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 τ(1) and τ(2) time constants that denote carrier relaxation and quantum decoherence, respectively. Fits to existing experimental data yield τ(2) < 1 fs due to carrier-carrier scattering. τ(1) is found to be on the timescale from 250 fs to 550 fs, showing agreement with experimental data obtained by differential transmission measurements.
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