The electric field of an intense laser pulse can directly modify the electronic properties of materials via electromodulation up to the petahertz regime. In this regime, the energy of the quiver motion of the electron-hole pair is comparable with the photon energy, which results in complex nonadiabatic dynamics. This regime opens opportunities to probe the electronic structure of materials on the attosecond timescale. Here, we show how the quasistatic electromodulation spectroscopy based on the Franz-Keldysh effect (FKE) connects with its nonadiabatic limit, which we find to be determined by resonant transitions between Floquet-Bloch states. This insight can be applied to measure the effective mass, ponderomotive and binding energies of the electron-hole pair on a few-femtosecond timescale. We demonstrate this by experimentally investigating laser-field-driven fused silica, a prototypical material for light-wave electronics, with extreme-ultraviolet attosecond pulse trains. We reproduce the experimental transient absorption spectra with an effective band structure and a dynamical Franz-Keldysh model, offering a simple parametrization for a theoretically challenging but technologically abundant material. Ab initio calculations in α-quartz highlight the contributions of specific bands, symmetry, and crystal orientation that are hidden in the experimental data due to randomized crystallographic orientation and finite temporal and spatial coherence. We show that the dynamical FKE can be explained as a third-order nonlinear process in the weak-field regime. The delay-dependent position of the absorption maxima and minima has a minimum tilt angle, determined by transitions between the underlying Floquet-Bloch states. In our analysis, we discuss the main experimental observables and show their connection to the parameters of the solid, providing the basis for nonadiabatic electromodulation spectroscopy.

• Received 14 October 2022
• Revised 23 December 2022
• Accepted 23 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.184304

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society