Single charge regime electrodynamic force measuring in solution by upconversion photonic force microscope

Abstract

Precise force measurement is critical to probing biological events and physics processes, spanning from molecular motor’s motion to the Casimir effect1 and the detection of gravitational wave2. Yet, despite extensive technology developments, the 3D nanoscale measurement of weak forces in aqueous solutions poses a significant challenge. Techniques that rely on the optically trapped nanoprobe are beset with difficulties, including low light scattering for force measuring and high localization error from their Brownian motion. Here, we report the measurement of the long-distance electrodynamic force on single nanocrystals suspended in aqueous solution with only 11 net charges. To achieve this, we develop an upconversion photonic force microscope that encompasses a diffraction-limited tracking-based force sensing theory and the advance of lanthanide ion resonance force probe3,4. The tracking method is based on neural network empowered super-resolution localization, where the position of force probe is extracted from the optical astigmatism modified point spread functon(PSF), enabling the measurement of trap stiffness for nanoparticles through equipartition theorem with a force sensitivity down to 592.9 attoNewtons (aN), that is, 5 times lower than the reported best sensitivity value5. We further demonstrate that the technology can measure a single nanocrystal's electrophoresis force and zeta potential, experimentally verifying Loeb's empirical relationship. This work offers new opportunities for detecting single-charge dynamics over long-distance and sub-cellular single molecular level biomechanical force.