Angle-of-arrival detection of radio-frequency waves via Rydberg atom fluorescence imaging of standing waves in a glass vapor cell

We present a method for measuring the angle-of-arrival of 40 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 and low-complexity, has an active area of nearly 4$\pi$ steradians, and is sensitive to all RF polarizations. For in-plane measurements ($\phi = 0$), we demonstrate quantitative angle-of-arrival measurements with an uncertainty on the order of one degree in an 11~s measurement, and for out-of-plane measurements (arbitrary $\theta$,$\phi$), we demonstrate angle-of-arrival detection with uncertainty on the order of several degrees.