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Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle

Nature Physics volume 19, pages 1003–1008 (2023)Cite this article

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Abstract

Controlling the motional degrees of isolated, single nanoparticles trapped within optical fields in a high vacuum are seen as ideal candidates for exploring the limits of quantum mechanics in a new mass regime. These systems are also massive enough to be considered for future laboratory tests of the quantum nature of gravity. Recently, the translational motion of trapped particles has been cooled to microkelvin temperatures, but controlling all the observable degrees of freedom, including their orientational motion, remains an important goal. Here we report the control and cooling of all the translational and rotational degrees of freedom of a nanoparticle trapped in an optical tweezer, accomplished by cavity cooling via coherent elliptic scattering. We reached temperatures in the range of hundreds of microkelvins for the translational modes and temperatures as low as 5 mK for the librational degrees of freedom. This work brings within reach applications in quantum science and the study of single isolated nanoparticles via imaging and diffractive methods, free of interference from a substrate.

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Fig. 1: Overview of the experiment.
Fig. 2: Direct observation of CS cooling for five DoFs of a trapped particle.
Fig. 3: Evidence of γ diffusion: heterodyne spectrogram at intermediate pressures.
Fig. 4: Evidence for trapping of the γ librational mode: heterodyne spectrogram at the lowest pressure.

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Data availability

Source data are provided with this paper. All other 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. Seis, Y. et al. Ground state cooling of an ultracoherent electromechanical system. Nat. Commun. 13, 1507 (2022).

    ADS  Google Scholar 

  2. Ockeloen-Korppi, C. et al. Stabilized entanglement of massive mechanical oscillators. Nature 556, 478–482 (2018).

    ADS  Google Scholar 

  3. Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nat. Nanotechnol. 7, 509–514 (2012).

    ADS  Google Scholar 

  4. Higginbotham, A. et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat. Phys. 14, 1038–1042 (2018).

    Google Scholar 

  5. Middlemiss, R. et al. Measurement of the Earth tides with a MEMS gravimeter. Nature 531, 614–617 (2016).

    ADS  Google Scholar 

  6. Magrini, L. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021).

    ADS  Google Scholar 

  7. Kamba, M., Shimizu, R. & Aikawa, K. Optical cold damping of neutral nanoparticles near the ground state in an optical lattice. Opt. Express 30, 26716–26727 (2022).

    ADS  Google Scholar 

  8. Tebbenjohanns, F. et al. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 595, 378–382 (2021).

    ADS  Google Scholar 

  9. Delić, U. et al. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 367, 892–895 (2020).

    ADS  Google Scholar 

  10. Ranfagni, A. et al. Two-dimensional quantum motion of a levitated nanosphere. Phys. Rev. Research 4, 033051 (2022).

    ADS  Google Scholar 

  11. Piotrowski, J. et al. Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle. Nat. Phys. https://doi.org/10.1038/s41567-023-01956-1 (2023).

  12. Windey, D. et al. Cavity-based 3D cooling of a levitated nanoparticle via coherent scattering. Phys. Rev. Lett. 122, 123601 (2019).

    ADS  Google Scholar 

  13. Delić, U. et al. Cavity cooling of a levitated nanosphere by coherent scattering. Phys. Rev. Lett. 122, 123602 (2019).

    ADS  Google Scholar 

  14. Toroš, M. & Monteiro, T. S. Quantum sensing and cooling in three-dimensional levitated cavity optomechanics. Phys. Rev. Research 2, 023228 (2020).

    ADS  Google Scholar 

  15. Toroš, M. et al. Coherent-scattering two-dimensional cooling in levitated cavity optomechanics. Phys. Rev. Research 3, 023071 (2021).

    ADS  Google Scholar 

  16. Vuletić, V. & Chu, S. Laser cooling of atoms, ions, or molecules by coherent scattering. Phys. Rev. Lett. 84, 3787 (2000).

