Ultrafast Coherent Bandgap Modulation Probed by Parametric Nonlinear Optics

Abstract

Light-matter interactions in crystals are powerful tools that seamlessly allow both functionalities of sizeable bandgap modulation and non-invasive spectroscopy. While we often assume that the border between the two regimes of modulation and detection is sharp and well-defined, there are experiments where the boundaries fade. The study of these transition regions allows us to identify the real potentials and inherent limitations of the most commonly used optical spectroscopy techniques. Here, we measure and explain the co-existence between bandgap modulation and non-invasive spectroscopy in the case of resonant perturbative nonlinear optics in an atomically thin direct gap semiconductor. We report a clear deviation from the typical quadratic power scaling of second-harmonic generation near an exciton resonance, and we explain this unusual result based on all-optical modulation driven by the intensity-dependent optical Stark and Bloch-Siegert shifts in the $\pm$K valleys of the Brillouin zone. Our experimental results are corroborated by analytical and numerical analysis based on the semiconductor Bloch equations, from which we extract the resonant transition dipole moments and dephasing times of the used sample. These findings redefine the meaning of perturbative nonlinear optics by revealing how coherent light-matter interactions can modify the band structure of a crystal, even in the weak-field regime. Furthermore, our results strengthen the understanding of ultrafast all-optical control of electronic states in two-dimensional materials, with potential applications in valleytronics, Floquet engineering, and light-wave electronics.