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Optomechanical vector sensing of new forces at 6 micron separation
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  • Published: 13 January 2026

Optomechanical vector sensing of new forces at 6 micron separation

  • Gautam Venugopalan1,
  • Clarke A. Hardy1,
  • Kenneth Kohn1,
  • Yuqi Zhu1,
  • Charles P. Blakemore1,
  • Alexander Fieguth1,
  • Jacqueline Huang1,
  • Chengjie Jia1,
  • Meimei Liu1,
  • Lorenzo Magrini1,
  • Nadav Priel1,
  • Zhengruilong Wang2 &
  • …
  • Giorgio Gratta1,3 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Optics and photonics
  • Physics

Abstract

The search for new gravity-like interactions at the sub-millimeter scale is a compelling area of research, with important implications for the understanding of classical gravity and its connections with quantum physics. We report improved constraints on Yukawa-type interactions in the \(10\,\mathrm {\mu m}\) regime using optically levitated dielectric microspheres as test masses. The search is performed, for the first time, sensing multiple spatial components of the force vector, and with sensitivity improved by a factor of \(\sim 100\) with respect to previous measurements using the same technique. The resulting upper limit on the strength of a hypothetical new force is \(10^7\) at a Yukawa range \(\lambda \simeq 5\;\mu\)m and close to \(10^6\) for \(\lambda \gtrsim 10\;\mu\)m. This result also advances our efforts to measure gravitational effects using micrometer-size objects, with important implications for embryonic ideas to investigate the quantum nature of gravity.

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Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

References

  1. Merkowitz, S.M.: Tests of Gravity Using Lunar Laser Ranging. Living Reviews in Relativity 13(1), 7 (2010) https://doi.org/10.12942/lrr-2010-7 . Accessed 2024-12-04

  2. The LIGO Scientific Collaboration and the Virgo Collaboration. Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1. Physical Review D 100(10), 104036. https://doi.org/10.1103/PhysRevD.100.104036 (2019).

    Google Scholar 

  3. LIGO Scientific Collaboration and Virgo Collaboration. Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog. Physical Review D 103(12), 122002. https://doi.org/10.1103/PhysRevD.103.122002 (2021).

    Google Scholar 

  4. Lee, J. G., Adelberger, E. G., Cook, T.S., Fleischer, S. M. & Heckel, B. R. New Test of the Gravitational \(1/{r}^{2}\) Law at Separations down to \(52 \,\text{m}\). Physical Review Letters 124(10), 101101.https://doi.org/10.1103/PhysRevLett.124.101101. (2020).

  5. Adelberger, E. G., Heckel, B. R. & Nelson, A. E. Tests of the Gravitational Inverse-Square Law. Annual Review of Nuclear and Particle Science 53(1), 77–121. https://doi.org/10.1146/annurev.nucl.53.041002.110503 (2003).

    Google Scholar 

  6. Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. The Universe’s UNSEEN DIMENSIONS. Scientific American 283(2), 62–69 (2000).

    Google Scholar 

  7. Antoniadis, I., Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. New dimensions at a millimeter to a fermi and superstrings at a TeV. Physics Letters B 436(3), 257–263. https://doi.org/10.1016/S0370-2693(98)00860-0 (1998).

    Google Scholar 

  8. Sundrum, R. Fat gravitons, the cosmological constant and submillimeter tests. Physical Review D 69(4), 044014. https://doi.org/10.1103/PhysRevD.69.044014 (2004).

    Google Scholar 

  9. Montero, M., Vafa, C. & Valenzuela, I. The dark dimension and the Swampland. Journal of High Energy Physics 2023(2), 22. https://doi.org/10.1007/JHEP02(2023)022 (2023).

    Google Scholar 

  10. Safronova, M.S., et al.: Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018) https://doi.org/10.1103/RevModPhys.90.025008

  11. Murata, J. & Tanaka, S. A review of short-range gravity experiments in the lhc era. Classical and Quantum Gravity 32(3), 033001. https://doi.org/10.1088/0264-9381/32/3/033001 (2015).

    Google Scholar 

  12. Chen, Y.-J. et al. Stronger Limits on Hypothetical Yukawa Interactions in the 30–8000 nm Range. Physical Review Letters 116(22), 221102. https://doi.org/10.1103/PhysRevLett.116.221102 (2016).

    Google Scholar 

  13. Tan, W.-H. et al. Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range. Physical Review Letters 124(5), 051301. https://doi.org/10.1103/PhysRevLett.124.051301 (2020).

