Giant optical nonlinearity of graphene in a strong magnetic field

We show that graphene in a magnetic field possesses by far the highest third-order optical nonlinearity among all known materials. The giant nonlinearity originates from unique electronic properties and selection rules for transitions between Landau levels near the Dirac point. As a result, even one monolayer of graphene gives rise to appreciable nonlinear frequency conversion efficiency for incident infrared radiation. We present quantum-mechanical density-matrix formalism for calculating the nonlinear optical response of graphene in the magnetic field, valid for arbitrarily strong magnetic and optical fields.