A Theory of Atomic Beamforming

Leveraging the quantum advantages of highly excited atoms, Rydberg atomic receivers (RAREs) represent a paradigm shift in microwave detection with extremely high sensitivity and broadband tunability.

However, existing studies often model RAREs as isotropic point receivers and neglect the spatial variation of Rydberg atomic states within vapor cells, which can lead to inaccurate characterization of their reception patterns.

To address this issue, we theoretically analyze the spatial response of a local-oscillator (LO) field-dressed RARE.

Our results reveal that as the vapor-cell length increases, a receiving beam aligned with the LO field is formed, and its beamwidth is inversely proportional to the cell length.

This finding enables atomic beamforming with only a single atomic vapor cell to enhance signal-to-noise ratio.

Furthermore, we analyze the maximum beamforming gain of a single vapor cell by balancing the fundamental tradeoff between improved spatial selectivity and increased laser attenuation in the atomic medium as the vapor cell length becomes longer.

To mitigate the beamforming-gain loss caused by laser attenuation, we further propose a segmental-vapor-cell architecture.

In this architecture, multiple short vapor cells are arranged along the optical propagation path and separated by clear-air gaps.

This design effectively expands the reception aperture while keeping the total vapor-cell length, and hence attenuation loss, fixed.

As a result, it achieves a narrower beamwidth and higher beamforming gain than a conventional single-vapor-cell receiver, as demonstrated by extensive numerical results.