Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Ultrasensitive torque detection with an optically levitated nanorotor

Abstract

Torque sensors such as the torsion balance enabled the first determination of the gravitational constant by Henri Cavendish1 and the discovery of Coulomb’s law. Torque sensors are also widely used in studying small-scale magnetism2,3, the Casimir effect4 and other applications5. Great effort has been made to improve the torque detection sensitivity by nanofabrication and cryogenic cooling. Until now, the most sensitive torque sensor has achieved a remarkable sensitivity of 2.9 × 10−24 N m Hz−1/2 at millikelvin temperatures in a dilution refrigerator6. Here, we show a torque sensor reaching sensitivity of (4.2 ± 1.2) × 10−27 N m Hz−1/2 at room temperature. It is created by an optically levitated nanoparticle in vacuum. Our system does not require complex nanofabrication. Moreover, we drive a nanoparticle to rotate at a record high speed beyond 5 GHz (300 billion r.p.m.). Our calculations show that this system will be able to detect the long sought after vacuum friction7,8,9,10 near a surface under realistic conditions. The optically levitated nanorotor will also have applications in studying nanoscale magnetism2,3 and the quantum geometric phase11.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental schematic and rotation spectra of an optically levitated nanoparticle.
Fig. 2: Vibration and rotation of optically levitated silica nanoparticles.
Fig. 3: Ultrasensitive detection of an external torque.
Fig. 4: Calculated vacuum friction on a rotating nanosphere near a surface.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

References

  1. Cavendish, H. Experiments to determine the density of the earth. Philos. Trans. R. Soc. London 88, 469–526 (1798).

    Google Scholar 

  2. Wu, M. et al. Nanocavity optomechanical torque magnetometry and radiofrequency susceptometry. Nat. Nanotechnol. 12, 127 (2017).

    Article  CAS  Google Scholar 

  3. Losby, J. E., Sauer, V. T. K. & Freeman, M. R. Recent advances in mechanical torque studies of small-scale magnetism. J. Phys. D. 51, 483001 (2018).

    Article  Google Scholar 

  4. Chan, H. B., Aksyuk, V. A., Kleiman, R. N., Bishop, D. J. & Capasso, F. Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science 291, 1941–1944 (2001).

    Article  CAS  Google Scholar 

  5. He, L., Li, H. & Li, M. Optomechanical measurement of photon spin angular momentum and optical torque in integrated photonic devices. Sci. Adv. 2, e1600485 (2016).

    Article  Google Scholar 

  6. Kim, P. H., Hauer, B. D., Doolin, C., Souris, F. & Davis, J. P. Approaching the standard quantum limit of mechanical torque sensing. Nat. Commun. 7, 13165 (2016).

    Article  CAS  Google Scholar 

  7. Kardar, M. & Golestanian, R. The ‘friction’ of vacuum, and other fluctuation-induced forces. Rev. Mod. Phys. 71, 1233–1245 (1999).

    Article  CAS  Google Scholar 

  8. Manjavacas, A. & García de Abajo, F. J. Vacuum friction in rotating particles. Phys. Rev. Lett. 105, 113601 (2010).

    Article  CAS  Google Scholar 

  9. Zhao, R., Manjavacas, A., García de Abajo, F. J. & Pendry, J. B. Rotational quantum friction. Phys. Rev. Lett. 109, 123604 (2012).

    Article  Google Scholar 

  10. Manjavacas, A., Rodríguez-Fortuño, F. J., de Abajo, F. J. G. & Zayats, A. V. Lateral Casimir force on a rotating particle near a planar surface. Phys. Rev. Lett. 118, 133605 (2017).

    Article  Google Scholar 

  11. Chen, X.-Y., Li, T. & Yin, Z.-Q. Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin. Sci. Bull. 64, 380–384 (2019).

    Article  CAS  Google Scholar 

  12. Yin, Z.-Q., Geraci, A. A. & Li, T. Optomechanics of levitated dielectric particles. Int. J. Mod. Phys. B. 27, 1330018 (2013).

    Article  Google Scholar 

  13. Ranjit, G., Cunningham, M., Casey, K. & Geraci, A. A. Zeptonewton force sensing with nanospheres in an optical lattice. Phys. Rev. A. 93, 053801 (2016).

    Article  Google Scholar 

  14. Rider, A. D. et al. Search for screened interactions associated with dark energy below the 100 μm length scale. Phys. Rev. Lett. 117, 101101 (2016).

    Article  Google Scholar 

  15. Tebbenjohanns, F., Frimmer, M., Militaru, A., Jain, V. & Novotny, L. Cold damping of an optically levitated nanoparticle to microkelvin temperatures. Phys. Rev. Lett. 122, 223601 (2019).

    Article  CAS  Google Scholar 

  16. Arita, Y., Mazilu, M. & Dholakia, K. Laser-induced rotation and cooling of a trapped microgyroscope in vacuum. Nat. Commun. 4, 2374 (2013).