    Google Scholar 

  14. Sushkov, A. O., Kim, W. J., Dalvit, D. A. R. & Lamoreaux, S. K. New Experimental Limits on Non-Newtonian Forces in the Micrometer Range. Physical Review Letters 107(17), 171101. https://doi.org/10.1103/PhysRevLett.107.171101 (2011).

    Google Scholar 

  15. Geraci, A. A., Smullin, S. J., Weld, D. M., Chiaverini, J. & Kapitulnik, A. Improved constraints on non-Newtonian forces at 10 microns. Physical Review D 78(2), 022002. https://doi.org/10.1103/PhysRevD.78.022002 (2008).

    Google Scholar 

  16. Microparticles GmbH. https://www.microparticles-shop.de/index.php?language=en. Accessed 2024-12-04

  17. Kawasaki, A. et al. High sensitivity, levitated microsphere apparatus for short-distance force measurements. Review of Scientific Instruments 91(8), 083201. https://doi.org/10.1063/5.0011759 (2020).

    Google Scholar 

  18. Maurer, P., Gonzalez-Ballestero, C. & Romero-Isart, O. Quantum theory of light interaction with a Lorenz-Mie particle: Optical detection and three-dimensional ground-state cooling. Physical Review A 108(3), 033714. https://doi.org/10.1103/PhysRevA.108.033714 (2023).

    Google Scholar 

  19. Acheson, E.G.: AquaDAG Patent US844989A. US844989A, February 19 1907. Original patent describing the water-based colloidal graphite coating known as AquaDAG, used for conductive and lubricating purposes. https://patents.google.com/patent/US844989A

  20. Moore, D. C., Rider, A. D. & Gratta, G. Search for millicharged particles using optically levitated microspheres. Phys. Rev. Lett. 113, 251801. https://doi.org/10.1103/PhysRevLett.113.251801 (2014).

    Google Scholar 

  21. Blakemore, C. P. et al. Three-dimensional force-field microscopy with optically levitated microspheres. Phys. Rev. A 99, 023816. https://doi.org/10.1103/PhysRevA.99.023816 (2019).

    Google Scholar 

  22. Wang, Q., et al.: A Density Staggered Cantilever for Micron Length Gravity Probing. In: 2017 IEEE 67th Electronic Components and Technology Conference (ECTC), 1773–1778 (2017). https://doi.org/10.1109/ECTC.2017.274

  23. Blakemore, C. P. et al. Search for non-Newtonian interactions at micrometer scale with a levitated test mass. Physical Review D 104(6), 061101. https://doi.org/10.1103/PhysRevD.104.L061101 (2021).

    Google Scholar 

  24. Venugopalan, G. & Gratta, G.: Platinum Black for stray-light mitigation on high-aspect-ratio micromechanical cantilever. arXiv (2024). arxiv:2411.14324 Accessed 2024-12-04

  25. Allen, B., Hua, W. & Ottewill, A.: Automatic cross-talk removal from multi-channel data. arXiv (1999). arxiv:org/abs/gr-qc/9909083 Accessed 2024-12-04

  26. Vajente, G.: Data mining and machine learning improve gravitational-wave detector sensitivity. Phys. Rev. D 105, 102005 (2022) https://doi.org/10.1103/PhysRevD.105.102005

  27. Blakemore, C. P. et al. Precision mass and density measurement of individual optically levitated microspheres. Phys. Rev. Appl. 12, 024037. https://doi.org/10.1103/PhysRevApplied.12.024037 (2019).

    Google Scholar 

  28. See Supplemental Material at URL-will-be-inserted-by-publisher for the experimental configurations under which data was collected for this result.

  29. Priel, N. et al. Dipole moment background measurement and suppression for levitated charge sensors. Science Advances 8(41), 2361. https://doi.org/10.1126/sciadv.abo2361 (2022).

    Google Scholar 

  30. Blakemore, C. P. et al. Librational feedback cooling. Physical Review A 106(2), 023503. https://doi.org/10.1103/PhysRevA.106.023503 (2022).

    Google Scholar 

  31. Acktar MagicBlack. https://acktar.com/product/magic-black/. (2024)

  32. Hardy, C.A.: In search of Majorana neutrinos and micron-scale interactions. PhD thesis, Stanford University, Stanford, CA (2025). https://purl.stanford.edu/cc863pp6175

  33. Wilks, S. S. The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. The Annals of Mathematical Statistics 9(1), 60–62. https://doi.org/10.1214/aoms/1177732360 (1938).

