Optical signatures of the Floquet-Bloch states in laser-driven ZnO crystal

We theoretically propose an all-optical measure to detect the Floquet-Bloch states in bulk solids using realistic first-principle based computations. To do this, we develop a practical and accurate strategy to extend our theory of optical absorption of laser-dressed solids (Phys. Rev. B 108, 064308 (2023)) to incorporate first-principle model within the Floquet formalism. This strategy overcomes the challenging requirement of a large number of bands for convergence in velocity gauge and its incompatibility with non-local pseudopotential plane wave methods. We then use this strategy to compute the realistic absorption spectra of a driven wurtzite ZnO crystal. In the spectra, we discover intense absorption and stimulated emissions at infrared (IR) frequencies for a wide range of drive laser parameters. Further investigation shows that these low-frequency features arise due to the hybridization of Floquet-Bloch modes, the time- and space-periodic functions that define the Floquet-Bloch states. These signals indicate the formation of Floquet-Bloch states in bulk and are expected to be clearly visible in electroabsorption spectroscopy experiments with driven solids away from the exciton and bulk signals. Overall, this work introduces a useful theoretical tool for simulating Floquet engineering in realistic solids and proposes a purely optical signature to detect the formation of Floquet-Bloch states.