  We present the non-linear DC photoconductivity of graphene under strong
infra-red (IR) radiation. The photoconductivity is obtained as the response to
a strong DC electric field, with field strengths outside of the linear-response
regime, while the IR radiation is described by a strong AC electric field. The
conductivity displays two distinct regimes in which either the DC or the AC
field dominates. We explore these regimes and associate them with the dynamics
of driven Landau-Zener quenches in the case of a large DC field. In the limit
of large AC field, we describe the conductivity in a Floquet picture and
compare the results to the closely related Tien-Gordon effect. We present
analytical calculations for the non-linear differential photoconductivity, for
both regimes based on the corresponding mechanisms. As part of this discussion
of the non-equilibrium state of graphene, we present analytical estimates of
the conductivity of undriven graphene as a function of temperature and DC bias
field strength that show very good agreement with our simulations.
