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IEEE Transactions on Instrumentation and Measurement

Measurement of Doppler Frequency Shift and Angle of Arrival With Rydberg Atom-Based Sensors

Shaochen Yan, LI Xin-yao, Xiaoyan Pang, Ruiqiong Wang, Wen Wen, Weile Zhai, Wanzhao Cui, Yongsheng Gao

Published Jan 1, 2025• 10 citations

Abstract

Doppler frequency shift (DFS) and angle of arrival (AOA) measurements play a crucial role in modern radar, aviation, and satellite communication systems. Rydberg atom-based receivers are renowned for the high sensitivity, wide operating frequency range, and immunity to electromagnetic interference in microwave electric field sensing. In this work, the concept of electromagnetically induced transparency (EIT) with Rydberg atoms, along with heterodyne mixing techniques, is employed to accurately measure both the DFS and AOA of microwave field within a unified experimental system. The proposed scheme utilizes the dual-coupled beams in the Rydberg atom vapor cell to reduce experimental errors and improve the measurement accuracy. The experimental results indicate that within the frequency measurement range from 11 to 18 GHz, the experimental error in measuring the DFS of different Rydberg states is within ±0.5 Hz, showcasing the wideband tunability of the system. Moreover, the AOA measurement for the echo signal reveal that the measurement error is less than 0.5° within the range from –30° to 35°. This research shows the first instance of simultaneously measuring DFS and AOA within the same Rydberg atom system. Additionally, by introducing the concept of ’relative frequency zero point’ in DFS measurement for the first time, the differentiation of the direction of the DFS can be identified. Furthermore, the accuracy of AOA measurement based on Rydberg atoms has been further improved in this research. Overall, this research provides a novel approach for measuring DFS and AOA using Rydberg atomic system.

DOI: 10.1109/tim.2025.3568981

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Doppler frequency shift (DFS) and angle of arrival (AOA) measurements play a crucial role in modern radar, aviation, and satellite communication systems. Rydberg atom-based receivers are renowned for the high sensitivity, wide operating frequency range, and immunity to electromagnetic interference in microwave electric field sensing. In this work, the concept of electromagnetically induced transparency (EIT) with Rydberg atoms, along with heterodyne mixing techniques, is employed to accurately measure both the DFS and AOA of microwave field within a unified experimental system. The proposed scheme utilizes the dual-coupled beams in the Rydberg atom vapor cell to reduce experimental errors and improve the measurement accuracy. The experimental results indicate that within the frequency measurement range from 11 to 18 GHz, the experimental error in measuring the DFS of different Rydberg states is within ±0.5 Hz, showcasing the wideband tunability of the system. Moreover, the AOA measurement for the echo signal reveal that the measurement error is less than 0.5° within the range from –30° to 35°. This research shows the first instance of simultaneously measuring DFS and AOA within the same Rydberg atom system. Additionally, by introducing the concept of ’relative frequency zero point’ in DFS measurement for the first time, the differentiation of the direction of the DFS can be identified. Furthermore, the accuracy of AOA measurement based on Rydberg atoms has been further improved in this research. Overall, this research provides a novel approach for measuring DFS and AOA using Rydberg atomic system.

The determination of the angle of arrival (AoA) of Ku-band microwave signals is of great significance in satellite communications, spectrum monitoring, and national defense security, which has created an urgent demand for high-precision and interference-resistant passive detection techniques. In this study, we propose a Rydberg-atom-based passive measurement method for estimating the AoA of Ku-band incident signals. Based on well-established quantum optical techniques, the proposed method converts the EIT-AT splitting intervals induced by waves or signals incident from different directions in Rydberg atoms within a single vapor cell into the electric-field intensity at the atomic sensor. An electric-field-intensity-angle response model is then established for AoA estimation of a 13.6 GHz wave or signal. Simulation results demonstrate that the proposed method can determine the incident direction within a certain angular range, with an estimation error of less than 3.8°. Without the need for self-calibration and free from interference caused by actively emitted probing electromagnetic waves or reference electric fields, the proposed approach enables AoA determination of incident waves or signals using a single vapor cell with a length of 5 cm.

