Floquet-Bloch Photonic Drive

Floquet theory applies to periodically driven quantum systems H(t+T)=H(t). By Bloch's theorem in time, solutions are Floquet states ψ(t) = e^{−iεt/ħ}u(t) where ε is the quasi-energy (defined mod ħΩ). A two-level system driven at frequency Ω develops photon replica bands at ε ± nħΩ. When the driving amplitude A is large enough, avoided crossings at quasi-energy zone boundaries open Floquet gaps. The Bloch sphere shows the driven spin trajectory for the selected parameters.