Direct Experimental Access to the Nonadiabatic Initial Momentum Offset upon Tunnel Ionization

S. Eckart, K. Fehre, N. Eicke, A. Hartung, J. Rist, D. Trabert, N. Strenger, A. Pier, L. Ph. H. Schmidt, T. Jahnke, M. S. Schöffler, M. Lein, M. Kunitski, and R. Dörner

Phys. Rev. Lett. 121, 163202 – Published 15 October 2018

Abstract

We report on the nonadiabatic offset of the initial electron momentum distribution in the plane of polarization upon single ionization of argon by strong field tunneling and show how to experimentally control the degree of nonadiabaticity. Two-color counter- and corotating fields (390 and 780 nm) are compared to show that the nonadiabatic offset strongly depends on the temporal evolution of the laser electric field. We introduce a simple method for the direct access to the nonadiabatic offset using two-color counter- and corotating fields. Further, for a single-color circularly polarized field at 780 nm, we show that the radius of the experimentally observed donutlike distribution increases for increasing momentum in the light propagation direction. Our observed initial momentum offsets are well reproduced by the strong-field approximation. A mechanistic picture is introduced that links the measured nonadiabatic offset to the magnetic quantum number of virtually populated intermediate states.

Received 3 May 2018
Revised 16 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.163202

Physics Subject Headings (PhySH)

Light-matter interaction Multiphoton or tunneling ionization & excitation Quantum description of light-matter interaction Strong electromagnetic field effects Ultrafast phenomena Ultrashort pulses

Atomic, Molecular & Optical

Authors & Affiliations

S. Eckart^1,*, K. Fehre¹, N. Eicke², A. Hartung¹, J. Rist¹, D. Trabert¹, N. Strenger¹, A. Pier¹, L. Ph. H. Schmidt¹, T. Jahnke¹, M. S. Schöffler¹, M. Lein², M. Kunitski¹, and R. Dörner^1,†

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

^*eckart@atom.uni-frankfurt.de
^†doerner@atom.uni-frankfurt.de

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Vol. 121, Iss. 16 — 19 October 2018

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Images

Figure 1
Two-color field composed of a strong fundamental ( $E_{780} = 0.046 a . u .$ ) and a weaker second harmonic ( $E_{390} = 0.005 a . u .$ ) field. Both wavelengths are circularly polarized and corotating (a) and (c) or counterrotating (b) and (d). Depending on the helicity of the second harmonic the derivative of the electric field can be modified (phase of highest field is shown as a dot). The angular velocity of the laser electric field for the corotating case is $ω_{eff} = 1.1 ω$ ( $ω_{eff} = 0.9 ω$ ) and $ω_{eff} = 0.7 ω$ ( $ω_{eff} = 1.4 ω$ ) for the counterrotating case at the maximal (minimal) electric field. (c) and (d) show the corresponding experimental electron momentum distributions for single ionization of Ar. The black dashed circle guides the eye and has the same radius in all panels. The arrows indicate the temporal evolution of the laser electric field $\vec{E} (t)$ and the negative vector potential $- \vec{A} (t)$ .
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Figure 2
The golden line in (a) and (b) shows the negative vector potentials from Fig. 1 in cylindrical coordinates. The minimal vector potential is identical in (a) and (b) and marked with a long red and a short blue arrow that indicate the two driving fields that have antiparallel vector potentials at this time. The effective angular frequency is not equal at this instant [ $ω_{eff} = 0.9 ω$ in (a) and $ω_{eff} = 0.7 ω$ in (b)]. (c)–(e) show the data from Fig. 1 in cylindrical coordinates where $p_{x}$ is the momentum component parallel to the light propagation and $p_{r} = \sqrt{p_{y}^{2} + p_{z}^{2}}$ (subset of data with $| p_{x} | = 0.15 \pm 0.05 a . u .$ ). The data in (c) and (d) have been normalized columnwise. The most probable radial momentum $p_{r}^{peak} (φ)$ is angle dependent. The minimal and the maximal $p_{r}^{peak}$ in (c) are marked as black dashed lines and guide the eye in (c) and (d). (e) shows subsets of (c) and (d), restricting the angle to $132 \pm 10 °$ in (c) and $0 \pm 10 °$ in (d). The angular gates are indicated by blue and green vertical lines, which are shifted with respect to the corresponding vector potential due to the Coulomb rotation (obtained from the CTS model). Contour lines indicate the intensity in (c) and (d) prior to normalization of each angle individually. The dark gray, light gray, and white lines indicate 45%, 70%, and 95% of maximal intensity, respectively.
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Figure 3
Theoretical modeling of the experimental data shown in Fig. 2. The left column shows corotating fields, the right column, counterrotating fields. The black dashed lines from Fig. 3 serve as references in all panels. (a) and (b) show the (nonadiabatic) SFA result neglecting intracycle interference. (c) and (d) show the result from the (adiabatic) CTS model. The intensity has been chosen for SFA ( $E_{780} = 0.046 a . u .$ and $E_{390} = 0.005 a . u .$ ) and CTS ( $E_{780} = 0.060 a . u .$ and $E_{390} = 0.005 a . u .$ ) independently such that (a) and (c) match Fig. 2. (e) and (f) show subsets of (a) [(c) and Fig. 2] restricting the angle to $- 30 \pm 10 °$ and $150 \pm 10 °$ ( $- 48 \pm 10 °$ and $132 \pm 10 °$ ). (g) shows subsets of (b) [(d) and 2] restricting the angle to $18 \pm 10 °$ ( $0 \pm 10 °$ ). The corresponding angular gates are indicated by colored vertical lines. The golden lines in (a)–(d) show the negative vector potentials. Contour lines in (a)–(d) indicate the intensity prior to normalization as in Fig. 2. All data shown is restricted to $| p_{x} | = 0.15 \pm 0.05 a . u$ .
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Figure 4
Influence of the electron momentum $p_{x}$ (along the laser propagation direction) on $p_{r}$ (radial electron momentum in the plane of polarization). (a) experimental electron momentum distributions from single ionization of Ar by circularly polarized light at 780 nm. (b) shows the same data as (a) but in cylindrical coordinates. (c) illustrates the geometry at the instant of tunneling $t_{0}$ : the direction of the laser electric field $E (t_{0})$ , the direction of the tunnel exit $r_{0} (t_{0})$ , the nonadiabatic offset (red arrow), the negative vector potential $- A (t_{0})$ , and the initial momentum ( $p_{i}$ ) distribution at the tunnel exit. (d) shows the same as (b) after every column is normalized individually. The maximum of each column in (b) and (d) is indicated by the black solid line to guide the eye. The horizontal golden line shows the negative vector potential. The classical two-step (CTS) simulation with a peak vector potential of $A_{\max} = 0.87 a . u .$ , including the initial momentum offset from SFA, has been calculated without (white dots) and including Coulomb interaction (green dots) of the electron with the ion after tunneling. The black crosses show the CTS simulation for increased peak vector potential ( $A_{\max} = 1.03 a . u .$ ) and without initial momentum offset but with Coulomb interaction.
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