  Landau level lasers have the advantage of tunability of the laser frequency
by means of the external magnetic field. The crucial prerequisite of such a
laser is a population inversion between optically coupled Landau levels.
Efficient carrier-carrier and carrier-phonon scattering generally suppresses
this effect in conventional materials. Based on microscopic calculations, we
predict for the first time the occurrence of a long-lived population inversion
in Landau-quantized graphene and reveal the underlying many-particle
mechanisms. To guide the experimental demonstration, we present optimal
conditions for the observation of a maximal population inversion in terms of
experimentally accessible parameters, such as the strength of the magnetic
field, pump fluence, temperature, and doping. We reveal that in addition to the
tunability of the Landau-level laser frequency, also the polarization of the
emitted light can be tuned via gate voltage controlling the doping of the
sample.
