High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations and the detection of surface roughness of nanostructures. Recent years have witnessed much progress on sensing alternating electromagnetic forces for the rapidly advancing quantum technology—orders of magnitude improvement has been accomplished on the detection sensitivity with atomic sensors, whereas such high-precision measurements for static electromagnetic forces have rarely been demonstrated. Here, based on quantum atomic matter waves confined by a two-dimensional optical lattice, we perform precision measurement of static electromagnetic forces by imaging coherent wave mechanics in the reciprocal space. The lattice confinement causes a decoupling between real-space and reciprocal dynamics, and provides a rigid coordinate frame for calibrating the wavevector accumulation of the matter wave. With that we achieve a state-of-the-art sensitivity of $2.30(8)\times {10}^{-26}$ N/$\sqrt{\mathrm{Hz}}$. Long-term stabilities on the order of ${10}^{-28}$ N are observed in the two spatial components of a force, which allows probing atomic Van der Waals forces at one millimeter distance. As a further illustrative application, we use our atomic sensor to calibrate the control precision of an alternating electromagnetic force applied in the experiment. Future developments of this method hold promise for delivering unprecedented atom-based quantum force sensing technologies.

矢量力的高精度传感对基础研究和技术应用都有广泛的影响，例如真空波动的检查和纳米结构表面粗糙度的检测。近年来，随着量子技术的快速发展，在感应交变电磁力方面取得了很大进展——原子传感器的检测灵敏度已经实现了数量级的提高，而这种对静态电磁力的高精度测量却很少被证明。在这里，基于二维光学晶格限制的量子原子物质波，我们通过在倒易空间中成像相干波力学来精确测量静态电磁力。晶格限制导致真实空间和相互动力学之间的解耦，并为校准物质波的波矢量积累提供了一个刚性坐标系。由此，我们实现了最先进的灵敏度$2.30(\mathrm{8个})\times {10}^{-26}$否/$\sqrt{\mathrm{赫兹}}$. 长期稳定性的顺序${10}^{-28}$在一个力的两个空间分量中观察到 N，这允许在一毫米距离处探测原子范德华力。作为进一步的说明性应用，我们使用我们的原子传感器来校准实验中施加的交变电磁力的控制精度。这种方法的未来发展有望提供前所未有的基于原子的量子力传感技术。