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# 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.

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## 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.

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## 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

### 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.

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

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

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