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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The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
References
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
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).
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).
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).
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).
Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. The Universe’s UNSEEN DIMENSIONS. Scientific American 283(2), 62–69 (2000).
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).
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).
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).
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
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).
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).
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).
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).
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).
Microparticles GmbH. https://www.microparticles-shop.de/index.php?language=en. Accessed 2024-12-04
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).
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).
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
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).
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).
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
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).
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
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
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
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).
See Supplemental Material at URL-will-be-inserted-by-publisher for the experimental configurations under which data was collected for this result.
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).
Blakemore, C. P. et al. Librational feedback cooling. Physical Review A 106(2), 023503. https://doi.org/10.1103/PhysRevA.106.023503 (2022).
Acktar MagicBlack. https://acktar.com/product/magic-black/. (2024)
Hardy, C.A.: In search of Majorana neutrinos and micron-scale interactions. PhD thesis, Stanford University, Stanford, CA (2025). https://purl.stanford.edu/cc863pp6175
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).
Hough, E.: Novel Techniques to Measure Micron-Scale Gravity. https://purl.stanford.edu/rc763nv9924. Bachelor’s Thesis, Stanford University (2022)
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).
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).
Kilian, E. et al. Dark matter searches with levitated sensors. AVS Quantum Science 6(3), 030503. https://doi.org/10.1116/5.0200916 (2024).
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).
Bose, S. et al. Spin entanglement witness for quantum gravity. Phys. Rev. Lett. 119, 240401. https://doi.org/10.1103/PhysRevLett.119.240401 (2017).
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).
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).
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.
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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.
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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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DOI: https://doi.org/10.1038/s41598-026-35656-6


