Solid state core-exciton dynamics in NaCl observed by tabletop attosecond four-wave mixing spectroscopy

James D. Gaynor, Ashley P. Fidler, Yen-Cheng Lin, Hung-Tzu Chang, Michael Zuerch, Daniel M. Neumark, and Stephen R. Leone

Phys. Rev. B 103, 245140 – Published 25 June 2021

Abstract

Nonlinear wave mixing in solids with ultrafast x-rays can provide insight into complex electronic dynamics of materials. Here, tabletop-based attosecond noncollinear four-wave mixing (FWM) spectroscopy using one extreme ultraviolet (XUV) pulse from high harmonic generation and two separately timed few-cycle near-infrared (NIR) pulses characterizes the dynamics of the ${Na}^{+}$ $L_{2, 3}$ edge core-excitons in NaCl around 33.5 eV. An inhomogeneous distribution of core-excitons underlying the well-known doublet absorption of the ${Na}^{+}$ $Γ がんま$ point core-exciton spectrum is deconvoluted by the resonance-enhanced nonlinear wave mixing spectroscopy. In addition, other dark excitonic states that are coupled to the XUV-allowed levels by the NIR pulses are characterized spectrally and temporally. Approximately $< 10 fs$ coherence lifetimes of the core-exciton states are observed. The core-excitonic properties are discussed in the context of strong electron-hole exchange interactions, electron-electron correlation, and electron-phonon broadening. This investigation successfully indicates that tabletop attosecond FWM spectroscopies represent a viable technique for time-resolved solid state measurements.

Received 5 March 2021
Accepted 8 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.245140

Physics Subject Headings (PhySH)

Electronic structure of atoms & molecules Excitons

Insulators Ionic solids

Attosecond laser spectroscopy Four-wave mixing High-harmonic generation

Condensed Matter, Materials & Applied PhysicsNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

James D. Gaynor ^1,2,*, Ashley P. Fidler ^1,2,†, Yen-Cheng Lin ^1,2, Hung-Tzu Chang ¹, Michael Zuerch ^1,3, Daniel M. Neumark ^1,2,‡, and Stephen R. Leone ^1,2,4,§

¹Department of Chemistry, University of California, Berkeley, California 94720, USA
²Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴Department of Physics, University of California, Berkeley, California 94720, USA

^*Corresponding author: jgaynor@berkeley.edu
^†Present address: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
^‡dneumark@berkeley.edu
^§srl@berkeley.edu

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Vol. 103, Iss. 24 — 15 June 2021

