Self-attention enabled quantum path analysis of high-harmonic generation in solids

Abstract

High-harmonic generation (HHG) in solids provides a powerful platform to probe ultrafast electron dynamics and interband--intraband coupling. However, disentangling the complex many-body contributions in the HHG spectrum remains challenging. Here we introduce a machine-learning approach based on a Transformer encoder to analyze and reconstruct HHG signals computed from a one-dimensional Kronig--Penney model. The self-attention mechanism inherently highlights correlations between temporal dipole dynamics and high-frequency spectral components, allowing us to identify signatures of nonadiabatic band coupling that are otherwise obscured in standard Fourier analysis. By combining attention maps with Gabor time--frequency analysis, we extract and amplify weak coupling channels that contribute to even-order harmonics and anomalous spectral features. Our results demonstrate that multi-head self-attention acts as a selective filter for strong-coupling events in the time domain, enabling a physics-informed interpretation of high-dimensional quantum dynamics. This work establishes Transformer-based attention as a versatile tool for solid-state strong-field physics, opening new possibilities for interpretable machine learning in attosecond spectroscopy and nonlinear photonics.