Stimulated Rayleigh Scattering Enhanced by a Longitudinal Plasma Mode in a Periodically Driven Dirac Semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$

Using broadband (12–45 THz) multi-terahertz spectroscopy, we show that stimulated Rayleigh scattering dominates the transient optical conductivity of cadmium arsenide, a Dirac semimetal, under an optical driving field at 30 THz. The characteristic dispersive line shape with net optical gain is accounted for by optical transitions between light-induced Floquet subbands, strikingly enhanced by the longitudinal plasma mode. Stimulated Rayleigh scattering with an unprecedentedly large refractive index change may pave the way for slow light generation in conductive solids at room temperature.

Figure 1

(a) Band structure of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ around the $\mathrm{\Gamma }$ point [26]. (b) Schematic picture of the Floquet state formation by a periodic optical field. (c) Setup of the pump-probe experiment. (d) Optical conductivity of the sample. The model fitting (dotted line) takes into account the lower-frequency data outside the panel [25].

Figure 2

(a) Change of the optical conductivity as a function of frequency (horizontal axis) and pump-probe delay time $\mathrm{\Delta }t$ (vertical axis). Waveform of the pump pulse is shown on the left. The equilibrium optical conductivity is plotted on the bottom along with the pump power spectrum. Pump and probe pulses are collinearly polarized. (b) Transient optical conductivity at several delay times. The equilibrium spectrum is shown as a dotted line. (c) Optical conductivity at $\mathrm{\Delta }t=0.04\mathrm{ps}$ for different pump frequencies, i.e., 29.4 [the same as in (a),(b)] and 18.2 THz (with a fluence of $0.25\mathrm{mJ}/{\mathrm{cm}}^2$, a peak electric field of $0.9\mathrm{MV}/\mathrm{cm}$). (d) Delay time dependence of the peak and dip values extracted from (a). Temporal profile of the pump intensity is shown as the shaded curve. (e) Top: Positions of the peak and the dip in optical conductivity at $\mathrm{\Delta }t=0.04\mathrm{ps}$, as a function of pump fluence. Bottom: A similar plot for the conductivity values at the peak and the dip. Equilibrium values at 28.2 and 31.3 THz are added as open triangles.

Figure 3

(a) Change of the optical conductivity $\mathrm{\Delta }{\sigma }_1$ calculated by a phenomenological model. Theoretical details are given in Supplemental Material [27]. (b) Two-dimensional plot of $\mathrm{\Delta }{\sigma }_1$ as a function of frequency (horizontal axis) and pump-probe delay time (vertical axis). (c) Transient optical conductivity calculated by a microscopic model. (d) Contributions from the paramagnetic (blue) and diamagnetic (red) currents in the total optical conductivity (black) at $\mathrm{\Delta }t=-0.12\mathrm{ps}$. (e) Geometric picture of stimulated Rayleigh scattering (SRLS) and four-wave mixing (FWM). ${\mathbf{k}}_0$ and ${\mathbf{k}}_1$ denote wave vectors of the pump and the probe, respectively. (f) SRLS induced by Floquet states in continuous bands. Ordinary ac Stark effect corresponds to transitions between the topmost and bottom peaks, and between the intermediate peaks, in the right panel.

Figure 4

(a) Transient optical conductivity for broader (thin) and narrower (thick) pump pulses. Pump power spectra are plotted on the bottom with their FWHM indicated in the figure. The broader pump is the same as in Fig. 2, while the narrower one has a pulse width of 0.88 ps, a fluence of $1.7\mathrm{mJ}/{\mathrm{cm}}^2$, and a peak electric field of $1.2\mathrm{MV}/\mathrm{cm}$. (b) Refractive index $n$ (top), extinction coefficient $\kappa$ (middle), and group refractive index $n_g$ (bottom) measured at $\mathrm{\Delta }t=-0.48\mathrm{ps}$ for the narrower pump in (a). Equilibrium spectra are shown as dotted lines. (c) The same dataset for $\mathrm{\Delta }t=-0.24\mathrm{ps}$.