We report an $\textit{in situ}$ mass measurement of approximately-$4.7{\text -}μ$m-diameter, optically levitated microspheres with an electrostatic co-levitation technique. The mass of a trapped, charged microsphere is measured by holding its axial (vertical) position fixed with an optical feedback force, under the influence of a known electrostatic force. A mass measurement with $1.8\%$ systematic uncertainty is obtained by extrapolating to the electrostatic force required to support the microsphere against gravity in the absence of optical power. In three cases, the microspheres are recovered from the trap on a polymer-coated silicon beam and imaged with an electron microscope to measure their radii. The simultaneous precision characterization of the mass and radius of individual microspheres implies a density of $1.55\pm0.08~$g/cm$^3$. The ability to recover individual microspheres from an optical trap opens the door to further diagnostics.
Force and acceleration sensing with optically levitated nanogram masses at microkelvin temperatures
本文演示了冷却的质心运动的10个$μ$ m直径的光学悬浮二氧化硅球的有效温度为$50\pm22 μ$ K，通过最大限度地减少技术指向噪声的捕获激光。这种低噪声导致在接近50 Hz的频率下，$95\pm41$ n $g/\sqrt{\mathrm{Hz}}$（$g = 9.8$ m/s $^2$）和$0.95\pm0.11$ a N $/\sqrt{\mathrm{Hz}}$分别具有加速度和力灵敏度。该力灵敏度与质量小$10^4$倍的光学悬浮纳米球所证明的力灵敏度相当，对应于好几个数量级的加速度灵敏度。进一步表明，在这些条件下，球体在$\sim 10^{-7}$ mbar的压力下保持稳定捕获，而没有主动冷却超过一天。反馈冷却仍然是必要的，在中等压力制度，激励的损耗机制的微球的全面研究，并提供更好的理解的要求，在真空中的无反馈光阱。这项工作可以实现高灵敏度搜索作用在微米级质量上的加速度和力，包括那些可能由标准模型之外的新物理产生的加速度和力。
