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arXiv:2502.09835 · Journal of Applied Physics

Determining angle of arrival of radio-frequency fields using subwavelength, amplitude-only measurements of standing waves in a Rydberg atom sensor

Rajavardhan Talashila, William J. Watterson, Benjamin L. Moser, Joshua A. Gordon, Alexandra B. Artusio‐Glimpse, Nikunjkumar Prajapati, Noah Schlossberger, Matthew T. Simons, Christopher L. Holloway

Published Sep 15, 2025• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0285778

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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.
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 ∣mJ∣|m_J|∣mJ​∣ 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∘−40∘20^\circ-40^\circ20∘−40∘ region of highest angular sensitivity, the estimated repeatability-based 1σ1σ1σ AoA uncertainty ranges from approximately 0.6∘0.6^\circ0.6∘ to 2∘2^\circ2∘ 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.
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.
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.
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.
We present a method for measuring the angle of arrival of 37-GHz radio-frequency (rf) radiation by mapping the standing waves generated in a rectangular glass vapor cell. These standing waves have regular and well-defined structure from which we can infer the angle and sign of the wavevector of the rf field. We map the field using spatially resolved light sheet spectroscopy of Rydberg states of rubidium atoms in the cell. Unlike traditional phased arrays, this detection scheme is compact, has an active area of nearly 4 π steradians, and is sensitive to all rf polarizations. For in-plane measurements ( ϕ = 0 ), we demonstrate quantitative angle-of-arrival measurements with an uncertainty of the order of 1 ∘ in an 11-s measurement, and for out-of-plane measurements (arbitrary θ , ϕ ), we demonstrate angle-of-arrival detection with uncertainty of the order of several degrees.