Despite recent tremendous progress in optical imaging and metrology^1,2,3,4,5,6, there remains a substantial resolution gap between atomic-scale transmission electron microscopy and optical techniques. Is optical imaging and metrology of nanostructures exhibiting Brownian motion possible with such resolution, beyond thermal fluctuations? Here we report on an experiment in which the average position of a nanowire with a thermal oscillation amplitude of ∼150 pm is resolved in single-shot measurements with subatomic precision of 92 pm, using light at a wavelength of λ = 488 nm, providing an example of such sub-Brownian metrology with ∼λ/5,300 precision. To localize the nanowire, we employ a deep-learning analysis of the scattering of topologically structured light, which is highly sensitive to the nanowire’s position. This non-invasive metrology with absolute errors down to a fraction of the typical size of an atom, opens a range of opportunities to study picometre-scale phenomena with light.

尽管最近在光学成像和计量学方面取得了巨大进展^1,2,3,4,5,6 ，但原子级透射电子显微镜和光学技术之间仍然存在很大的分辨率差距。表现出布朗运动的纳米结构的光学成像和计量是否可能以这种分辨率超越热波动？在这里，我们报告了一项实验，其中使用波长λ = 488 nm 的光，以 92 pm 的亚原子精度单次测量解析了热振荡幅度约为150 pm 的纳米线的平均位置，提供了这种亚布朗计量学的例子，精度为∼ λ /5,300。为了定位纳米线，我们对拓扑结构光的散射进行了深度学习分析，这对纳米线的位置高度敏感。这种非侵入式计量技术的绝对误差低至原子典型尺寸的一小部分，为利用光研究皮米级现象提供了一系列机会。