Ionization enhancement and suppression by phase-locked ultrafast pulse pairs

David B. Foote, Y. Lin, Liang-Wen Pi, J. M. Ngoko Djiokap, Anthony F. Starace, and W. T. Hill, III

Phys. Rev. A 96, 023425 – Published 29 August 2017

Abstract

We present the results of a study of ionization of Xe atoms by a pair of phase-locked pulses, which is characterized by interference produced by the twin peaks. Two types of interference are considered: ordinary optical interference, which changes the intensity of the composite pulse and thus the ion yield, and a quantum interference, in which the excited electron wave packets interfere. We use the measured ${Xe}^{+}$ yield as a function of the temporal delay and/or relative phase between the peaks to monitor the interferences and compare their relative strengths. We model the interference with a pulse intensity function and by calculating the ionization yield with the time-dependent Schrödinger equation. Our results provide insight into optimal control pulses generated with learning algorithms. The results also show that the relative phase between peaks of a control pulse, along with small features such as distortions and imperfections in the wings of an ideal shape, play a significant role in the control process.

Received 20 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.023425

Physics Subject Headings (PhySH)

Coherent control Multiphoton or tunneling ionization & excitation Optical interferometry Ultrafast phenomena

Atomic, Molecular & Optical

Authors & Affiliations

David B. Foote^1,2,*, Y. Lin³, Liang-Wen Pi⁴, J. M. Ngoko Djiokap⁴, Anthony F. Starace⁴, and W. T. Hill, III^1,2,3,†

¹Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
²Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
³Department of Physics, University of Maryland, College Park, Maryland 20742, USA
⁴Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0299, USA

^*dbfoote@umd.edu
^†wth@umd.edu

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Issue

Vol. 96, Iss. 2 — August 2017

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Images

Figure 1
The normalized measured phase-dependent ${Xe}^{+}$ signal summed over all ${Xe}^{+}$ isotopes, captured from 1000 TOF waveforms per point. (a) The yield induced by a ${TPP}_{PS}$ at $τ = 150$ fs. Maximal ion yield occurred between $0.2 π$ and $0.4 π$ rad. The dotted blue curve is the fit of the data to $Y = {(I_{TPP}^{(\max)})}^{3 / 2}$ , where the TPP maximum intensity $I_{TPP}^{(\max)}$ is calculated for $T \equiv τ / Δ t = 3$ and assuming an input pulse with a pedestal, defined in Eq. (11) with $β = 0.23$ and $ϕ_{p} = 1.17 π$ rad (see text). (b) The FROG reconstructed intensity profile (solid black curve) and phase (dashed red curve) for the ${TPP}_{PS}$ responsible for the red $\oplus$ datum point in panel (a), where $Δ ϕ ≃ π$ rad. (c) The ${Xe}^{+}$ signal vs $τ$ from $τ = 135$ to 150 fs, in steps of approximately 0.067 fs, induced by a ${TPP}_{MZ}$ . The Fourier transform of panel (c) is shown in panel (d).
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Figure 2
(a) The top spectrum is the measured ${Xe}^{+}$ yield generated by a ${TPP}_{MZ}$ vs $τ$ , between 50 and 230 fs in steps of 0.67 fs. The yield is normalized to 1 when $τ ≫ Δ t$ . The middle spectrum is $I_{sim}^{(\max)}$ from Eq. (7) with $λ_{0} = 810$ nm. The bottom spectrum is the TDSE calculation with $λ_{0} = 808$ nm described in Sec. 3. The peaks of the top trace are shifted from the middle and bottom traces, but this is due to the large uncertainty in $τ$ . The oscillation frequencies of the top trace are not affected due to the small uncertainty in $δ τ$ , the relative delay between points. (b) The Fourier transforms of the spectra in panel (a): measured (solid blue curve), $I_{sim}^{(\max)}$ (dotted red curve), and TDSE (dash-dotted green curve). (c) $I (t)$ (solid) and $ϕ (t)$ (dotted) SD-FROG reconstructions for the input pulse used in the simulations.
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Figure 3
(a) The temporal intensity profile of the model pulses: with (red dashed) and without (solid blue) a pedestal defined in Eq. (11) and $β = 0.23, ϕ_{p} = 1.17 π$ rad. (b) $I_{TPP}^{(\max)} / I_{0}$ (solid black curve), $f_{O I}$ (dashed red curve), and $f_{E C}$ (dot-dashed blue curve) with no pedestal as a function of relative phase $Δ ϕ$ , for $T \equiv τ / Δ t = 3$ , which closely approximates the experimental ${TPP}_{PS}$ parameters. (c) Same as panel (b) but with the pedestal. For ease of viewing, $f_{O I}$ and $f_{E C}$ have been multiplied by 2 and 0.5, respectively.
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Figure 4
(upper) Temporal intensity of a FROG-reconstructed ${TPP}_{PS}$ [black squares, same TPP as Fig. 1] and a fit of of this TPP to a model hyperbolic-secant TPP with $Δ ϕ = 1.04 π$ rad (red curve). The fit is to Eq. (4) with proportional modulations added; i.e., the heights and widths of the two peaks were allowed to differ. The fit recovers widths for the first and second peaks, respectively, of $Δ t_{1} = 49.0 (7)$ and $Δ t_{2} = 48.7 (8)$ fs, and amplitudes $I_{01} = 1.35 (2)$ and $I_{02} = 1.27 (2)$ . (lower) Residual of the fit shown in the upper panel (data minus fit curve).
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