# Precision Mass and Density Measurement of Individual Optically Levitated Microspheres

## TL;DR

This paper presents a precise in situ method for measuring the mass and density of individual optically levitated microspheres using electrostatic forces and optical feedback, achieving low uncertainty and enabling microsphere recovery for further analysis.

## Contribution

It introduces a novel electrostatic co-levitation technique for accurate in situ mass measurement of optically trapped microspheres with systematic uncertainty below 2%.

## Key findings

- Achieved 1.8% systematic uncertainty in mass measurement.
- Measured density of microspheres as 1.55±0.08 g/cm³.
- Demonstrated recovery and imaging of microspheres post-measurement.

## Abstract

We report an $\textit{in situ}$ mass measurement of approximately-$4.7{\text -}\mu$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.