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arXiv:2601.18426

A Theory of Single-Antenna Atomic Beamforming

Mingyao Cui, Qunsong Zeng, Kaibin Huang

quant-phcs.ITSubmitted Jan 26, 2026• Announced Jan 27, 2026• 0 citations
v1 · Jan 26, 2026v2 · Jul 5, 2026
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Abstract

Leveraging the quantum advantages of highly excited atoms, Rydberg atomic receivers (RAREs) represent a paradigm shift in radio wave detection, offering high sensitivity and broadband reception. However, existing studies largely model RAREs as isotropic point receivers and overlook the spatial variations of atomic quantum states within vapor cells, thus inaccurately characterizing their reception patterns. To address this issue, we present a theoretical analysis of the aforementioned spatial responses of a standard local-oscillator (LO)- dressed RARE. Our results reveal that increasing the vapor-cell length produces a receive beam aligned with the LO field, with a beamwidth inversely proportional to the cell length. This finding enables atomic beamforming to enhance received signal-to-noise ratio using only a single-antenna RARE. Furthermore, we derive the achievable beamforming gain by characterizing and balancing the fundamental tradeoff between the effects of increasing the vapor cell length and the exponential power decay of laser propagating through the cell. To overcome the limitation imposed by exponential decay, we propose a novel RARE architecture termed segmental vapor cell. This architecture consists of vapor-cell segments separated by clear-air gaps, allowing the total cell length (and hence propagation loss) to remain fixed while the effective cell length increases. As a result, this segmented design expands the effective atom-field interaction area without increasing the total vapor cell length, yielding a narrower beamwidth and thus higher beamforming gain as compared with a traditional continuous vapor cell.

Comments
14 pages, 8 figures. Submitted to IEEE JSAC

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Leveraging the quantum advantages of highly excited atoms, Rydberg atomic receivers (RAREs) represent a paradigm shift in radio wave detection, offering high sensitivity and broadband reception. However, existing studies largely model RAREs as isotropic point receivers and overlook the spatial variations of atomic quantum states within vapor cells, thus inaccurately characterizing their reception patterns. To address this issue, we present a theoretical analysis of the aforementioned spatial responses of a standard local-oscillator (LO)- dressed RARE. Our results reveal that increasing the vapor-cell length produces a receive beam aligned with the LO field, with a beamwidth inversely proportional to the cell length. This finding enables atomic beamforming to enhance received signal-to-noise ratio using only a single-antenna RARE. Furthermore, we derive the achievable beamforming gain by characterizing and balancing the fundamental tradeoff between the effects of increasing the vapor cell length and the exponential power decay of laser propagating through the cell. To overcome the limitation imposed by exponential decay, we propose a novel RARE architecture termed segmental vapor cell. This architecture consists of vapor-cell segments separated by clear-air gaps, allowing the total cell length (and hence propagation loss) to remain fixed while the effective cell length increases. As a result, this segmented design expands the effective atom-field interaction area without increasing the total vapor cell length, yielding a narrower beamwidth and thus higher beamforming gain as compared with a traditional continuous vapor cell.
Beamforming is conventionally understood as a collective property of many discrete antenna elements in both communication and radar fields, which links angular selectivity to array size, element spacing, and band-specific hardware. Here we uncover a fundamentally different beamforming mechanism achieved by a Rydberg atomic receiver: a Rydberg-atom vapor cell dressed by a local-oscillator field constitutes a continuous quantum aperture. In this regime, spatially-varying quantum coherence across the aperture provides continuous amplitude-phase control, allowing a directional beam pattern to emerge from one sensing volume rather than from an engineered array. We establish the theory of continuous quantum aperture and show that tailoring the local-oscillator field can directly program the aperture response. This enables reconfigurable single-peak, multipeak, and multiband beamforming within a single vapor cell. Experiments on a Rydberg atomic receiver prototype verify that practical beam patterns agree with theoretical predictions across aperture sizes, frequency bands, and local-oscillator configurations. Leveraging this new beamforming mechanism, we further demonstrate interference mitigation, multiuser access, and multiband multiuser access with the single-vapor-cell platform. Our results identify the continuous quantum aperture as a new operating principle of Rydberg atomic receivers and establish single-vapor-cell beamforming as an integrated and reconfigurable platform for spatially selective electromagnetic reception.
Rydberg atom, which exhibits a strong response to weak electric fields, is regarded as a promising atomic receiver to surpass the sensitivity of conventional receivers. However, its sensitivity is strongly limited by the noise coming from both classical and quantum levels, and how to enhance it significantly remains challenging. In theory, we aim to optimize the laser array, highlighting the importance of coherence among microwave signals and the uniformity of laser beam power within the array, to enhance the signal-to-noise ratio (SNR) and elevate sensitivity to a new standard. To enhance practical application mobility and integration, we propose two optimization schemes: a six-port fiber-coupled vapor cell probe array and cascaded diffraction gratings. We maintain steady MW signal coherence in the laser array by using identical vapor cells and positioning the probe lasers on the incident wave’s equal phase plane. Our findings reveal that the wavefront phase difference for the six-port fiber-coupled vapor cell array is 10°, while the cascaded diffraction gratings show a 16° difference, with laser intensity uniformity reaching 90.4%. In our experiment, a 4.6-dB SNR enhancement was achieved by utilizing the cascaded diffraction gratings to generate2×22 \times 22×2probe laser arrays compared to the performance of a laser beam, which can be enhanced further just by adding more laser beams. In particular, a2×22 \times 22×2laser array experimental verification yielded19 nv/cm/Hz19~\text {nv/cm}/\sqrt {\textrm {Hz}}19 nv/cm/Hz​@8.57 GHz. More importantly, the intermediate signals of the laser array maintain coherence. Therefore, SNR improvement is allowed even in detecting weak target signals amid strong noise and clutter. The results could offer an avenue for the design and optimization of ultrahigh-sensitivity Rydberg atomic receivers and promote applications in cosmology, meteorology, communication, and MW quantum technology.