    ADS  Google Scholar 

  17. Kuhn, S. et al. Full rotational control of levitated silicon nanorods. Optica 4, 356–360 (2017).

    ADS  Google Scholar 

  18. Stickler, B. A. et al. Probing macroscopic quantum superpositions with nanorotors. New J. Phys. 20, 122001 (2018).

    MathSciNet  ADS  Google Scholar 

  19. Ma, Y. et al. Quantum persistent tennis racket dynamics of nanorotors. Phys. Rev. Lett. 125, 053604 (2020).

    MathSciNet  ADS  Google Scholar 

  20. Rashid, M. et al. Precession motion in levitated optomechanics. Phys. Rev. Lett. 121, 253601 (2018).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  22. van der Laan, F. et al. Optically levitated rotor at its thermal limit of frequency stability. Phys. Rev. A 102, 013505 (2020).

    ADS  Google Scholar 

  23. Miao, J. et al. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).

    ADS  Google Scholar 

  24. Gao, Y. et al. Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging. Proc. Natl Acad. Sci. USA 116, 4018–4024 (2019).

    ADS  Google Scholar 

  25. van der Laan, F. et al. Sub-kelvin feedback cooling and heating dynamics of an optically levitated librator. Phys. Rev. Lett. 127, 123605 (2021).

    ADS  Google Scholar 

  26. Bang, J. et al. Five-dimensional cooling and nonlinear dynamics of an optically levitated nanodumbbell. Phys. Rev. Research 2, 043054 (2020).

    ADS  Google Scholar 

  27. Schäfer, J. et al. Cooling nanorotors by elliptic coherent scattering. Phys. Rev. Lett. 126, 163603 (2021).

    ADS  Google Scholar 

  28. Rudolph, H. et al. Theory of nanoparticle cooling by elliptic coherent scattering. Phys. Rev. A 103, 043514 (2021).

    MathSciNet  ADS  Google Scholar 

  29. Sihvola, A. Dielectric polarization and particle shape effects. J. Nanomater. 2007, 1 (2007).

    Google Scholar 

  30. Bullier, N. P., Pontin, A. & Barker, P. F. Quadratic optomechanical cooling of a cavity-levitated nanosphere. Phys. Rev. Research 3, L032022 (2021).

    ADS  Google Scholar 

  31. Cavalleri, A. et al. Gas damping force noise on a macroscopic test body in an infinite gas reservoir. Phys. Lett. A 374, 3365–3369 (2010).

    MATH  ADS  Google Scholar 

  32. Pontin, A. et al. Ultranarrow-linewidth levitated nano-oscillator for testing dissipative wave-function collapse. Phys. Rev. Research 2, 023349 (2020).

    ADS  Google Scholar 

  33. Zheng, D. et al. Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator. Phys. Rev. Research 2, 013057 (2020).

    ADS  Google Scholar 

  34. Millen, J. et al. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. Nat. Nanotechnol. 9, 425–429 (2014).

    ADS  Google Scholar 

  35. Papendell, B., Stickler, B. A. & Hornberger, K. Quantum angular momentum diffusion of rigid bodies. New J. Phys. 19, 122001 (2017).

    MathSciNet  ADS  Google Scholar 

  36. Stickler, B. A., Schrinski, B. & Hornberger, K. Rotational friction and diffusion of quantum rotors. Phys. Rev. Lett. 121, 040401 (2018).

    ADS  Google Scholar 

  37. Toroš, M., Rashid, M. & Ulbricht, H. Detection of anisotropic particles in levitated optomechanics. Phys. Rev. A 98, 053803 (2018).

    ADS  Google Scholar 

  38. Millen, J. et al. Cavity cooling a single charged levitated nanosphere. Phys. Rev. Lett. 114, 123602 (2015).

    ADS  Google Scholar 

  39. Fonseca, P. Z. G. et al. Nonlinear dynamics and strong cavity cooling of levitated nanoparticles. Phys. Rev. Lett. 117, 173602 (2016).

    ADS  Google Scholar 

  40. Kiesel, N. et al. Cavity cooling of an optically levitated submicron particle. Proc. Natl Acad. Sci. USA 110, 14180–14185 (2013).

