Restrictions of microwave electrometry due to nonlocal interactions in Rydberg atoms

Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.