Despite recent tremendous progress in optical imaging and metrology1,2,3,4,5,6, there remains a substantial resolution gap between atomic-scale transmission electron microscopy and optical techniques. Is optical imaging and metrology of nanostructures exhibiting Brownian motion possible with such resolution, beyond thermal fluctuations? Here we report on an experiment in which the average position of a nanowire with a thermal oscillation amplitude of ∼150 pm is resolved in single-shot measurements with subatomic precision of 92 pm, using light at a wavelength of λ = 488 nm, providing an example of such sub-Brownian metrology with ∼λ/5,300 precision. To localize the nanowire, we employ a deep-learning analysis of the scattering of topologically structured light, which is highly sensitive to the nanowire’s position. This non-invasive metrology with absolute errors down to a fraction of the typical size of an atom, opens a range of opportunities to study picometre-scale phenomena with light.
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The data from this paper can be obtained from the University of Southampton ePrints research repository: https://doi.org/10.5258/SOTON/D2544.
Hell, S. W. & Wichmann, J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19, 780–782 (1994).
Rust, M. J., Bates, M. & Zhuang, X. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3, 793–796 (2006).
Betzig, E. et al. Imaging intracellular fluorescent proteins at nanometer resolution. Science 313, 1642–1645 (2006).
Hess, S. T., Girirajan, T. P. & Mason, M. D. Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. Biophys. J. 91, 4258–4272 (2006).
Guerra, J. M. Super‐resolution through illumination by diffraction‐born evanescent waves. Appl. Phys. Lett. 66, 3555–3557 (1995).
Gustafsson, M. G. L. Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution. Proc. Natl Acad. Sci. USA 102, 13081–13086 (2005).
Rendón-Barraza, C. et al. Deeply sub-wavelength non contact optical metrology of sub-wavelength objects. APL Photonics 6, 066107 (2021).
Cahillane, C. & Mansell, G. Review of the advanced LIGO gravitational wave observatories leading to observing run four. Galaxies 10, 36 (2022).
Zheludev, N. I. & Yuan, G. Optical superoscillation technologies beyond the diffraction limit. Nat. Rev. Phys. 4, 16–32 (2022).
Yuan, G., Rogers, E. T. F. & Zheludev, N. I. ‘Plasmonics’ in free space: observation of giant wavevectors, vortices, and energy backflow in superoscillatory optical fields. Light. Sci. Appl. 8, 2 (2019).
Liu, T. et al. Picophotonics - subatomic optical localization beyond thermal fluctuations. In MRS Spring Meeting 2023 paper EL06.05.01 (San Francisco, 2023).
Wang, M. C. & Uhlenbeck, G. E. On the theory of the Brownian motion II. Rev. Mod. Phys. 17, 323–342 (1945).
Berry, M. V. & Shukla, P. Hamiltonian curl forces. Proc. R. Soc. A 471, 20150002 (2015).
Rodriguez, A. W., Capasso, F. & Johnson, S. G. The Casimir effect in microstructured geometries. Nat. Photon. 5, 211–221 (2011).
Aspelmeyer, M. Gravitational quantum physics, or: how to avoid the appearance of the classical world in gravity experiments? In 8th International Topical Meeting on Nanophotonics and Metamaterials MON1o.1 (European Physical Society, Seefeld-in-Tirol, 2022).
Liu, T. et al. Ballistic dynamics of flexural thermal movements in a nano-membrane revealed with subatomic resolution. Sci. Adv. 8, eabn8007 (2022).
Zhu, W. et al. Quantum mechanical effects in plasmonic structures with subnanometre gaps. Nat. Commun. 7, 11495 (2016).
Baumberg, J. J., Aizpurua, J., Mikkelsen, M. H. & Smith, D. R. Extreme nanophotonics from ultrathin metallic gaps. Nat. Mater. 18, 668–678 (2019).
Yang, B. et al. Sub-nanometre resolution in single-molecule photoluminescence imaging. Nat. Photonics 14, 693–699 (2020).
Englander, S. W. & Mayne, L. The nature of protein folding pathways. Proc. Natl Acad. Sci. USA 111, 15873–15880 (2014).
Morozov, S. V. et al. Giant intrinsic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 100, 016602 (2008).
Mariani, E. & von Oppen, F. Flexural phonons in free-standing graphene. Phys. Rev. Lett. 100, 076801 (2008).
Lindsay, L., Broido, D. A. & Mingo, N. Flexural phonons and thermal transport in graphene. Phys. Rev. B 82, 115427 (2010).
This work was supported by the Engineering and Physical Sciences Research Council, UK (grant number EP/T02643X/1; N.I.Z., K.F.M., J.-Y.O.), the Ministry of Education, Singapore (MOE2016-T3-1-006; N.I.Z.), the National Research Foundation Singapore (NRF-CRP23-2019-0006) and the China Scholarship Council (201806160012; T.L.).
The authors declare no competing interests.
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Liu, T., Chi, CH., Ou, JY. et al. Picophotonic localization metrology beyond thermal fluctuations. Nat. Mater. (2023). https://doi.org/10.1038/s41563-023-01543-y