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.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.
Cavendish, H. Experiments to determine the density of the earth. Philos. Trans. R. Soc. London 88, 469–526 (1798).
Wu, M. et al. Nanocavity optomechanical torque magnetometry and radiofrequency susceptometry. Nat. Nanotechnol. 12, 127 (2017).
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).
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).
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).
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).
Kardar, M. & Golestanian, R. The ‘friction’ of vacuum, and other fluctuation-induced forces. Rev. Mod. Phys. 71, 1233–1245 (1999).
Manjavacas, A. & García de Abajo, F. J. Vacuum friction in rotating particles. Phys. Rev. Lett. 105, 113601 (2010).
Zhao, R., Manjavacas, A., García de Abajo, F. J. & Pendry, J. B. Rotational quantum friction. Phys. Rev. Lett. 109, 123604 (2012).
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).
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).
Yin, Z.-Q., Geraci, A. A. & Li, T. Optomechanics of levitated dielectric particles. Int. J. Mod. Phys. B. 27, 1330018 (2013).
Ranjit, G., Cunningham, M., Casey, K. & Geraci, A. A. Zeptonewton force sensing with nanospheres in an optical lattice. Phys. Rev. A. 93, 053801 (2016).
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).
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).
Arita, Y., Mazilu, M. & Dholakia, K. Laser-induced rotation and cooling of a trapped microgyroscope in vacuum. Nat. Commun. 4, 2374 (2013).
Kuhn, S. et al. Optically driven ultra-stable nanomechanical rotor. Nat. Commun. 8, 1670 (2017).
Ahn, J. et al. Optically levitated nanodumbbell torsion balance and GHz nanomechanical rotor. Phys. Rev. Lett. 121, 033603 (2018).
Reimann, R. et al. GHz rotation of an optically trapped nanoparticle in vacuum. Phys. Rev. Lett. 121, 033602 (2018).
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).
Rider, A. D. et al. Electrically driven, optically levitated microscopic rotors. Phys. Rev. A. 99, 041802 (2019).
Hoang, T. M. et al. Torsional optomechanics of a levitated nonspherical nanoparticle. Phys. Rev. Lett. 117, 123604 (2016).
Rashid, M., Torosš, M., Setter, A. & Ulbricht, H. Precession motion in levitated optomechanics. Phys. Rev. Lett. 121, 253601 (2018).
Li, T., Kheifets, S., Medellin, D. & Raizen, M. G. Measurement of the instantaneous velocity of a Brownian particle. Science 328, 1673–1675 (2010).
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).
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).
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).
Xu, Z. & Li, T. Detecting Casimir torque with an optically levitated nanorod. Phys. Rev. A. 96, 033843 (2017).
Haiberger, L., Weingran, M. & Schiller, S. Highly sensitive silicon crystal torque sensor operating at the thermal noise limit. Rev. Sci. Instrum. 78, 025101 (2007).
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).
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).
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).
Diehl, R. et al. Optical levitation and feedback cooling of a nanoparticle at subwavelength distances from a membrane. Phys. Rev. A. 98, 013851 (2018).
Magrini, L. et al. Near-field coupling of a levitated nanoparticle to a photonic crystal cavity. Optica 5, 1597–1602 (2018).
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.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
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
Synthesis of High‐purity Solid SiO2 Nanodumbbells Via Induced Aggregation for Levitated Optomechanics
Science Advances (2021)
Quantum Science and Technology (2021)
Initiating revolutions for optical manipulation: the origins and applications of rotational dynamics of trapped particles
Advances in Physics: X (2021)
Quantum Science and Technology (2021)