Giant Optical Nonlinearity of Graphene in a Strong Magnetic Field

We calculate the nonlinear optical response of graphene in strong magnetic and optical fields, using a quantum-mechanical density-matrix formalism. We show that graphene in a magnetic field possesses a giant mid- or far-infrared optical nonlinearity, perhaps the highest among known materials. The high nonlinearity originates from unique electronic properties and selection rules near the Dirac point. As a result, even one monolayer of graphene gives rise to an appreciable nonlinear frequency conversion efficiency for incident infrared radiation.