Disentangling the subcycle electron momentum spectrum in strong-field ionization

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Disentangling the subcycle electron momentum spectrum in strong-field ionization

Nicholas Werby, Adi Natan, Ruaridh Forbes, and Philip H. Bucksbaum

Phys. Rev. Research 3, 023065 – Published 22 April 2021

Abstract

Quantum calculations of tunneling in strong-field ionization predict intricate momentum distributions due to sub-laser-cycle attosecond electron dynamics. These are obscured in most experiments by the dominance of intercycle interference patterns, which are the hallmark of above-threshold ionization (ATI). Highly controlled one- to two-cycle laser pulses produce less intercycle interference but cannot accurately recreate the subcycle features produced by uniform-cycle calculations due to the effect of the carrier envelope of the pulse. We present a simple and effective technique to recover these subcycle features in experimental multicycle spectra. We time-filter the momentum distribution to highlight features originating from the interference of electron trajectory pairs with ionization times less than one field cycle apart. This method removes the ATI patterns and reveals subcycle interference structures in detail. We can resolve modulations in holographic structures that provide a reference for comparing with calculations.

Received 18 February 2021
Accepted 1 April 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.023065

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electronic excitation & ionization Multiphoton or tunneling ionization & excitation Strong-field-induced spectra Ultrafast phenomena

Atomic, Molecular & Optical

Authors & Affiliations

Nicholas Werby^1,2, Adi Natan ^1,2, Ruaridh Forbes^1,2, and Philip H. Bucksbaum ^1,2,3

¹Stanford PULSE Institute, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
²Department of Physics, Stanford University, Stanford, California 94305, USA
³Department of Applied Physics, Stanford University, Stanford, California 94305, USA

Article Text

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Issue

Vol. 3, Iss. 2 — April - June 2021

Subject Areas

Atomic and Molecular Physics

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Images

Figure 1
Comparison of the photoelectron trajectories produced by three distinct 800-nm laser pulses. (a) and (b) show the electric field of a 2-cycle ( $\sim 5.3$ fs) pulse and a 15-cycle ( $\sim 40$ fs) pulse, respectively. The carrier envelope is indicated by the dashed black lines for each. (c) shows a uniform-cycle laser field pulse. In (a)–(c) the ionization times are plotted as crosses for an electron which ends up at $(p_{∥}, p_{⊥}) = (0.5, 0)$ on the detector (see text). (d) displays the electron trajectories propagating in each of the laser fields above. Each trajectory begins at the time of ionization indicated in (a), (b), or (c) and arrives at the same final momentum $(0.5, 0)$ . The 15-cycle pulse much better reproduces the trajectories generated by the uniform-cycle pulse, as the carrier envelope parameter has less of an impact. For simplicity, no rescattering trajectories are shown.
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Figure 2
The application of the time-filtering technique to our argon spectrum. Here, we have zoomed into the spectrum to emphasize the region within $2 U_{p}$ where the filtering has the greatest effect. The red arrows outline the order of the data processing, and the color scale indicates the normalized photoelectron yield. (a) The top half of the image shows the reconstructed $p_{∥} - p_{⊥}$ momentum slice from polar onion peeling [34]. (b) Transforming the onion-peeled spectrum to a polar energy plot yields the top half of the image. In this representation the ATI rings are equally spaced, the radial axis counts the ATI order, and the $x$ and $y$ axes label the projection of the squared components of momenta as indicated. (c) The bottom half shows the filtered energy-spaced spectrum as detailed in the text on the same scale. (d) The bottom half shows the filtered momentum slice on the same scale as the original spectrum. Importantly, for (c) and (d) we note that the time filtering has only removed the ATI rings, and all other visible structures remain unaffected.
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Figure 3
(a) The $β_{6} (E_{r})$ parameter of the spectrum in Fig. 2 presented in units of the energy of a single photon at the central laser frequency $ℏ ω_{c}$ . [ $β_{6} (E_{r})$ is depicted as an example of the filtering method. The other orders are analyzed in an identical way.] Shown is the same parameter before (blue) and after (orange) time filtering. Prior to filtering we see the evenly spaced ATI comb quite prominently. After we apply the time filter we see that the filtering only removes the ATI comb and does not disrupt the underlying shape of the parameter. (b) The Fourier transform of $β_{6} (E_{r})$ . The large spike at $t = 1$ field cycle is due to the ATI comb. A low-pass filter with a cutoff (black dashed line) just below this peak removes only the ATI comb. Below the cutoff, the filtered and unfiltered ${\tilde{β}}_{6} (t)$ match very closely. This is achieved by designing a filter that is maximally flat in the passband. (c) The magnitude response of the low-pass filter applied to each $β_{n} (E_{r})$ parameter. Note the smoothness of the magnitude response in the passband below the cutoff, which helps prevent nonphysical artifacts from appearing in the data as a result of the filtering.
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Figure 4
Magnified image of a single quadrant of the filtered spectrum shown in Fig. 2 on the same logarithmic color scale. The spider-leg structure, fan structure, and wiggling modulations along the spider-leg structures are highlighted by dashed lines. Periodic minima along the polarization axis can also be seen. These modulations are normally obscured by the ATI rings.
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