The electric field sensing technology based on the Rydberg atom has attracted widespread attention due to its powerful detection ability for the amplitude, phase, and polarization of the electric field. In this work, based on the electromagnetically induced transparency (EIT) of the Rydberg atom and combined with a heterodyne Rydberg atom-based mixer, we measured the binary array composed of the Rydberg Field Probes (RFPs). The measured phase difference of the electric field at two different RFPs is related to the direction of incidence. We digitally transform the received signal at 2.63 GHz and conduct digital beamforming (DBF) processing to obtain its array pattern and beam direction. The measurement accuracy and reliability are greatly improved compared with the phase comparison method, and the angle-of-arrival (AOA) variance is less than 1.5°. The effectiveness of DBF based on the Rydberg atomic sensor is verified, which lays the foundation for the subsequent linear and planar array reception of the Rydberg atomic sensor. In addition, the occlusion based on RFPs is also measured, and its weak occlusion characteristics are confirmed. This unique feature provides feasible support for the 3-D receiving array based on the Rydberg atomic sensor.

We demonstrate a method for determining the magnitude of the angle of arrival (AoA) of a linearly polarized radio-frequency (RF) field using the angle-dependent spectral amplitudes of AC Stark-shifted electromagnetically induced transparency (EIT) resonances. An off-resonant RF field produces distinct Stark shifts of the

|m_J|

sublevels, while their relative excitation strengths depend strongly on the relative orientation of the RF and optical polarizations. Under the controlled polarization geometry considered here, this dependence enables determination of the AoA magnitude without requiring RF phase measurements or spatially separated sensing locations. We experimentally demonstrate the method at RF frequencies of 1.27 GHz, 2 GHz, 3 GHz, and 4 GHz using a subwavelength cesium vapor cell. Within the

20^\circ-40^\circ

region of highest angular sensitivity, the estimated repeatability-based

1σ

AoA uncertainty ranges from approximately

0.6^\circ

to

2^\circ

across the investigated RF frequencies. A model combining Floquet-Shirley calculations of the RF-dressed Rydberg states with a coherent hyperfine-to-fine-structure optical excitation model qualitatively reproduces the experimental observations. These results establish a path toward compact, phase-independent AoA sensing using spatially localized Rydberg-atom spectroscopy.

Deep subwavelength radio-frequency (RF) imaging with atomic Rydberg sensors has overcome fundamental limitations of traditional antennas and enabled ultra-wideband detection of omni-directional time varying fields all in a compact form factor. However, in most applications, Rydberg sensors require the use of a secondary strong RF reference field to serve as a phase reference. Here, we demonstrate a new type of Rydberg sensor for angle-of-arrival (AoA) sensing, which utilizes subwavelength imaging of standing wave fields. By placing a metallic plate within the Rydberg cell, we can determine the AoA independent of the strength of incoming RF field and without requiring a secondary strong RF phase reference field. We perform precision AoA measurements with a robotic antenna positioning system for 4.2, 5.0, and 5.7 GHz signals and demonstrate a 1.7° polar angular resolution from 0° to 60° AoA and 4.1° over all possible angles.

Microwave angle-of-arrival(AoA) measurement is essential for radar, communication, and spectrum mon-itoring. Existing Rydberg-atom-based AoA schemes employ phase-difference measurements with local oscil-lators, standing-wave fluorescence imaging, or amplitude-ratio readout with internal metal reflectors. Here we demonstrate a new approach: a cylindrical glass vapor cell serving directly as an angle-encoding dielectric structure, eliminating the need for multiple apertures, local oscillators, or imaging optics. The cylindrical geometry produces angle-dependent reflection and field redistribution, mapping the incident AoA onto the effective microwave field sampled by the Rydberg ensemble. This effective field is read out optically via the Autler-Townes(A-T) splitting in the electromagnetically induced transparency(EIT) spectrum. Full-wave simulations and experiments at 11.64 GHz confirm a deterministic, geometry-mediated response over 0°-90°.Over the monotonic operating range(55°-125°), the angular resolution(minimum distinguishable increment)is 0.05°, and the angular accuracy(RMSE of repeated measurements) is 0.13° across the full range, improving to 0.05° in the optimal region(65°-115°). Occupying a sensing volume of~2.5 cm3, this method offers a compact, single-sensor pathway toward Rydberg AoA receivers.

In this work, we demonstrate the use of a Rydberg atom-based sensor for determining the angle of arrival of an incident radio frequency (RF) wave or signal. The technique uses electromagnetically induced transparency in Rydberg atomic vapor in conjunction with a heterodyne Rydberg atom-based mixer. The Rydberg atom mixer measures the phase of the incident RF wave at two different locations inside an atomic vapor cell. The phase difference at these two locations is related to the direction of arrival of the incident RF wave. To demonstrate this approach, we measure phase differences of an incident 19.18 GHz wave at two locations inside a vapor cell filled with cesium atoms for various incident angles. Comparisons of these measurements with both the full-wave simulation and the plane wave theoretical model show that these atom-based sub-wavelength phase measurements can be used to determine the angle of arrival of an RF field.