Quantum Force Sensing by Digital Twinning of Atomic Bose-Einstein Condensates

High sensitivity detection plays a vital role in science discoveries and technological applications. While intriguing methods utilizing collective many-body correlations and quantum entanglements have been developed in physics to enhance sensitivity, their practical implementation remains challenging due to rigorous technological requirements. Here, we propose an entirely data-driven approach that harnesses the capabilities of machine learning, to significantly augment weak-signal detection sensitivity. In an atomic force sensor, our method combines a digital replica of force-free data with anomaly detection technique, devoid of any prior knowledge about the physical system or assumptions regarding the sensing process. Our findings demonstrate a significant advancement in sensitivity, achieving an order of magnitude improvement over conventional protocols in detecting a weak force of approximately $10^{-25}~\mathrm{N}$. The resulting sensitivity reaches $1.7(4) \times 10^{-25}~\mathrm{N}/\sqrt{\mathrm{Hz}}$. Our machine learning-based signal processing approach does not rely on system-specific details or processed signals, rendering it highly applicable to sensing technologies across various domains.