Title: Chiral and coherent manipulation of photonic quantum states with Rydberg arrays

Abstract: 
We propose a novel approach to achieve unprecedentedly strong photon-photon interaction and subsequently chiral manipulation of photonic quantum states based on a two-dimensional Rydberg array driven around two-photon Raman resonance in the Autler-Townes regime. We find that a completely blocked 2D Rydberg array is equivalent to a single spatially-extended ``giant atom'' losslessly coupled to a paraxial probe field with arbitrary spatial profile, leading to perfect anticorrelation between the reflected probe photons. Combination of this ``giant atom'' with linear optical elements like beam splitters can realize chiral coupling between the atom and the probe photons with nearly perfect coupling efficiency, this further enables remarkably high-fidelity photon sorter in an almost deterministic manner.