A quantum-dynamical theory for nonlinear optical interactions in graphene

We use a quantum-dynamical model to investigate the optical response of graphene under low excitation power. Ultrafast carrier relaxation processes, which play an important role for understanding the optical response of graphene, are included phenomenologically into the model. We obtain analytical solutions for the linear and third-order nonlinear optical response of graphene, and four-wave mixing in particular. This theory shows agreement with recently reported experimental data on linear complex optical conductivity and four-wave mixing, providing evidence for ultrafast quantum-dephasing times of approximately 1 fs.