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We reveal that optical saturation of the low-energy states takes place ingraphene for arbitrarily weak electromagnetic fields. This effect originatesfrom the diverging field-induced interband coupling at the Dirac point. Usingsemiconductor Bloch equations to model the electronic dynamics of graphene, weargue that the charge carriers undergo ultrafast Rabi oscillations leading tothe anomalous saturation effect. The theory is complemented by a many-bodystudy of the carrier relaxations dynamics in graphene. It will be demonstratedthat the carrier relaxation dynamics is slow around the Dirac point, which inturn leads to a more pronounced saturation. The implications of this effect tothe nonlinear optics of graphene is then discussed. Our analysis show that theconventional perturbative treatment of the nonlinear optics, i.e., expandingthe polarization field in a Taylor series of the electric field, is problematicfor graphene, in particular at small Fermi levels and large field amplitudes.

Anomalous optical saturation of low-energy Dirac states in graphene and its implication for nonlinear optics