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# An optical tweezer phonon laser

## Abstract

Phonon lasers are mechanical analogues of the ubiquitous optical laser and have been realized in a variety of contexts1,2,3,4,5,6,7,8,9,10,11,12. However, no such demonstration exists for mesoscopic levitated optomechanical systems, which are emerging as important platforms for conducting fundamental tests of quantum mechanics13,14,15 and gravity16, as well as for developing sensing modalities that couple mechanical motion to electron spin17,18,19,20 and charge21. Inspired by the pioneering work of Arthur Ashkin on optical tweezers22,23, we introduce a mesoscopic, frequency-tunable phonon laser based on the centre-of-mass oscillation of a silica nanosphere levitated in an optical tweezer under vacuum. Unlike previous levitated realizations, our scheme is general enough to be used on single electrons, liquid droplets or even small biological organisms24. Our device thus provides a pathway for a coherent source of phonons on the mesoscale that can be applied to both fundamental problems in quantum mechanics as well as tasks of precision metrology25,26,27.

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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 authors upon reasonable request.

## References

1. 1.

Wallentowitz, S., Vogel, W., Siemers, I. & Toschek, P. E. Vibrational amplification by stimulated emission of radiation. Phys. Rev. A 54, 943–946 (1996).

2. 2.

Liu, H. C. et al. Coupled electron–phonon modes in optically pumped resonant intersubband lasers. Phys. Rev. Lett. 90, 077402 (2003).

3. 3.

Bargatin, I. & Roukes, M. L. Nanomechanical analog of a laser: amplification of mechanical oscillations by stimulated Zeeman transitions. Phys. Rev. Lett. 91, 138302 (2003).

4. 4.

Vahala, K. et al. A phonon laser. Nat. Phys. 5, 682–686 (2009).

5. 5.

Beardsley, R. P., Akimov, A. V., Henini, M. & Kent, A. J. Coherent terahertz sound amplification and spectral line narrowing in a Stark ladder superlattice. Phys. Rev. Lett. 104, 085501 (2010).

6. 6.

Grudinin, I. S., Lee, H., Painter, O. & Vahala, K. J. Phonon laser action in a tunable two–level system. Phys. Rev. Lett. 104, 083901 (2010).

7. 7.

Kabuss, J., Carmele, A., Brandes, T. & Knorr, A. Optically driven quantum dots as source of coherent cavity phonons: a proposal for a phonon laser scheme. Phys. Rev. Lett. 109, 054301 (2012).

8. 8.

Jing, H. et al. PT-symmetric phonon laser. Phys. Rev. Lett. 113, 053604 (2014).

9. 9.

Lü, H., Özdemir, S. K., Kuang, L.-M., Nori, F. & Jing, H. Exceptional points in random-defect phonon lasers. Phys. Rev. Appl. 8, 044020 (2017).

10. 10.

Wang, G. et al. Demonstration of an ultra-low-threshold phonon laser with coupled microtoroid resonators in vacuum. Photon. Res. 5, 73–76 (2017).

11. 11.

Zhang, J. et al. A phonon laser operating at an exceptional point. Nat. Photon. 12, 479–484 (2018).

12. 12.

Ip, M. et al. Phonon lasing from optical frequency comb illumination of trapped ions. Phys. Rev. Lett. 121, 043201 (2018).

13. 13.

Scala, M., Kim, M. S., Morley, G. W., Barker, P. F. & Bose, S. Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin. Phys. Rev. Lett. 111, 180403 (2013).

14. 14.

Yin, Z.-q., Li, T., Zhang, X. & Duan, L. M. Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling. Phys. Rev. A 88, 033614 (2013).

15. 15.

Bateman, J., Nimmrichter, S., Hornberger, K. & Ulbricht, H. Near-field interferometry of a free-falling nanoparticle from a point-like source. Nat. Commun. 5, 4788 (2014).

16. 16.

Bose, S. et al. Spin entanglement witness for quantum gravity. Phys. Rev. Lett. 119, 240401 (2017).

17. 17.

Neukirch, L. P., Gieseler, J., Quidant, R., Novotny, L. & Vamivakas, A. N. Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond. Opt. Lett. 38, 2976–2979 (2013).

18. 18.

