Femtosecond Population Inversion and Stimulated Emission of Dense Dirac Fermions in Graphene

We show that strongly photoexcited graphene monolayers with 35 fs pulses quasi-instantaneously build up a broadband, inverted Dirac fermion population. Optical gain emerges and directly manifests itself via a negative conductivity at the near-infrared region for the first 200 fs, where stimulated emission completely compensates absorption loss in the graphene layer. Our experiment-theory comparison with two distinct electron and hole chemical potentials reproduce absorption saturation and gain at 40 fs, revealing, particularly, the evolution of the transient state from a hot classical gas to a dense quantum fluid with increasing the photoexcitation.

Figure 1

(a) Schematics of ultrafast optical interband excitations. (b) Dispersion of our electron-doped graphene monolayers ($\mu =0.4\mathrm{eV}$) illustrating state filling (left) and band filling (right) that leads to stimulated emission from a broadband, inverted population (red arrow). Also shown together is the pump pulse spectrum. (c) STM images of tomography of the sample used. (d) The static differential reflectivity spectra (red dots). The threshold $\Delta R/R_c$ for zero conductivity can be directly determined $\sim -1.46\%$ (black line, see text for details).

Figure 2

(a) The degenerate differential reflectivity at 1.55 eV for the graphene monolayer (solid dots and line) and SiC substract (empty dots) under the pump fluence of $1842\mu {\mathrm{J}/\mathrm{cm}}^2$. Inset: $\Delta R/R$ in logarithmic scale (black dots) together with the pump-probe autocorrelation (red line). (b) $\Delta R/R$ at 1.55 eV for different pump fluences. The dashed straight line is a guide for the eyes. The different curves were taken in the order as marked. The perfect overlap of the pair of curves indicates the signals are not caused by laser-induced permanent changes. (c) The peak $\frac{△R}{R}{|}_{\mathrm{peak}}$ as function of the pump fluence (black squares) and the corresponding conductivity (red solid dots). Blue arrow marks the threshold for zero conductivity $\Delta R/R{|}_c=-1.4582\%$ (see text). Dashed line: linear dependence (guide to the eyes).

Figure 3

(a) Ultrafast $\Delta R/R$ at 1.55 eV pump, 1.16 eV probe, at 1116 and $3960\mu {\mathrm{J}/\mathrm{cm}}^2$, and 1.33 eV probe, at $4390\mu {\mathrm{J}/\mathrm{cm}}^2$, respectively. Blue arrow marks $\Delta R/R{|}_c=-1.4582\%$ for zero conductivity. Shown together are the pump and probe spectra. (b), The peak transient reflectivity as function of the pump fluence. (c), The extracted transient fermion density at 40 fs (blue dots), as explained in the text, which is significantly lower than $A_0{I}_p/\hslash \omega$ obtained from the universal conductivity (open circles), as illustrated in shadow area. (d), Theory (lines) vs experimental values (rectangles) for nondegenerate (red) and degenerate (blue) transient conductivity at 40 fs. Shown together (lines) are two model simulations with the single (green) or distinct (black) chemical potentials.

Figure 4

(a) The calculated transient electron (${\mu }_e$), hole (${\mu }_h$) chemical potentials and transient temperature (inset) as function of photoexcited carrier density. (b) Transient electron and hole distribution function at 40 fs are plotted for different pump fluence. The two intersection planes represent the occupation probability of an electron-hole pair at the given excitation photon energy is equal to unity, i.e., $f_e(\omega /2)+f_h(\omega /2)=1$.