  The optical properties of graphene are made unique by the linear band
structure and the vanishing density of states at the Dirac point. It has been
proposed that even in the absence of a semiconducting bandgap, a relaxation
bottleneck at the Dirac point may allow for population inversion and lasing at
arbitrarily long wavelengths. Furthermore, efficient carrier multiplication by
impact ionization has been discussed in the context of light harvesting
applications. However, all these effects are difficult to test quantitatively
by measuring the transient optical properties alone, as these only indirectly
reflect the energy and momentum dependent carrier distributions. Here, we use
time- and angle-resolved photoemission spectroscopy with femtosecond extreme
ultra-violet (EUV) pulses at 31.5 eV photon energy to directly probe the
non-equilibrium response of Dirac electrons near the K-point of the Brillouin
zone. In lightly hole-doped epitaxial graphene samples, we explore excitation
in the mid- and near-infrared, both below and above the minimum photon energy
for direct interband transitions. While excitation in the mid-infrared results
only in heating of the equilibrium carrier distribution, interband excitations
give rise to population inversion, suggesting that terahertz lasing may be
possible. However, in neither excitation regime do we find indication for
carrier multiplication, questioning the applicability of graphene for light
harvesting. Time-resolved photoemission spectroscopy in the EUV emerges as the
technique of choice to assess the suitability of new materials for
optoelectronics, providing quantitatively accurate measurements of
non-equilibrium carriers at all energies and wavevectors.
