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The development of a microwave electrometer with inherent uncertaintyapproaching its ultimate limit carries both fundamental and technologicalsignificance. Recently, the Rydberg electrometer has garnered considerableattention due to its exceptional sensitivity, small-size, and broad tunability.This specific quantum sensor utilizes low-entropy laser beams to detectdisturbances in atomic internal states, thereby circumventing the intrinsicthermal noise encountered by its classical counterparts. However, due to thethermal motion of atoms, the advanced Rydberg-atom microwave electrometer fallsconsiderably short of the standard quantum limit by over three orders ofmagnitude. In this study, we utilize an optically thin medium withapproximately 5.2e5 laser-cooled atoms to implement heterodyne detection. Bymitigating a variety of noises and strategically optimizing the parameters ofthe Rydberg electrometer, our study achieves an electric-field sensitivity of10.0 nV/cm/Hz^1/2 at a 100 Hz repetition rate, reaching a factor of 2.6 abovethe standard quantum limit and a minimum detectable field of 540 pV/cm. We alsoprovide an in-depth analysis of noise mechanisms and determine optimalparameters to bolster the performance of Rydberg-atom sensors. Our workprovides insights into the inherent capacities and limitations of Rydbergelectrometers, while offering superior sensitivity for detecting weak microwavesignals in numerous applications.

Approaching the standard quantum limit of a Rydberg-atom microwave electrometer