Probing the low-energy electron-scattering dynamics in liquids with high-harmonic spectroscopy

High-harmonic spectroscopy (HHS) is a nonlinear all-optical technique with inherent attosecond temporal resolution, which has been applied successfully to a broad variety of systems in the gas phase and solid state. Here, we extend HHS to the liquid phase, and uncover the mechanism of high-harmonic generation (HHG) for this phase of matter. Studying HHG over a broad range of wavelengths and intensities, we show that the cut-off ($E_c$) is independent of the wavelength beyond a threshold intensity, and find that $E_c$ is a characteristic property of the studied liquid. We explain these observations within an intuitive semi-classical model based on electron trajectories that are limited by scattering to a characteristic length, which is connected to the electron mean-free path. Our model is validated against rigorous multi-electron time-dependent density-functional theory calculations in, both, supercells of liquid water with periodic boundary conditions, and large clusters of a variety of liquids. These simulations confirm our interpretation and thereby clarify the mechanism of HHG in liquids. Our results demonstrate a new, all-optical access to effective mean-free paths of slow electrons ($\leq$10 eV) in liquids, in a regime that is inaccessible to accurate calculations, but is critical for the understanding of radiation damage to living tissue. Our work also establishes the possibility of resolving sub-femtosecond electron dynamics in liquids, which offers a novel, all-optical approach to attosecond spectroscopy of chemical processes in their native liquid environment.