  We reveal that optical saturation of the low-energy states takes place in
graphene for arbitrarily weak electromagnetic fields. This effect originates
from the diverging field-induced interband coupling at the Dirac point. Using
semiconductor Bloch equations to model the electronic dynamics of graphene, we
argue that the charge carriers undergo ultrafast Rabi oscillations leading to
the anomalous saturation effect. The theory is complemented by a many-body
study of the carrier relaxations dynamics in graphene. It will be demonstrated
that the carrier relaxation dynamics is slow around the Dirac point, which in
turn leads to a more pronounced saturation. The implications of this effect to
the nonlinear optics of graphene is then discussed. Our analysis show that the
conventional perturbative treatment of the nonlinear optics, i.e., expanding
the polarization field in a Taylor series of the electric field, is problematic
for graphene, in particular at small Fermi levels and large field amplitudes.
