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Molecular orbital imprint in laser-driven electron recollision

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Science Advances  04 May 2018:
Vol. 4, no. 5, eaap8148
DOI: 10.1126/sciadv.aap8148
  • Fig. 1 Channel-specific continuum wave packets in 1,3-butadiene.

    (A) The upper part shows the D0 Dyson orbital. The lower part displays a snapshot of the simulated electron density isosurface of value Embedded Image(where a0 is the Bohr radius) for the D0 channel 0.7 fs after the peak electric field and was obtained for perpendicular laser polarization (θ = 90°, φ = 90°). The polar angle θ is defined with respect to the principal axis with the lowest moment of inertia, and φ is the azimuthal angle (see the coordinate system on top). The color visualizes the phase of the continuum wave function. (B) The same as (A) but for the D1 channel.

  • Fig. 2 Experimental data.

    (A) Electron kinetic energy distributions acquired in coincidence with different ion species, allowing one to distinguish between the D0 and D1 ionization channels. The distributions are normalized to the same total yield for better comparison. The green and orange areas indicate integration limits for the determination of the yields of direct (MD) and rescattered (MR) electrons, respectively, in the angle-dependent data in (C). (B) Delay scan of the nonadiabatic alignment, showing the 1,3-butadiene parent ion yield around the rotational half-revival. The error bars are given by counting statistics. Shown as a red solid line and shaded area are the best fits and confidence intervals from the extraction procedure of the alignment distribution, which uses a symmetric-top approximation. The experimental data shown in (C) were acquired at the delay ta corresponding to peak alignment. (C) Channel-resolved yield of direct (Embedded Image, Embedded Image) and rescattered (Embedded Image, Embedded Image) electrons as a function of the angle α′ between the polarizations of the alignment and SFI laser fields, using the integration limits shown in (A). Solid lines denote best fits from the deconvolution of the molecular-frame ionization and rescattering probabilities using the known alignment distribution. Error bars, given by counting statistics, are smaller than the symbols used for Embedded Image, Embedded Image, and Embedded Image.

  • Fig. 3 Effect of the shape of the continuum wave packet on rescattering.

    (A and C) Channel-resolved molecular-frame polar angle–dependent ionization probability S(θ) (A) and rescattering probability R(θ) × Q(θ) (C), as obtained from the deconvolution of the experimental data shown in Fig. 2C with the alignment distribution of the molecular ensemble. The shaded areas delimit the confidence intervals arising from the uncertainty of the alignment distribution (vertical shading) and from the statistical error of the measurements in Fig. 2C (horizontal shading) (see the Supplementary Materials). The latter error contributes significantly only to the D1 rescattering probability. (B and D) The same observables as in (A) and (C) obtained from the TD-RIS calculation. Note that while the ionization probability of the D0 channel in (A) and (B) has been scaled arbitrarily, the relative scale between D0 and D1 reflects their contributions to ionization.

  • Fig. 4 Channel indepedence of the high-angle scattering probability.

    Simulated strong laser field–driven scattering of a three-dimensional Gaussian continuum wave packet (replacing the actual channel-dependent wave packet launched by SFI) off the Embedded Image 1,3-butadiene ion in the electronic ground state (D0) and in the first excited state (D1). (A) Snapshots of the electron density isosurfaces (of value Embedded Image, where a0 is the Bohr radius) at two instants in time during the 2.7-fs period laser field (see the Supplementary Materials), for a laser polarization perpendicular to the plane of the molecule (θ = 90°, φ = 90°) and the ion in the D0 ground state. For the definition of θ and φ, see the coordinate system in Fig. 1. The maximum of the oscillatory electric field defines zero time. The color scale describing the phase of the electron wave function is the same as in Fig. 1. (B) Comparison of the computationally obtained θ-dependent, φ-averaged scattering probability R(θ) × Q(θ) for a Gaussian wave packet scattering off the Embedded Image ion in the D0 and the D1 state. Because the return probability R(θ) is channel- and angle-independent by design in this calculation [that is, R(θ) = R], the calculation proves that the high-angle scattering probability Q(θ) is near-independent of the electronic state of the 1,3-butadiene molecular cation, as expected.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/5/eaap8148/DC1

    section S1. Computational details to the coupled channels rescattering simulations

    section S2. Effects of adiabatic polarization on the electronic structure

    section S3. Experimental methods

    section S4. Data analysis

    section S5. Determination of the alignment distribution

    section S6. Confidence interval of the deconvoluted molecular-frame properties

    section S7. SFA analysis of photoelectron rescattering in the presence of symmetries

    fig. S1. Electric field (black line) of the 800-nm pulse with a total duration of 4.4 fs and a peak intensity of 3 × 1013 W/cm2.

    fig. S2. Channel- and polarization-resolved rescattering probability in the molecular frame for the D0 channel (blue) and the D1 channel (red) of 1,3-butadiene.

    fig. S3. Electric field mimicking a half-cycle 800-nm pulse with a peak intensity of 3 × 1013 W/cm2 used for the SFI simulations (see Fig. 3B in the main text).

    fig. S4. Influence of adiabatic polarization on the Dyson orbitals for the two lowest ionization channels of 1,3-butadiene (D0 and D1).

    fig. S5. Measured parent ion (Formula) yield as a function of the laboratory-frame angle α′ between the linear polarizations of the alignment and the SFI beams, for maximally aligned molecules (Δt = 58 ps).

    fig. S6. Number of counts on the ion detector as a function of the ion time of flight and the spatial impact position in molecular beam direction (x).

    fig. S7. Determination of the alignment distribution present in the experiment.

    table S1. Overlap of adiabatically polarized cationic many-electron wave functions [D0(F), D1(F)] in 1,3-butadiene with the corresponding field-free wave functions [D0, D1].

    References (3942)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Computational details to the coupled channels rescattering simulations
    • section S2. Effects of adiabatic polarization on the electronic structure
    • section S3. Experimental methods
    • section S4. Data analysis
    • section S5. Determination of the alignment distribution
    • section S6. Confidence interval of the deconvoluted molecular-frame properties
    • section S7. SFA analysis of photoelectron rescattering in the presence of symmetries
    • fig. S1. Electric field (black line) of the 800-nm pulse with a total duration of 4.4 fs and a peak intensity of 3 × 1013 W/cm2.
    • fig. S2. Channel- and polarization-resolved rescattering probability in the molecular frame for the D0 channel (blue) and the D1 channel (red) of 1,3- butadiene.
    • fig. S3. Electric field mimicking a half-cycle 800-nm pulse with a peak intensity of 3 × 1013 W/cm2 used for the SFI simulations (see Fig. 3B in the main text).
    • fig. S4. Influence of adiabatic polarization on the Dyson orbitals for the two lowest ionization channels of 1,3-butadiene (D0 and D1).
    • fig. S5. Measured parent ion (C4H+6) yield as a function of the laboratory-frame angle α′ between the linear polarizations of the alignment and the SFI beams, for maximally aligned molecules (Δt = 58 ps).
    • fig. S6. Number of counts on the ion detector as a function of the ion time of flight and the spatial impact position in molecular beam direction (x).
    • fig. S7. Determination of the alignment distribution present in the experiment.
    • table S1. Overlap of adiabatically polarized cationic many-electron wave functions D0(F), D1(F) in 1,3-butadiene with the corresponding field-free wave functions D0, D1.
    • References (39–42)

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