Metasurfaces mould the flow of classical light waves by engineering subwavelength patterns from dielectric or metallic thin films. We introduce and analyse a method in which quantum operator-valued reflectivity can be used to control both the spatiotemporal and quantum properties of transmitted and reflected light. Such quantum metasurfaces are realized by entangling the macroscopic response of atomically thin atom arrays to light. We show that such a system allows for parallel quantum operations between atoms and photons as well as for the generation of highly entangled photonic states such as photonic Greenberger–Horne–Zeilinger and three-dimensional cluster states suitable for quantum information processing. We analyse the influence of imperfections as well as specific implementations based on atom arrays excited into Rydberg states.

超表面通过工程化电介质或金属薄膜的亚波长图案来塑造经典光波的流动。我们介绍并分析了一种方法，其中量子算子值反射率可用于控制透射光和反射光的时空和量子特性。通过纠缠原子薄原子阵列对光的宏观响应来实现这种量子超表面。我们证明了这样一个系统可以在原子和光子之间进行并行量子操作，还可以生成高度纠缠的光子状态，例如光子Greenberger–Horne–Zeilinger和适用于量子信息处理的三维簇状态。我们分析不完美的影响以及基于激发到里德堡状态的原子阵列的特定实现。