Achievement of a vacuum-levitated metal mechanical oscillator with ultra-low damping rate at room temperature

A vacuum-levitated metal mechanical oscillator with an ultra-low damping rate is an ideal tool for detecting mass-related short-range forces; however, its realization at room temperature has not yet been achieved, limiting its practical applications. In this study, we developed such an oscillator using a diamagnetically levitated bismuth sphere. We derived an accurate general formula for the sphere's eddy current damping rate and, based on this, constructed the oscillator from microparticles, successfully reducing its damping rate experimentally to (144 +/- 6) mu Hz-nearly three orders of magnitude lower than that of the untreated sphere. This improvement allows the sub-millimeter-sized levitated metal mechanical oscillator to theoretically achieve a force sensitivity of (5.17 +/- 0.12)fN/Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(5.17\pm 0.12)\,\,{\mbox{fN}}/\sqrt{{\mbox{Hz}}\,}$$\end{document} and an acceleration sensitivity of (0.30 +/- 0.01)ng/Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0.30\pm 0.01)\,\,{\mbox{ng}}/\sqrt{{\mbox{Hz}}\,}$$\end{document} at room temperature. Calculations indicate that using this sphere as a test mass can detect gravitational forces from sub-milligram sources, highlighting its potential for short-range force sensing and the exploration of quantum gravity.