# Subfemtonewton force fields measured with ergodic Brownian ensembles

## TL;DR

This paper demonstrates a method to measure and reconstruct radiation pressure force fields with sub-femtonewton resolution using an ergodic ensemble of colloidal particles, enabling ultra-sensitive force measurements in fluids.

## Contribution

The authors introduce a novel approach leveraging ergodic Brownian ensembles to achieve unprecedented force measurement resolution in colloidal systems.

## Key findings

- Force resolution of 0.3 fN achieved
- Ergodic ensemble allows for high-precision force reconstruction
- Method applicable to various force fields in fluids

## Abstract

We demonstrate that radiation pressure force fields can be measured and reconstructed with a resolution of $0.3$ fN (at a $99.7\%$ confidence level) using an ergodic ensemble of overdamped colloidal particles. The outstanding force resolution level is provided by the large size of the statistical ensemble built by recording all displacements from all diffusing particles, regardless of trajectory and time. This is only possible because the noise driving the particles is thermal, white and stationary, so that the colloidal system is ergodic, as we carefully verify. Using an ergodic colloidal dispersion for performing ultra-sensitive measurements of external forces is not limited to non-conservative optical force fields. Our experiments therefore give way to interesting opportunities in the context of weak force measurements in fluids.