Neukirch, L. P., von Haartman, E., Rosenholm, J. M. & Vamivakas, A. N. Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond. Nat. Photon. 9, 653–657 (2015).

19. 19.

Hoang, T. M., Ahn, J., Bang, J. & Li, T. Electron spin control of optically levitated nanodiamonds in vacuum. Nat. Commun. 7, 12250 (2016).

20. 20.

Pettit, R. M., Neukirch, L. P., Zhang, Y. & Vamivakas, A. N. Coherent control of a single nitrogen-vacancy center spin in optically levitated nanodiamond. J. Opt. Soc. Am. B 34, C31–C35 (2017).

21. 21.

Millen, J., Fonseca, P. Z. G., Mavrogordatos, T., Monteiro, T. S. & Barker, P. F. Cavity cooling a single charged levitated nanosphere. Phys. Rev. Lett. 114, 123602 (2015).

22. 22.

Ashkin, A. & Dziedzic, J. M. Optical levitation in high vacuum. Appl. Phys. Lett. 28, 333–335 (1976).

23. 23.

Ashkin, A., Dziedzic, J. M., Bjorkholm, J. E. & Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986).

24. 24.

Romero-Isart, O. et al. Large quantum superpositions and interference of massive nanometer-sized objects. Phys. Rev. Lett. 107, 020405 (2011).

25. 25.

Geraci, A. A., Papp, S. B. & Kitching, J. Short-range force detection using optically cooled levitated microspheres. Phys. Rev. Lett. 105, 101101 (2010).

26. 26.

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

27. 27.

Hempston, D. et al. Force sensing with an optically levitated charged nanoparticle. Appl. Phys. Lett. 111, 133111 (2017).

28. 28.

Streltsov, A., Adesso, G. & Plenio, M. B. Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017).

29. 29.

Rodenburg, B., Neukirch, L. P., Vamivakas, A. N. & Bhattacharya, M. Quantum model of cooling and force sensing with an optically trapped nanoparticle. Optica 3, 318–323 (2016).

30. 30.

Jain, V. et al. Direct measurement of photon recoil from a levitated nanoparticle. Phys. Rev. Lett. 116, 243601 (2016).

31. 31.

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).

32. 32.

Gieseler, J., Spasenović, M., Novotny, L. & Quidant, R. Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle. Phys. Rev. Lett. 112, 103603 (2014).

33. 33.

Gieseler, J., Novotny, L., Moritz, C. & Dellago, C. Non-equilibrium steady state of a driven levitated particle with feedback cooling. New J. Phys. 17, 045011 (2015).

34. 34.

Scully, M. O. & Zubairy, M. S. in Quantum Optics 327–361 (Cambridge Univ. Press, 1997).

35. 35.

Gerry, C. C. & Knight, P. L. in Introductory Quantum Optics 115–134 (Cambridge Univ. Press, 2005).

36. 36.

Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

37. 37.

Dell’Anno, F., De Siena, S. & Illuminati, F. Multiphoton quantum optics and quantum state engineering. Phys. Rep. 428, 53–168 (2006).

38. 38.

Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrödinger kittens for quantum information processing. Science 312, 83–86 (2006).

39. 39.

Beresnev, S. A., Chernyak, V. G. & Fomyagin, G. A. Motion of a spherical particle in a rarefied gas. Part 2. Drag and thermal polarization. J. Fluid Mech. 219, 405–421 (1990).

## Acknowledgements

R.M.P., D.R.L-M., J.T.S. and A.N.V. acknowledge generous support from the Institute of Optics and the Department of Physics and Astronomy at the University of Rochester and Office of Naval Research awards N00014-17-1-2285 and N00014-18-1-2370. W.G., P.K. and M.B. acknowledge support from Office of Naval Research awards N00014-14-1-0803 and N00014-17-1-2291 and useful discussions with J. Lawall and A.K. Jha.

## Author information

M.B. and A.N.V. conceived the research. W.G. and P.K. performed the theoretical calculations, guided by M.B. R.M.P. performed the measurements. All authors discussed the data and wrote the manuscript.

Correspondence to Robert M. Pettit or Wenchao Ge or M. Bhattacharya or A. Nick Vamivakas.

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### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

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• #### DOI

https://doi.org/10.1038/s41566-019-0395-5