Attosecond-resolved probing of recolliding electron wave packets in liquids and aqueous solutions

TL;DR

This work addresses attosecond-resolved probing of recolliding electron wave packets in liquids and aqueous solutions using high-harmonic spectroscopy (HHS) to reveal ultrafast electronic dynamics in disordered media. It combines active interferometry with phase-controlled two-colour fields and passive interferometry based on solvent–solute spectral interference to extract the emission-time $t_e$ and transit-time $\tau=t_e-t_i$ variations across harmonic orders. Key findings include slopes of $208 \pm 55$ as/eV (ethanol) and $124 \pm 42$ as/eV (water) for the two-colour delay optimization, supported by ab initio TDDFT yields of $125 \pm 48$ as/eV, and a gas-phase ethanol slope of $58 \pm 4$ as/eV, indicating a large attochirp in liquids. In NaCl solutions, destructive interference between solvent and solute emissions produces a minimum and yields a transit-time variation of $113 \pm 32$ as/eV, with passive and active methods in agreement. Overall, HHS is established as an attosecond-resolved probe of electron dynamics in liquids, enabling studies of charge migration, energy transfer, and proton dynamics in liquids and solutions.

Abstract

High-harmonic spectroscopy (HHS) in liquids promises real-time access to ultrafast electronic dynamics in the native environment of chemical and biological processes. While electron recollision has been established as the dominant mechanism of high-harmonic generation (HHG) in liquids, resolving the underlying electron dynamics has remained elusive. Here we demonstrate attosecond-resolved measurements of recolliding electron wave packets, extending HHS from neat liquids to aqueous solutions. Using phase-controlled two-colour fields, we observe a linear scaling of the two-colour delay that maximizes even-harmonic emission with photon energy, yielding slopes of 208+/-55 as/eV in ethanol and 124+/-42 as/eV in water, the latter matching ab initio simulations (125+/-48 as/eV). In aqueous salt solutions, we uncover interference minima whose appearance depends on solute type and concentration, arising from destructive interference between solute and solvent emission. By measuring the relative phase of solvent and solute HHG, we retrieve a variation of electron transit time by 113+/-32 as/eV, consistent with our neat-liquid results. These findings establish HHS as a powerful attosecond-resolved probe of electron dynamics in disordered media, opening transformative opportunities for studying ultrafast processes such as energy transfer, charge migration, and proton dynamics in liquids and solutions.

Figures (11)

• Figure 1: Active and passive attosecond interferometry of liquids.a Active interferometry consists in driving the HHG process with a phase-controlled two-colour ($\omega$/2$\omega$) laser field. This causes a different excursion of the laser-driven electron wave packet in consecutive half cycles, which translates into the emission of even harmonics that depend on the phase delay between the two colours. b Intensity of high harmonics generated in liquid ethanol with 1800/900-nm two-colour laser pulses of 59 fs/42 fs duration, focused to a peak intensity of 2.4 $\times$10$^{13}$ W/cm$^2$/1.8 $\times$10$^{10}$ W/cm$^2$. The black line connects the maxima of even harmonic orders. c Passive interferometry consists in driving HHG in a salt solution. This leads to high-harmonic emission from the solvent molecules and the solvated anions, whereas emission from the solvated cations remains negligible. Their different binding energies ($E_b$) result in different excursions, which translate into a phase shift of the emitted harmonics that depends on the difference of binding energies $\Delta E_{\rm b}$. d High-harmonic spectrum of a 0.8-M solution of NaCl in water driven by a 1800-nm, 3.3 $\times$10$^{13}$ W/cm$^2$ laser pulse. The emission of H17 is strongly suppressed as a consequence of destructive interference between the emissions of water and Cl$^-$.
• Figure 2: Active attosecond interferometry of liquids.a Schematic of the experimental setup. Laser pulses centered at 1800 nm and a weak ($\sim$ 0.07 % in intensity) parallel-polarized second harmonic are focused on the flat liquid jet, in which they generate both even and odd harmonics. The delay between the fundamental and second harmonic is controlled by a pair of fused-silica wedges. The generated high harmonics pass through a slit onto a grating that disperses the harmonic orders, which are then detected using an microchannel plate (MCP) coupled to a phosphor screen and a camera. A heatable bubbler setup is mounted on the same manipulator as the flat jet at a distance of 2.5 cm from its center for measuring gas-phase HHG after a lateral translation of the manipulator. b Relative phase of the intensity oscillations of even harmonics emitted from liquid H$_2$O (blue circles) and liquid ethanol (yellow circles) at peak fundamental intensities of 3.6$\times$10$^{13}$ W/cm$^2$ and 2.4$\times$10$^{13}$ W/cm$^2$, respectively. c Same as b from an experiment on gas-phase ethanol (red circles) using 1800 nm pulses with a duration of 59 fs and a peak intensity of 3.7$\times$10$^{13}$ W/cm$^2$ and a weak 900 nm component ($\sim$ 0.5% in intensity of 1800 nm) and calculations based on the strong-field approximation (SFA, yellow circles) using $E_b=10.48$ eV (ethanol). d Same as b from a TDDFT calculation on water clusters using 1800 nm pulses with a duration of 24 fs (FWHM) and a peak intensity of 5$\times$10$^{13}$ W/cm$^2$ with a weak 900 nm component (0.04% intensity of 1800 nm). Linear regressions and their slopes are shown where applicable.
• Figure 3: Passive attosecond interferometry of salt solutions.a Dependence of harmonic yields on the concentration of NaCl in water, showing the suppression of H17 (11.7 eV) for concentrations around 1M. The inset shows the harmonic spectrum for a 0.8-M NaCl solution. These data were obtained with 1800-nm pulses focused to a peak intensity of 3.3$\times$10$^{13}$ W/cm$^2$. b TDDFT calculation of the high-harmonic spectrum of a 1-M NaCl solution in water using an 1800-nm driving pulse with a peak intensity of 2$\times$10$^{13}$ W/cm$^2$. c Measured yield of H17 (11.7 eV) as a function of NaCl concentration (circles). The orange dashed line is a fit based on a two-species (H$_2$O and Cl$^-$) interference model. d Variation of the relative phase of emission from Cl$^-$ and H$_2$O, extracted from a fit to the interference model (left axis) and variation of the electron transit time (right axis), as a function of the emitted photon energy.
• Figure 4: Attosecond timing of electron dynamics in liquids. a Variation of electron transit time with photon energy from single-colour measurements on aqueous NaCl solutions (Fig. 3d, red), two-colour delays maximizing even harmonics from measurements on liquid H$_2$O (Fig. 2b, dark blue) and their interpolation onto the odd-harmonic axis (light blue). The difference of the two times, corresponding to the variation of ionization times with photon energy, is shown in yellow. b Comparison of the extracted variations of ionization (yellow circles) and emission times (blue circles) with a quantum-orbit calculation (lines) described in the Methods Section, at a peak intensity of 3.3$\times$10$^{13}$ W/cm$^2$, for $E_b=$8.83 eV (bandgap of liquid water). The experimental data has been shifted by constants offsets of 0.7 fs (for ionization time, yellow circles) and 1.9 fs (for the emission time, blue circles), to overlay on the curves of the quantum-orbit calculations. These constant shifts were determined from the mean of the difference of the experimental and quantum-orbit results. The driving wavelength used in all experiments and calculations is 1800 nm.
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