Enhanced metrology at the critical point of a many-body Rydberg atomic system

The spectral properties of an interacting many-body system may display critical character and have potential applications in precision metrology. Here, we demonstrate such many-body enhanced metrology for microwave (MW) electric fields in a non-equilibrium Rydberg atomic gas. Near criticality the high sensitivity of Rydberg atoms to external MW electric fields, combined with many-body enhancement induces significant changes in the optical transmission. We quantify this behavior using the Fisher information. For continuous optical transmission at the critical point, the Fisher information is three orders of magnitude larger than in independent particle systems, the measured data provides an equivalent sensitivity of 49 nV/cm/$\textrm{Hz}^{1/2}$. The reported results constitute a milestone towards the application of many-body effects in precision metrology.