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
