Sub-femtonewton force sensing in solution by super-resolved photonic force microscopy

Precise force measurement is critical to probe biological events and physics processes, spanning from molecular motor's motion to the Casimir effect, as well as the detection of gravitational waves. Yet, despite extensive technological developments, the three-dimensional nanoscale measurement of weak forces in aqueous solutions still faces major challenges. Techniques that rely on optically trapped nanoprobes are of significant potential but are beset with limitations, including probe heating induced by high trapping power, undetectable scattering signals and localization errors. Here we report the measurement of the long-distance interaction force in aqueous solutions with a minimum detected force value of 108.2 ± 510.0 attonewton. To achieve this, we develop a super-resolved photonic force microscope based on optically trapped lanthanide-doped nanoparticles coupled with nanoscale three-dimensional tracking-based force sensing. The tracking method leverages neural-network-empowered super-resolution localization, where the position of the force probe is extracted from the optical-astigmatism-modified point spread function. We achieve a force sensitivity down to 1.8 fN Hz–1/2, which approaches the nanoscale thermal limit. We experimentally measure electrophoresis forces acting on single nanoparticles as well as the surface-induced interaction force on a single nanoparticle. This work opens the avenue of nanoscale thermally limited force sensing and offers new opportunities for detecting sub-femtonewton forces over long distances and biomechanical forces at the single-molecule level. Super-resolved photonic force microscopy employs the fluorescence of lanthanide-doped nanoparticles as a force probe, enabling the measurement of sub-femtonewton forces with a sensitivity of 1.8 fN Hz–1/2, approaching the thermal limit.