Low-energy population inversion in graphene evidenced in a three-pulse pump-probe experiment

Population inversion and optical gain are often difficult to measure in systems that do not exhibit lasing. For example, two-color pump-probe experiments targeting gain require precise reference measurements in order to distinguish gain from simple absorption bleaching due to Pauli blocking. In the mid-infrared (MIR) and far-infrared (FIR) spectral range such experiments are even more difficult as free-carrier absorption complicates the analysis. Here we utilize a three-pulse technique [1], which has been employed to find evidence for gain and spectral hole burning in the near-infrared (NIR), to study the dynamics of the MIR population inversion in optically pumped intrinsic graphene. Graphene is an interesting material to apply this technique since there are on one hand many reports on ultrafast thermalization, excluding inversion, but on the other hand many suggestions to realize gain, in particular in the THz range.

The principle of the technique is sketched in Fig. 1a. A strong NIR “gain” pulse (photon energy 1.55 eV) excites interband transitions in an epitaxial multilayer graphene sample on SiC. The majority of graphene layers is almost intrinsic. The low-energy carrier dynamics is monitored by measuring the differential transmission change in a degenerate MIR (photon energy 250 meV) pump-probe experiment. This differential transmission generally is positive, corresponding to bleaching via Pauli blocking by carriers that are photoexcited by the MIR pump pulse. If, however, the gain pulse is strong enough to induce an inverted population at 250 meV, the situation is qualitatively different: Now the mid-infrared pulse causes stimulated emission from the inverted population, thus decreasing the number of carriers in the conduction band at the probed energy. Consequently, the differential transmission with regard to the MIR pump pulse changes from positive to negative (cf. Fig.1b)

In addition to the NIR fluence dependence shown in Fig. 1b we also present for the gain dynamics varying the time delay between gain pulse and mid-infrared pump pulse. The observed transient gain is a consequence of a bottleneck of carrier relaxation via optical phonons and the decreasing density of states in the vicinity of the Dirac point. NIR transient gain has been observed previously in doped graphene [2], where a bottleneck appears above the Fermi level.
References
[1] K. Kim, J. Urayama, T. B. Norris, J. Singh, J. Phillips, and P. Bhattacharya, "Gain dynamics and ultrafast spectral hole burning in In(Ga)As self-organized quantum dots," Appl. Rev. Lett. 81, 670 (2002).
[1] T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, "Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene," Phys. Rev. Lett. 108, 167401 (2012).