    Article  Google Scholar 

  17. Kuhn, S. et al. Optically driven ultra-stable nanomechanical rotor. Nat. Commun. 8, 1670 (2017).

    Article  Google Scholar 

  18. Ahn, J. et al. Optically levitated nanodumbbell torsion balance and GHz nanomechanical rotor. Phys. Rev. Lett. 121, 033603 (2018).

    Article  CAS  Google Scholar 

  19. Reimann, R. et al. GHz rotation of an optically trapped nanoparticle in vacuum. Phys. Rev. Lett. 121, 033602 (2018).

    Article  CAS  Google Scholar 

  20. Monteiro, F., Ghosh, S., van Assendelft, E. C. & Moore, D. C. Optical rotation of levitated spheres in high vacuum. Phys. Rev. A. 97, 051802 (2018).

    Article  CAS  Google Scholar 

  21. Rider, A. D. et al. Electrically driven, optically levitated microscopic rotors. Phys. Rev. A. 99, 041802 (2019).

    Article  CAS  Google Scholar 

  22. Hoang, T. M. et al. Torsional optomechanics of a levitated nonspherical nanoparticle. Phys. Rev. Lett. 117, 123604 (2016).

    Article  Google Scholar 

  23. Rashid, M., Torosš, M., Setter, A. & Ulbricht, H. Precession motion in levitated optomechanics. Phys. Rev. Lett. 121, 253601 (2018).

    Article  CAS  Google Scholar 

  24. Li, T., Kheifets, S., Medellin, D. & Raizen, M. G. Measurement of the instantaneous velocity of a Brownian particle. Science 328, 1673–1675 (2010).

    Article  CAS  Google Scholar 

  25. Millen, J., Deesuwan, T., Barker, P. & Anders, J. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. Nat. Nanotechnol. 9, 425–429 (2014).

    Article  CAS  Google Scholar 

  26. Gieseler, J., Quidant, R., Dellago, C. & Novotny, L. Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state. Nat. Nanotechnol. 9, 358–364 (2014).

    Article  CAS  Google Scholar 

  27. Hoang, T. M. et al. Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states. Phys. Rev. Lett. 120, 080602 (2018).

    Article  CAS  Google Scholar 

  28. Xu, Z. & Li, T. Detecting Casimir torque with an optically levitated nanorod. Phys. Rev. A. 96, 033843 (2017).

    Article  Google Scholar 

  29. Haiberger, L., Weingran, M. & Schiller, S. Highly sensitive silicon crystal torque sensor operating at the thermal noise limit. Rev. Sci. Instrum. 78, 025101 (2007).

    Article  CAS  Google Scholar 

  30. Ricci, F., Cuairan, M. T., Conangla, G. P., Schell, A. W. & Quidant, R. Accurate mass measurement of a levitated nanomechanical resonator for precision force-sensing. Nano Lett. 19, 6711–6715 (2019).

    Article  CAS  Google Scholar 

  31. Kischkat, J. et al. Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride. Appl. Opt. 51, 6789–6798 (2012).

    Article  CAS  Google Scholar 

  32. Slezak, B. R., Lewandowski, C. W., Hsu, J.-F. & D’Urso, B. Cooling the motion of a silica microsphere in a magneto-gravitational trap in ultra-high vacuum. New J. Phys. 20, 063028 (2018).

    Article  Google Scholar 

  33. Diehl, R. et al. Optical levitation and feedback cooling of a nanoparticle at subwavelength distances from a membrane. Phys. Rev. A. 98, 013851 (2018).

    Article  CAS  Google Scholar 

  34. Magrini, L. et al. Near-field coupling of a levitated nanoparticle to a photonic crystal cavity. Optica 5, 1597–1602 (2018).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank F. Robicheaux, T. Seberson, R. Zhao, Z. Jacob, Q. Han and R.M. Ma for helpful discussions. We are grateful to support from the Office of Naval Research under grant no. N00014-18-1-2371, the NSF under grant no. PHY-1555035 and the DARPA NLM program.

Author information

Authors and Affiliations

Authors

Contributions

J.A. and T.L. conceived and designed the project. J.A., J.B. and P.J. performed experiments. Z.X. and X.G. calculated the vacuum friction. J.A., Z.X. and T.L. analysed the results. T.L. supervised the project. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Tongcang Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–3, Discussion and Table 1.

Source data

Source Data Fig. 1

Raw data for Fig. 1b

Source Data Fig. 2

Raw data for Fig. 2c,d and 2d inset

Source Data Fig. 3

Raw data for Fig. 3b,d–f

Source Data Fig. 4

Raw data for Fig. 4a,b

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahn, J., Xu, Z., Bang, J. et al. Ultrasensitive torque detection with an optically levitated nanorotor. Nat. Nanotechnol. 15, 89–93 (2020). https://doi.org/10.1038/s41565-019-0605-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-019-0605-9

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing