A Theory of Single-Antenna Atomic Beamforming

TL;DR

This work demonstrates that Rydberg atomic receivers (RAREs) with spatially varying quantum states inside vapor cells can act as single-antenna beamformers, aligning a directional receive beam with the local oscillator (LO) field. By deriving a closed-form signal/noise model for continuous and segmental vapor cells, it shows that long cells yield directional patterns with beamwidth ~$\lambda_l/L$, while laser attenuation imposes a PSN-limited decay; a segmental vapor-cell architecture mitigates this by enlarging the effective interaction length without increasing propagation loss. The results establish a trade-off between BBR- and PSN-limited SNR, reveal optimal lengths and segmentation strategies, and demonstrate substantial beamforming gains and channel-capacity benefits, including interference mitigation. These insights pave the way for low-cost, broadband, and highly directional quantum receivers with potential applications in next-generation wireless sensing and communication systems.

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.

Figures (8)

• Figure 1: (a) Atomic energy levels and (b) architecture of a Rydberg atomic receiver .
• Figure 2: Long vapor cell as an atomic beamformer.
• Figure 3: Architecture of a segmental vapor cell.
• Figure 4: Antenna patterns of continuous vapor cells. The LO's incident directions are set as $0$, $\frac{\pi}{4}$, and $\frac{\pi}{2}$, and the cell length grows from $1\:{\rm cm}$ to $20\:{\rm cm}$.
• Figure 5: Influence of length, $L$, of a continuous vapor cell on SNR. (a) Evaluations of asymptotic SNRs for short and long cells. (b) Evaluations of SNRs in BBR and PSN regimes.