    Google Scholar 

  34. Hough, E.: Novel Techniques to Measure Micron-Scale Gravity. https://purl.stanford.edu/rc763nv9924. Bachelor’s Thesis, Stanford University (2022)

  35. Moore, D. C. & Geraci, A. A. Searching for new physics using optically levitated sensors. Quantum Science and Technology 6(1), 014008. https://doi.org/10.1088/2058-9565/abcf8a (2021).

    Google Scholar 

  36. Monteiro, F. et al. Search for composite dark matter with optically levitated sensors. Phys. Rev. Lett. 125, 181102. https://doi.org/10.1103/PhysRevLett.125.181102 (2020).

    Google Scholar 

  37. Kilian, E. et al. Dark matter searches with levitated sensors. AVS Quantum Science 6(3), 030503. https://doi.org/10.1116/5.0200916 (2024).

    Google Scholar 

  38. Carney, D., Leach, K. G. & Moore, D. C. Searches for massive neutrinos with mechanical quantum sensors. PRX Quantum 4, 010315. https://doi.org/10.1103/PRXQuantum.4.010315 (2023).

    Google Scholar 

  39. Bose, S. et al. Spin entanglement witness for quantum gravity. Phys. Rev. Lett. 119, 240401. https://doi.org/10.1103/PhysRevLett.119.240401 (2017).

    Google Scholar 

  40. Gonzalez-Ballestero, C., Aspelmeyer, M., Novotny, L., Quidant, R. & Romero-Isart, O. Levitodynamics: Levitation and control of microscopic objects in vacuum. Science 374(6564), 3027. https://doi.org/10.1126/science.abg3027 (2021).

    Google Scholar 

  41. Millen, J., Monteiro, T. S., Pettit, R. & Vamivakas, A. N. Optomechanics with levitated particles. Reports on Progress in Physics 83(2), 026401. https://doi.org/10.1088/1361-6633/ab6100 (2020).

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge early contributions of Akio Kawasaki (AIST, Japan), Alex Rider (Scitech, Boulder CO), and Qidong Wang (IME-CAS, Beijing). We thank Giovanni Ferraro and Emiliano Fratini (University of Florence, Italy) for help in understanding some characteristics of Stöber microspheres, and David Moore (Yale) for his feedback on the manuscript.

Funding

This work was supported by NSF grant number 2406999, ONR grant number N000142312600, and the Heising-Simons Foundation. Part of the work was performed at the Stanford Nano Shared Facilities (SNSF) which is supported by the NSF under award ECCS-2026822.

Author information

Authors and Affiliations

  1. Physics Department, Stanford University, Stanford, 94305, CA, USA

    Gautam Venugopalan, Clarke A. Hardy, Kenneth Kohn, Yuqi Zhu, Charles P. Blakemore, Alexander Fieguth, Jacqueline Huang, Chengjie Jia, Meimei Liu, Lorenzo Magrini, Nadav Priel & Giorgio Gratta

  2. Applied Physics Department, Stanford University, Stanford, 94305, CA, USA

    Zhengruilong Wang

  3. Hansen Experimental Physics Lab, Stanford University, Stanford, 94305, CA, USA

    Giorgio Gratta

Authors
  1. Gautam Venugopalan
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Contributions

G.V., A.F. and G.G. led the conceptualization, design and implementation of the experimental setup used in this work. Y.Z., C.B., J.H., M.L, and L.M. designed and constructed important subsystems. C.H. and G.V. led the data analysis, building on a framework developed by A.F., C.B., and N.P., and K.K. developed numerical simulations used to validate the results. C.J. and Z.W. provided valuable insights on various subsytems. All authors reviewed the manuscript.

Corresponding authors

Correspondence to Gautam Venugopalan or Clarke A. Hardy.

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Venugopalan, G., Hardy, C.A., Kohn, K. et al. Optomechanical vector sensing of new forces at 6 micron separation. Sci Rep (2026). https://doi.org/10.1038/s41598-026-35656-6

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  • Received: 23 August 2025

  • Accepted: 07 January 2026

  • Published: 13 January 2026

  • DOI: https://doi.org/10.1038/s41598-026-35656-6

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Keywords

  • Optical levitation
  • Search for new physics
  • Force sensing
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