Objective Rydberg atom is a kind of alkali atoms whose outermost valence electrons are in the highly excited state with a large electric dipole moment and a very high polarization rate, which exhibits extreme sensitivity to external electric field and be utilized in microwave quantum sensing. Rydberg atom-based sensors have developed rapidly and have shown extensive applications in the fields of precise navigation, quantum metrology, communication and high-resolution remote sensing owing to its distinct advantages including high sensitivity, broad frequency bandwidth (DC-THz), SI traceability and self-calibration capability that are not available in conventional antenna-based receivers. As an emerging quantum sensor, the Rydberg atomic receiver employs laser-excited atoms to convert radio frequency (RF) fields into an optical signal that can be read out on a photodetector at baseband to detect the relevant information of the RF field. In Rydberg atom-based electrometry, under the effect of an intense coupling laser, the dispersion property of the medium changes, resulting in the absorption of the weak probe laser being reduced, which is the definition of electromagnetically induced transparency (EIT). Furthermore, when a RF field is applied near resonance using two Rydberg energy levels, the corresponding Rydberg energy levels split, resulting in a two-peak spectrum, known as Autler–Townes splitting (EIT-AT splitting). The EIT-AT splitting interval is proportional to the amplitude of the RF field, which can obtain a direct measurement of the external field by measuring the splitting interval. However, this practical deployment of this promising technology, particularly for advanced functionalities like direction positioning, faces numerous significant challenges. On the one hand, the existing single-beam detection architecture is incapable of acquiring the spatial phase differences critical for Angle of Arrival (AOA) estimation, which the multi-beam architecture could conceptually essential to overcome this limitation. On the other hand, the traditional optical beam splitters suffer from structural complexity and poor stability, which limit the application of this technology in reality positioning.

Methods In this work, in order to achieve the probe laser array and meet the exact alignment requirements of the Rydberg atoms for both the probe laser and coupling laser, we report and present a multi-beam Rydberg atomic receiver for AOA estimation utilizing a cascade liquid crystal polarization grating (LCPG), achieving a 2×2 two-dimensional (2D) collimated laser beam with an interval of 2.42 mm. First, we utilized the polarization-selective properties of the LCPG to design a beam-splitting grating with a period of 21.32 μm, which can split the incident laser into a 2×2 array of beams with deflection angles. Second, to achieve a collimated array output, we further proposed a four-zone collimating grating with a period of 14.95 μm which can collimate the four beams separately. This cascaded gratings optical system has a compact structure with beam power uniformity better than 95% and the effective collimation is over a distance greater than 15 cm, overcoming the inherent shortcomings of discrete optical components effectively. Moreover, we employ the EIT in Rydberg atomic vapor cell in conjunction with a atomic superheterodyne technology to measure the phase difference at different locations of the incident RF signal simultaneously, realizing the estimation of the angle of arrival.

Results and Discussions To demonstrate this approach, we simulated and measured phase differences of an incident X-band wave at 8.57 GHz by fixing the local oscillator signal (E_LO) and rotating the signal source (E_SIG) within the incident range of -40° to +40°. To simplify the complexity of the adjustment, we expanded the coupling laser to 5 mm to ensure full coverage of the 2×2 probe laser array and apply different photodetectors (PDs) to receive signals from each probe laser simultaneously and connect them to a multi-channel oscilloscope to obtain the phase difference \Delta \phi of the beat-note signal, thereby enabling precise determination of the AOA of the incident signal. The experimental results show that the functional relationship between the measured phase difference \Delta \phi and the AOA is highly consistent with the theoretical model and electromagnetic simulation results with the error less than 1.5°, indicating that the proposed atomic-based subwavelength multi-beam receiver can be used to determine the AOA of the RF signal.

Conclusions This work not only validates the fundamental principle of quantum-based RF direction positioning using Rydberg atom-based sensors but also establishes a practical and robust foundational unit for future advanced systems. The proposed integrated beam array scheme is highly scalable and versatile, and the 2D configuration can be directly extended to full three-dimensional (3D) arrays for omnidirectional sensing. Furthermore, the inherent design of the 2×2 laser array allows for the arbitrary combination of any three beams within a larger array to perform AOA estimation, providing redundancy and flexibility. This capability paves the way for developing sophisticated quantum sensor networks capable of multi-parameter estimation and multi-target recognition in complex spectral environments. By integrating miniaturized photonic components with atomic sensing, this research opens up new, viable avenues for the development of next-generation navigation systems, adaptive radar, and non-cooperative remote sensing technologies, marking a transition from laboratory demonstration towards practical quantum-enabled instrumentation.