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Images

Figure 1
Linear extreme ultraviolet (XUV) absorption spectrum of NaCl around ${Na}^{+}$ $L_{2, 3}$ edge. The linear absorption spectrum of a NaCl thin film (50 nm) used in the four-wave mixing (FWM) experiments of the ${Na}^{+}$ $L_{2, 3}$ edge. The inset zooms in on the ${Na}^{+}$ core-exciton absorption features of interest in this paper.
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Figure 2
Attosecond extreme ultraviolet (XUV) near-infrared (NIR) four-wave mixing (FWM) spectroscopy in a noncollinear beam geometry. (a) Schematic of the beam geometry and pulse sequence. Two few-cycle NIR beams ( $k_{NIR 1} / {NIR}_{1}$ , orange; $k_{NIR 2} / {NIR}_{2}$ , red) are vertically stacked and crossed with an attosecond XUV pulse train ( $k_{XUV} / XUV$ , blue) on the NaCl sample. The delays between each beam are independently tunable; the XUV-NIR delay is denoted ${τ たう}_{1}$ , and the delay between the two NIR pulses is ${τ たう}_{2}$ . The wave mixing signals ( $k_{FWM}$ ) are emitted at an angle ${θ しーた}_{emission}$ , and the attosecond transient absorption (ATA) signals are collinear with the XUV pulse. (b) The initially excited XUV-bright states are coupled through XUV-dark states and back to the bright state manifold through the two sequential NIR interactions. The phase-matching condition determines the emitted signal direction. Controlling the pulse timing determines whether the time-resolved XUV emission arises from the evolution of the XUV-bright states or the XUV-dark states.
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Figure 3
Extreme ultraviolet (XUV) near-infrared (NIR) nonlinear wave mixing signal of ${Na}^{+}$ core-excitons in NaCl. (a) The ${Na}^{+}$ $L_{2, 3}$ core-exciton signal observed under the four-wave mixing (FWM) experimental conditions (all beams unblocked, pulse sequence above) at temporal overlap ( ${τ たう}_{1} = {τ たう}_{2} = 0$ ). The background-free FWM signals are observed at $| {θ しーた}_{emission} | > 1 mrad$ , while the attosecond transient absorption (ATA) signals are found in the range $- 1 < {θ しーた}_{emission} < 1 mrad$ ; −ΔでるたOD indicates optical density of emission. (b) Confirmation of the nonlinear wave mixing nature of the detected signals from blocking $k_{NIR 1}$ ; only the ATA signal from $k_{NIR 2}$ is observed as expected. To avoid detector saturation, the ATA signals are collected with 0.7 s integration, while the FWM signals are collected with 2.0 s integration, resulting in the FWM signals shown in (a) effectively enhanced relative to the ATA signals by ∼2.86.
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Figure 4
Near-infrared (NIR) fluence dependence and generation efficiency of the four-wave mixing (FWM) signal. (a) The NIR fluence dependence of the strongest ${Na}^{+}$ core-exciton at 33.61 eV for $k_{NIR 1}$ (orange) and $k_{NIR 2}$ (red); spectra are collected at temporal overlap. (b) The excitonic FWM efficiency calculated for the three main core-excitons with increasing $k_{NIR 1}$ fluence observed at temporal overlap. Linear (solid) and quadratic (dashed) fits; $33.27 eV = black$ , $33.42 eV = light blue$ , and $33.61 eV = green$ . Fluence dependence of FWM signal and excitonic efficiencies are all linear $< 12 mJ / c m^{2}$ ( $< 2.14 TW / c m^{2}$ ), NIR fluences in the $8 - 10 mJ / c m^{2}$ ( $1.43 - 1.79 TW / c m^{2}$ ) were used in the FWM studies to stay in the linear regime.
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Figure 5
Time-dependent four-wave mixing (FWM) signals measure excitonic dynamics. (a) Time-resolved extreme ultraviolet (XUV) emission of the FWM signal ( $- 2.0 > {θ しーた}_{emission} > - 2.4 mrad$ ) collected as a function of XUV-bright state evolution ( ${τ たう}_{1}$ scanned, ${τ たう}_{2} = 0$ ). (b) Time-resolved XUV emission of FWM signal collected as a function of XUV-dark state evolution following initial two photon ( $k_{XUV} + k_{NIR 1}$ ) excitation into the XUV-dark states ( ${τ たう}_{1} = 0$ , ${τ たう}_{2}$ scanned).
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Figure 6
Deconvolution of core-exciton four-wave mixing (FWM) signals. Spectral deconvolution of the time-zero spectrum with core-excitonic components identified in both the bright and dark state scans. (a) Temporal overlap FWM spectrum (black) fit with the three primary core-excitons identified in the bright state scans with Gaussian distributions and (b) the fit residuals (blue, left axis) compared with the core-excitons (normalized, red, right axis) identified in the dark state scans following overlap at a 7 fs delay. The blocks above the top plot highlight the five distinct core-excitonic regions discussed in the text. The red blocks refer to distinct states observed only in the bright state scan in (a); blue blocks refer to distinct states identified through the comparison of the residuals and dark state scans in (b) and the purple block on the low energy region highlights features observed in both (a) and (b), which may correspond to more than one distinct state.
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