Floquet-engineering unveiled by high-harmonic generation

Ultrafast optical control of solids has uncovered new phenomena and advanced non-equilibrium condensed matter physics, where photon dressed electronic states - Floquet Bloch states (FBSs) - emerge under a strong oscillating laser field, also known as Floquet engineering. Although FBSs have been extensively investigated using time and angle resolved photoemission spectroscopy, direct evidence of their role in high-harmonic generation spectroscopy (HHGS) has remained elusive. Here, we present combined experimental and theoretical evidence that FBSs can be probed by HHG emission in the wide-bandgap solid magnesium oxide (MgO) driven by few cycle near infrared pulses. Experimentally, we observe clear evidence of FBSs in the HHG yield dependence on the crystal orientation. This specific feature is attributed to nonadiabatic coupling between FBSs and conduction bands near the Brillouin zone edge, where the strong laser field transiently breaks time reversal symmetry. We have confronted the experimental findings with numerical solutions of the time dependent Schr\"odinger equation, which reproduce the new feature and confirm its Floquet origin. The theoretical results show a coupling inducing a local band structure renormalization and Floquet like hybridization under strong field excitation. It also shows that FBS nonadiabatic dynamics persist in the strong field regime, establishing HHGS as a powerful probe of ultrafast light induced band hybridization in solids.