Coherent nonlinear optical response of graphene in the quantum Hall regime

We study the nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider the harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateau feature. The plateau heights depend on the laser intensity and broadening of the Landau levels so that they are not quantized exactly. This nonlinear effect remains robust against the significant broadening of the Landau levels. We predict realization of an experiment through the observation of the third-harmonic signal and nonlinear Faraday effect, which are within the experimental feasibility.