  We theoretically study the population inversion and negative dynamic
conductivity in intrinsic graphene in the terahertz (THz) frequency range upon
pulse photoexcitation with near-/mid-infrared wavelength. The threshold pulse
energy required for the population inversion and negative dynamic conductivity
can be orders-of-magnitude lower when the pulse photon energy is lower, due to
the inverse proportionality of the photoexcited carrier concentration to the
pulse photon energy and to the weaker carrier heating. We also investigate the
dependence of the dynamic conductivity on the momentum relaxation time. The
negative dynamic conductivity takes place either in high- or low-quality
graphene, where the Drude absorption by carriers in the THz frequency is weak.
