Observation of Floquet states in graphene

Floquet engineering-the coherent dressing of matter via time-periodic perturbations-is a mechanism to realize and control emergent phases in materials out of equilibrium. However, its applicability to metallic quantum materials and semimetals such as graphene is an open question. The report of light-induced anomalous Hall effect in graphene remains debated, and a time-resolved photoemission experiment has suggested that Floquet effects might not be realizable in graphene and other semimetals with relatively short decoherence times. Here we provide direct spectroscopic evidence of Floquet effects in graphene through electronic structure measurements. We observe light-matter-dressed Dirac bands by measuring the contribution of Floquet sidebands, Volkov sidebands and their quantum path interference to graphene's photoemission spectrum. Our results demonstrate that Floquet engineering in graphene is possible, even though ultrafast decoherence processes occur on the timescale of a few tens of femtoseconds. Our approach offers a way to experimentally realize Floquet engineering strategies in metallic and semimetallic systems and for the coherent stabilization of light-induced states with potentially non-trivial topological properties.