Robust purely optical signatures of Floquet states in laser-dressed crystals

Abstract

Strong light-matter interactions can create non-equilibrium materials with on-demand novel functionalities. For periodically driven solids, the Floquet theorem provides the natural states to characterize the physical properties of these laser-dressed systems. However, signatures of the Floquet states are needed, as common experimental conditions, such as pulsed laser excitation and dissipative many-body dynamics, can disrupt their formation and survival. Here, we identify a tell-tale signature of Floquet states in the linear optical response of laser-dressed solids that remains prominent even in the presence of strong spectral congestion of bulk matter. To do so, we introduce a computationally efficient strategy based on the Floquet formalism to finally capture the full frequency-dependence in the optical response properties of realistic laser-dressed crystals, and use it investigate the Floquet engineering in a first-principle model for ZnO of full dimensionality. The computations reveal intense, spectrally isolated, laser-controllable, absorption/stimulated emission features at mid-infrared energies present for a wide range of laser-driving conditions that arise due to the hybridization of the Floquet states. As such, these spectral features open a purely optical pathway to investigate the birth and survival of Floquet states while avoiding the experimental challenges of fully reconstructing the band structure.

Figures (3)

• Figure 1: Frequency ($\hbar\omega$) dependence of the optical absorption spectrum $A(\omega) n_{r}$ for ZnO dressed with near-resonant (a)-(c) and off-resonance (d)-(f) light of photon energy $\hbar\Omega$ and amplitude $E_{\mathrm{d}}$ (blue lines). Gray lines: spectra of pristine solid. Floquet engineering leads to strong modification of the optical response, including band-gap renormalization (feature I), below band-gap absorption (II) and the emergence of mid-IR features (III).
• Figure 2: Low-frequency transitions in the optical response as demonstrated in a minimal two-band model for near-resonance (top row) and off-resonance (bottom row) driving. (a-b) Quasienergies at a representative $k=0.1$ showing the avoided crossing as a function of (a) driving laser frequency $\hbar\Omega$ (with fixed $E_{\mathrm{d}} = 0.1$ V/Å) and (b) amplitude $E_{\mathrm{d}}$ (with fixed $\hbar\Omega=0.44$ eV). Vertical purple and green lines mark parameters before or at the avoided crossing, respectively. Panels (c) [or (d)] show the absorption spectra corresponding to (a) [or (b)] before (purple) and at (green) the avoided crossing. Transition lines signal the $k=0.1$ contribution only. Note that the low-frequency transitions emerge in the avoided crossing region where Floquet states hybridize.
• Figure 3: (a)-(b) Schematic of the laser-dressed band structure showing the emergence of the low-frequency transitions due to Floquet hybridization for (a) resonant and (b) non-resonant driving. Purple arrows signal possible low-frequency transitions. These transitions blue-shift with increasing driving-laser's (c) amplitude $E_{\mathrm{d}}$ in V/Å for resonant-driving ($\hbar\Omega=3.1$ eV) and (d) frequency $\hbar \Omega$ in eV ($E_{\mathrm{d}}=0.25$ V/Å) for non-resonant driving.