  The ability to tune the optical response of a material via electrostatic
gating is crucial for optoelectronic applications, such as electro-optic
modulators, saturable absorbers, optical limiters, photodetectors and
transparent electrodes. The band structure of single layer graphene (SLG), with
zero-gap, linearly dispersive conduction and valence bands, enables an easy
control of the Fermi energy E$_F$ and of the threshold for interband optical
absorption. Here, we report the tunability of the SLG non-equilibrium optical
response in the near-infrared (1000-1700nm/0.729-1.240eV), exploring a range of
E$_F$ from -650 to 250 meV by ionic liquid gating. As E$_F$ increases from the
Dirac point to the threshold for Pauli blocking of interband absorption, we
observe a slow-down of the photobleaching relaxation dynamics, which we
attribute to the quenching of optical phonon emission from photoexcited charge
carriers. For E$_F$ exceeding the Pauli blocking threshold, photobleaching
eventually turns into photoinduced absorption, due to hot electrons' excitation
increasing SLG absorption. The ability to control both recovery time and sign
of nonequilibrium optical response by electrostatic gating makes SLG ideal for
tunable saturable absorbers with controlled dynamics.
