numerical solution of the TDSE for the parameters that were used in (a). $α_{off}$ indicates the “angular offset” with respect to the minor axis of the ellipse of the laser electric field and the negative vector potential in (a) and (b). The intensity in (a) [(b)] has been normalized to a maximum of 1 [0.8]. (c) shows a comparison of the electron energy distribution for the data shown in (a) and (b). The error bars show statistical errors only.
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Figure 2
(a) [(b)] shows the electron momentum distribution from Fig. 1 [Fig. 1] in cylindrical coordinates ( $p_{r} = \sqrt{p_{x}^{2} + p_{y}^{2}}$ and $ϕ$ is the angle of ${\vec{p}}_{elec}$ in the laser polarization plane) after rowwise normalization. $α_{off}$ indicates the angular offset, the white contours indicate the ATI peak positions. (c) The rowwise normalized electron momentum distribution that is obtained from the CTS model with initial momenta distributed according to ADK theory, taking Coulomb interaction after tunneling into account and using the tunnel exit position from the TIPIS model in analogy to (a) and (b). (d) The result from our NACTS model. Within the NACTS model, the ionization probability and the initial conditions are taken from SFA. The black line guides the eye and is the same in all panels. The data in (a)–(d) have been symmetrized making use of the twofold symmetry. Every row has been normalized independently. The intensity in (a) [(b)–(d)] has been normalized to a maximum of 1 [0.8].
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Figure 3
(a) The angular offset $α_{off}$ is plotted as a function of the radial momentum $p_{r}$ for the data from Figs. 2. Error bars show statistical errors only. The gray dashed line guides the eye and shows the emission angle of electrons that tunnel at the peak electric field without taking Coulomb interaction into account. The magnitude of the negative vector potential at the peak of the laser pulse is 0.33 a.u. (b) Illustrates that the tunnel exit position within the TIPIS model does not depend on the initial momentum at the tunnel exit $p_{⊥}$ . SFA predicts decreasing values for the initial position ${\vec{r}}_{SFA}$ as a function of $p_{⊥}$ for $0 < p_{⊥} < 0.7$ a.u. The most probable value of $p_{⊥}$ from SFA is 0.15 a.u. (c) Visualization of a potential microscopic explanation for the dependence of ${\vec{r}}_{SFA}$ on $p_{⊥}$ (see text).
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