  High intensity laser pulses were recently shown to induce a population
inverted transient state in graphene [T. Li et al. Phys. Rev. Lett. 108, 167401
(2012)]. Using a combination of hydrodynamic arguments and a kinetic theory we
determine the post-transient state relaxation of hot, dense, population
inverted electrons towards equilibrium. The cooling rate and charge-imbalance
relaxation rate are determined from the Boltzmann-equation including
electron-phonon scattering. We show that the relaxation of the population
inversion, driven by inter-band scattering processes, is much slower than the
relaxation of the electron temperature, which is determined by intra-band
scattering processes. This insight may be of relevance for the application of
graphene as an optical gain medium.
