Rydberg atoms for electric field gradiometry

We propose a quantum sensor for electric fields based on networks of Rydberg atoms. The sensing mechanism exploits the strong dependence of the Rydberg blockade on the applied electric field near a F\"orster resonance. In this regime, variations of the electric field across the array lead to local changes in the blockade radius. Therefore, owing to its spatially distributed architecture, the device can operate as a gradiometer. Our analysis shows that our scheme enables detection of spatial variations in the electric field with a resolution of a few $\mu$m. We analyse the dynamics of Rydberg excitations for systems with different spatial geometries and electric field configurations to establish the relation between the applied field and the blockade response. For spatially inhomogeneous fields, we also provide another observable, density-density correlations, that can probe the field's spatial structure.