Phase Retrieval for Rydberg Quantum Arrays

Rydberg-aided atomic electrometry has recently garnered significant research interest for detecting external electric fields. However, the inability of Rydberg probes to detect phase remains a serious impediment to their realistic deployment. In phased array or synthetic aperture applications, if a Rydberg atom probe is used in place of an antenna, then measurements of only electric field intensity are possible at each spatial sample. In this paper, we cast the extraction of useful information from these Rydberg probe measurements as a novel phase retrieval problem. The resulting optimization is non-convex, which we address by developing a three-stage alternating projections algorithm. Our numerical experiments demonstrate the effectiveness of the proposed algorithm in terms of the beamformed array output.