    ADS  Google Scholar 

  41. Seberson, T. & Robicheaux, F. Parametric feedback cooling of rigid body nanodumbbells in levitated optomechanics. Phys. Rev. A 99, 013821 (2019).

    ADS  Google Scholar 

  42. Abdi, M. et al. Effect of phase noise on the generation of stationary entanglement in cavity optomechanics. Phys. Rev. A 84, 032325 (2011).

    ADS  Google Scholar 

  43. Rabl, P. et al. Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems. Phys. Rev. A 80, 063819 (2009).

    ADS  Google Scholar 

  44. Risken, H. The Fokker-Planck Equation (Springer, 1989).

  45. Douglas, P., Bergamini, S. & Renzoni, F. Tunable Tsallis distributions in dissipative optical lattices. Phys. Rev. Lett. 96, 110601 (2006).

    ADS  Google Scholar 

  46. Lutz, E. Anomalous diffusion and Tsallis statistics in an optical lattice. Phys. Rev. A 67, 051402 (2003).

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  48. Weiss, T. et al. Large quantum delocalization of a levitated nanoparticle using optimal control: applications for force sensing and entangling via weak forces. Phys. Rev. Lett. 127, 023601 (2021).

    ADS  Google Scholar 

  49. Gittes, F. & Schmidt, C. F. Interference model for back-focal-plane displacement detection in optical tweezers. Opt. Lett. 23, 7–9 (1998).

    ADS  Google Scholar 

  50. Gieseler, J. et al. Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. Phys. Rev. Lett. 109, 103603 (2012).

    ADS  Google Scholar 

  51. Seberson, T. A. Heating and Cooling Mechanisms for the Thermal Motion of an Optically Levitated Nanoparticle. PhD thesis, Purdue Univ. Graduate School (2020).

  52. Jackson, J. D. Classical Electrodynamics (Wiley, 1999).

  53. Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, 2012).

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Acknowledgements

A.P. thanks F. Marin for useful discussions. We acknowledge funding from EPSRC grant no. EP/N031105/1 and EP/S000267/1 . H.F. acknowledges the Engineering and Physical Sciences Research Council (grant no. EP/L015242/1). M.T. acknowledges funding by the Leverhulme Trust (RPG-2020-197).

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University College London, London, UK

    A. Pontin, H. Fu, T. S. Monteiro & P. F. Barker

  2. School of Physics and Astronomy, University of Glasgow, Glasgow, UK

    M. Toroš

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  1. A. Pontin
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  2. H. Fu
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  3. M. Toroš
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  4. T. S. Monteiro
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Contributions

A.P. and P.F.B. conceived and designed the experiment. A.P. and H.F. performed the experiment. A.P. performed the data analysis. A.P., M.T. and T.S.M. carried out the theoretical calculations including the stochastic numerical simulations. All the authors have engaged at every step and provided valuable input. A.P. and P.F.B. wrote the paper with important contributions from all the authors. P.F.B. coordinated the project.

Corresponding authors

Correspondence to A. Pontin or P. F. Barker.

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Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Comparison between measured effective temperatures and model estimates as a function of pressure.

Theoretical curves (solid lines) assume nominal parameters without any fitting. Also shown are bands (shaded regions) which reflect how the model is affected by experimental uncertainties. The CoM x, y and z are shown in panels a), b) and c) respectively. The angular DoFs α, β and γ in panels d), e) and f) respectively. The gray dashed line in all panel marks the room temperature. Data are presented as mean values ± SD on a sample size of 10 elements. Error bars for the pressure values reflect the accuracy of the gauge.

Supplementary information

Supplementary Information

Supplementary Sections I–VI, Figs. 1–8 and Tables I and II.

Source data

Source Data Fig. 2

Data for Fig. 2a–e.

Source Data Extended Data Fig. 1

Data for Extended Data Fig. 1.

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Pontin, A., Fu, H., Toroš, M. et al. Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle. Nat. Phys. 19, 1003–1008 (2023). https://doi.org/10.1038/s41567-023-02006-6

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