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Graphene exhibits extremely strong optical nonlinearity when a strongperpendicular magnetic field is applied, the response current shows strongfield dependence even for moderate light intensity, and the perturbation theoryfails. We nonperturbatively calculate full optical conductivities induced by aperiodic field in an equation-of-motion framework based on the Floquet theorem,with the scattering described phenomenologically. The nonlinear response athigh fields is understood in terms of the dressed electronic states, or Floquetstates, which is further characterized by the optical conductivity for a weakprobe light field. This approach is illustrated for a magnetic field at $5$ Tand a driving field with photon energy $0.05$ eV. Our results show that theperturbation theory works only for weak fields $<3$ kV/cm, confirming theextremely strong light matter interaction for Landau levels of graphene. Thisapproach can be easily extended to the calculation of optical conductivities inother systems.

Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field