Optical properties of Floquet Topological Insulators

Irradiated graphene may become a Floquet topological insulator - a time dependent topological system with a topological quasi energy spectrum and states. We derive an approximate expression for the optical conductivity of the system at zero temperature. We treat the probe field using linear response while taking care of the pump field via Floquet theory. An analytic expression is possible to obtain when the pump field is turned on suddenly (quench) and the quasi-energy states are approximated near avoided crossing points. We estimate the amplitude of various optical transitions which govern the optical response.