Manipulation of path state based on spatiotemporal dielectric metasurface

In this work, a spatiotemporal metasurface is proposed to manipulate the path of photons flexibly. The spatial modulation is induced by the rectangle silicon units aligned on silica in a manner with a phase gradient only for y-polarized photons, and the temporal modulation is contributed by the pumps of constructing Kerr dynamic gratings. By quantizing designed metasurfaces, the analytical solutions of output photon states can be derived correspondingly. Reversal design could be implemented by tailoring the profile of higher harmonics to infer the intensity of pumps, size of meta-atoms, and initial state. The path-polarization entanglement and correlations of output photons are realized, and then a CNOT gate is obtained by utilizing the deflection of the photon path. This work provides a scheme to deal with the spatiotemporal metasurfaces and expands the applications of metasurfaces in the quantum realm.