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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.

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Fig. 1: Nanoscale thermally limited force sensing by an SRPFM.
Fig. 2: Monte Carlo trapping simulation was used to analyse the force sensitivity.
Fig. 3: DNN-empowered optical astigmatism optical tweezers for 3D trapping.
Fig. 4: Thermally limited force sensing on single Ln-NP.
Fig. 5: Nanoscale interaction force sensing between Ln-NC and Au surface.

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Data availability

The data that support the findings of this study are available within the Article and its Supplementary Information. Other relevant data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

All the custom codes are available from the corresponding authors upon reasonable request.


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We thank the experimental assistance from M. Maddahfar, J. Liao and X. He; equipment support from C. Jagadish and the Analysis & Testing Center in Beihang University; and DNN assistance from P. Nie. We acknowledge financial support from the National Natural Science Foundation of China (62275010, 52073006), the Beijing Natural Science Foundation (1232027) and the fellowship of China Postdoctoral Science Foundation (2022TQ0020).

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Authors and Affiliations



F.W. conceived and supervised the project. L.D., X.S. and F.W. constructed the optical setup. F.W. and S.S.J.W. built the theoretical simulation and analytical model. X.S. and P.N. built the deep-learning model. S.W. and J.S. synthesized the nanoparticles. L.D. and H.Z. built the analysis of the net charge of the nanoparticles. L.D., X.S. and D.W. performed all the experiments. L.D., X.S. and F.W. analysed the results, prepared the figures and wrote the manuscript in consultation with all authors.

Corresponding authors

Correspondence to Xiaolan Zhong, Lingqian Chang or Fan Wang.

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Supplementary Sections 1–8, Equations (1)–(31), Tables 1–6 and Figs. 1–12.

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Shan, X., Ding, L., Wang, D. et al. Sub-femtonewton force sensing in solution by super-resolved photonic force microscopy. Nat. Photon. (2024).

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