Single atomic layer quantum holography

Quantum metasurfaces composed of subwavelength two-dimensional atomic arrays hold great promise as a practical and scalable atom-photon interface. However, these quantum metasurfaces are limited to amplitude control of photonic states thereby restricting the quantum information processing task they can implement. In this work, we present a method that enables precise control over the phase distribution of quantum photonic states. We achieve this by developing a quantum holography technique, which involves preparing a superposition of holograms and leveraging both electromagnetically induced transparency and long-range Rydberg interactions. Our method enables encoding of arbitrary recoverable images that are entangled with the atomic array degrees of freedom rapidly on the order of microseconds. Furthermore, we extend our analysis to include many-body atom-photon entangled states by establishing a quantitative mapping between the atomic and photonic states. Finally, we discuss the experimental realization of our approach, potential error mechanisms, and practical quantum optics applications.