  We show that strongly photoexcited graphene monolayers with 35fs pulses
quasi-instantaneously build up a broadband, inverted Dirac fermion population.
Optical gain emerges and directly manifests itself via a negative optical
conductivity for the first 200fs, 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 40fs, revealing, particularly, the evolution
of the transient state from a hot classical gas to a dense quantum fluid with
increasing the photoexcitation.
