High-frequency Light Reflector via Low-frequency Light Control

We show that the momentum of light can be reversed via the atomic coherence created by another light with one or two orders of magnitude lower frequency. Both the backward retrieval of single photons from a timed Dicke state and the reflection of continuous waves by high-order photonic band gaps are analysed. The required control field strength scales linearly with the nonlinearity order, which is explained by the dynamics of superradiance lattices. Experiments are proposed with $^{85}$Rb atoms and Be$^{2+}$ ions. This holds promise for light-controllable X-ray reflectors.