Floquet theory and computational method for the optical absorption of laser-dressed solids

Strong light-matter interactions provide powerful means for the manipulation of the physico-chemical properties of matter. Here we develop a general theory for the linear optical absorption spectroscopy of spatially-periodic solids driven out of equilibrium by time-periodic light of arbitrary strength and photon energy. The effects of the driving laser is treated exactly using Floquet theory. The effective optical properties of this driven system are probed through a weak laser whose effects are captured to first order in perturbation theory. The resulting formula for non-equilibrium optical absorption is akin to the regular near-equilibrium absorption theory but with the Floquet-Bloch modes playing the role of pristine eigenstates of matter. To exemplify the effect of laser-dressing in the optical absorption, we perform computations of a model solid with a cosine-shaped lattice potential. We identify dramatic changes in the optical absorption upon increasing the amplitude of the driving laser. The spectrum shows a blue-shift of the band edge and below band gap absorption that agree with the dynamical Franz-Keldysh effect. It also shows several replicas of transitions separated by integer multiples of the drive photon energy that we assign as purely-optical tell-tale signatures of the Floquet-Bloch states. Beyond the dynamical Franz-Keldysh effect, strikingly we also observe intense low-frequency absorption and stimulated emissions and the opening of dips in the absorption spectrum that emerge due to the hybridization of the Floquet-Bloch modes which are novel signatures of the non-equilibrium dynamics in the laser-dressed system. This work open new paths to control and characterize the physical properties of solids using strong laser fields.