Full-band quantum-dynamical theory of saturation and four-wave mixing in graphene

The linear and nonlinear optical response of graphene are studied within a quantum-mechanical, full-band, steady-state density-matrix model. This nonpurtabative method predicts the saturatable absorption and saturable four-wave mixing of graphene. The model includes τ1 and τ2 time constants that denote carrier relaxation and quantum decoherence, respectively. Fits to existing experimental data yield τ2<1 fs due to carrier–carrier scattering. τ1 is found to be on the timescale from 250 fs to 550 fs, showing agreement with experimental data obtained by differential transmission measurements.