The reception of electromagnetic signals becomes increasingly challenging at longer wavelengths, as conventional antenna feeds must scale with the operating wavelength, making it difficult to reconcile compactness with high sensitivity. Rydberg atoms enable direct field-to-optical conversion within deeply subwavelength sensing volumes, yet an effective receiving feed that couples incident fields into the atomic interaction volume remains underdeveloped. Here, we introduce a Rydberg atomic field-enhanced feed (RAFEF) that integrates electromagnetic field capture and enhancement with Rydberg-atomic transduction. We establish a physical model to quantify its receiving capability, Phi, that jointly accounts for sensitivity enhancement, receiving bandwidth and normalized three-dimensional volume, and experimentally obtain Phi_dB = 70.81 dB. Compared with a conventional loop-antenna feed, the RAFEF provides a higher received SNR and overall receiving capability, while its tunable narrowband response enables frequency selectivity directly at the receiving-feed stage. We further demonstrate selective recovery of a target channel from simultaneously incident signals and reception of a 93.5 MHz FM broadcast after approximately 10 km of over-the-air propagation. These results establish the RAFEF as an atomic receiving-feed architecture that exploits localized electric-field transduction to extend Rydberg-atomic reception beyond conventional electrically small antenna feeds.
Quantum microwave measurement techniques based on Rydberg atoms exhibit exceptional potential in microwave communication, sub-wavelength imaging and quantum metrology, due to the inherent advantages of self-calibration, minimal interference with external electric fields, and a broadband range of measurable frequencies. However, the current measurement sensitivity is not yet comparable to that of classical receivers. One contributing factor is the low utilization of atoms within the vapor cell, which remains a significant challenge to enhance substantially. To address this problem, scholars have proposed a variety of optical domain methods to enhance sensitivity. For example, increasing vapor cell length, utilizing multi-photons excitation or repump lasers. Despite these advancements, the study of the influence of laser beam diameter on the sensitivity is insufficient, and the lack of a comprehensive experimental investigation is not conducive to the practical application and optimization of the receiver. In this study, we investigate the impact of varying probe laser diameters on receiver sensitivity using a beam expander to adjust the diameter from 600 μm to 3 mm. Modifying the beam diameter could alter the light-atom interaction area in the vapor cell, offering a feasible approach to adjust the utilization of the atoms. Our findings indicate that under the experimental conditions, the sensitivity could be enhanced by expanding the beam diameter, where the sensitivity is changed from 299 nV cm-1 Hz-1/2 to 127 nV cm-1 Hz-1/2. These results could provide valuable insights for designing and optimizing ultrahigh-sensitivity Rydberg atomic receivers and facilitating applications in meteorology, communication, and quantum precision measurement.
In this paper, we propose a self-superheterodyne Rydberg uniform array receiver for satellite uplink communications, in which the Doppler shift naturally induced by satellite motion is exploited to generate the intermediate-frequency signal. We first develop a near-field local oscillator (LO) synthesis model and characterize the spatially varying LO electric field across the Rydberg vapor cells. Based on a vapor-cell-center approximation, a closed-form radio frequency (RF)-to-optical conversion is derived, establishing an explicit bridge between the incident satellite signal and the LO-induced cell-level response. The derived model reveals that the programmable LO serves as an analog-domain channel-shaping mechanism by controlling the cell-level transduction gain, phase response, and phase-matching behavior. Building upon this equivalent channel model, we formulate an LO design problem that maximizes the Shannon capacity of the effective channel, and develop an efficient optimization algorithm for the LO amplitudes and phases. Simulation results demonstrate that the vapor-cell transduction can reshape the effective channel, adjust the beam-pattern alignment, and moderately reduce the inter-user correlation under suitable LO configurations. Furthermore, the proposed LO design significantly improves the achievable capacity over benchmark schemes, offering a promising self-superheterodyne Rydberg architecture for future satellite communication systems.
Quantum sensing using Rydberg atoms offers unprecedented opportunities for next-generation radar systems, transcending classical limitations in miniaturization and spectral agility. This work proposes a quantum-enhanced radar reception architecture that replaces conventional antenna-tomixer chains with a centimeter-scale vapor cell as a quantum radio frequency (RF) field sensor and mixer, enabling this paradigm for radar sensing. This approach is based on electromagnetically induced transparency, which uses Autler-Townes splitting to enable direct RF-to-optical downconversion within the atomic medium via an external co-frequency reference. To circumvent the range-resolution limitation imposed by the narrow instantaneous response of the atomic receiver, we adopt a stepped-frequency synthesis strategy involving the hybrid manipulation of Rydberg energy states. This strategy combines coarse laser frequency tuning with fine AC-Stark shift compensation. Additionally, we establish a nonlinear response model of the Rydberg atomic homodyne receiver and propose a customized nonlinear compensation method that extends the linear dynamic range by over 7 dB. We developed a compressive sensing-based algorithm (CS-Rydberg) to suppress noise and mitigate the undersampling problem. Experimentally, we demonstrate a compact prototype that achieves centimeter-level ranging precision (RMSE = 1.06 cm) within 1.6–1.9 m. By synthesizing a 1-GHz equivalent bandwidth via sparse stepped-frequency sampling over 2.6–3.6 GHz, we observe resolvable target separations down to 15 cm under controlled sparse scenarios. These results validate the feasibility of quantum sensing based on Rydberg atomic receivers and underscore the architecture’s scalability. By harnessing the atoms’ ultrabroad spectral response, the synthesized bandwidth can extend well beyond the current range. This enables sub-centimeter resolution in future radar systems while preserving quantum traceable calibration and a highly simplified front end.