Light amplification without population inversion in magnetised monolayer graphene

We suggest a simple approach to achieve light amplification without population inversion in Landau-quantized graphene. We provide a detailed analysis of the interaction between the applied coherent and incoherent fields and a three-level cascade-type magnetized graphene. The optical response of the system is obtained by numerically solving the density matrix equation in the transient regime. Then, the analytical expressions for the steady-state populations in Landau levels and the coherence term related to the optical gain are derived using the perturbation theory. The results demonstrate that the proposed system can deliver optical gain without population inversion, making it applicable in graphene-based optical amplifiers and lasers operating at THz frequencies.