  Graphene is a unique platform for tunable opto-electronic applications thanks
to its linear band dispersion, which allows electrical control of resonant
light-matter interactions. Tuning the nonlinear optical response of graphene is
possible both electrically and in an all-optical fashion, but each approach
involves a trade-off between speed and modulation depth. Here, we combine
lattice temperature, electron doping, and all-optical tuning of third-harmonic
generation in a hBN-encapsulated graphene opto-electronic device and
demonstrate up to 85% modulation depth along with gate-tunable ultrafast
dynamics. These results arise from the dynamic changes in the transient
electronic temperature combined with Pauli blocking induced by the
out-of-equilibrium chemical potential. Our work provides a detailed description
of the transient nonlinear optical and electronic response of graphene, which
is crucial for the design of nanoscale and ultrafast optical modulators,
detectors and frequency converters.
