- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Quadratic optomechanical cooling of a cavity-levitated nanosphere

N. P. Bullier*, A. Pontin†, and P. F. Barker‡

  • Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

  • *Present address: National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom.
  • †a.pontin@ucl.ac.uk
  • ‡p.barker@ucl.ac.uk
PDF

Phys. Rev. Research 3, L032022 – Published 28 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032022

Abstract

We report on cooling of the center-of-mass motion of a nanoparticle via a coupling between its motion and the optical field within a high finesse cavity. The resulting coupling is purely quadratic in displacement and gives rise to a van der Pol nonlinear damping. These dynamics are analogous to conventional parametric feedback where the cavity provides passive feedback without an additional measurement. We show experimentally that as feedback cooling, the resulting energy distribution is strongly nonthermal and can be controlled by the nonlinear damping induced by the cavity. Our work represents a demonstration of a cavity cooling dominated by this type of coupling across all optomechanical platforms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature (London) 478, 89 (2011).
  2. U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparticle to the motional quantum ground state, Science 367, 892 (2020).
  3. E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Quantum squeezing of motion in a mechanical resonator, Science 349, 952 (2015).
  4. C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, and M. A. Sillanpää, Stabilized entanglement of massive mechanical oscillators, Nature (London) 556, 478 (2018).
  5. R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, Remote quantum entanglement between two micromechanical oscillators, Nature (London) 556, 473 (2018).
  6. P. F. Barker and M. N. Shneider, Cavity cooling of an optically trapped nanoparticle, Phys. Rev. A 81, 023826 (2010).
  7. D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, Cavity opto-mechanics using an optically levitated nanosphere, Proc. Natl. Acad. Sci. USA 107, 1005 (2010).
  8. O. Romero-Isart, M. L. Juan, R. Quidant, and J. I. Cirac, Toward quantum superposition of living organisms, New J. Phys. 12, 033015 (2010).
  9. Y. Arita, M. Mazilu, and K. Dholakia, Laser-induced rotation and cooling of a trapped microgyroscope in vacuum, Nat. Commun. 4, 2374 (2013).
  10. T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, Measurement of the instantaneous velocity of a Brownian particle, Science 328, 1673 (2010).
  11. J. Gieseler and J. Millen, Levitated nanoparticles for microscopic thermodynamics—a review, Entropy 20, 326 (2018).
  12. W.-J. Gu, Z. Yi, L.-H. Sun, and D. H. Xu, Mechanical cooling in single-photon optomechanics with quadratic nonlinearity, Phys. Rev. A 92, 023811 (2015).
  13. H. Shi and M. Bhattacharya, Quantum mechanical study of a generic quadratically coupled optomechanical system, Phys. Rev. A 87, 043829 (2013).
  14. Z. J. Deng, Y. Li, M. Gao, and C. W. Wu, Performance of a cooling method by quadratic coupling at high temperatures, Phys. Rev. A 85, 025804 (2012).
  15. A. Xuereb and M. Paternostro, Selectable linear or quadratic coupling in an optomechanical system, Phys. Rev. A 87, 023830 (2013).
  16. J. D. P. Machado, R. J. Slooter, and Y. M. Blanter, Quantum signatures in quadratic optomechanics, Phys. Rev. A 99, 053801 (2019).
  17. H. Tan, F. Bariani, G. Li, and P. Meystre, Generation of macroscopic quantum superpositions of optomechanical oscillators by dissipation, Phys. Rev. A 88, 023817 (2013).
  18. T. V. Gevorgyan, A. R. Shahinyan, and G. Y. Kryuchkyan, Generation of Fock states and qubits in periodically pulsed nonlinear oscillators, Phys. Rev. A 85, 053802 (2012).
  19. S. Rips, M. Kiffner, I. Wilson-Rae, and M. J. Hartmann, Steady-state negative Wigner functions of nonlinear nanomechanical oscillators, New J. Phys. 14, 023042 (2012).
  20. J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Strong and tunable nonlinear optomechanical coupling in a low-loss system, Nat. Phys. 6, 707 (2010).
  21. M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. D. Giuseppe, and D. Vitali, Tunable linear and quadratic optomechanical coupling for a tilted membrane within an optical cavity: Theory and experiment, J. Opt. 15, 025704 (2012).
  22. T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, Position-Squared Coupling in a Tunable Photonic Crystal Optomechanical Cavity, Phys. Rev. X 5, 041024 (2015).
  23. H. Kaviani, C. Healey, M. Wu, R. Ghobadi, A. Hryciw, and P. E. Barclay, Nonlinear optomechanical paddle nanocavities, Optica 2, 271 (2015).
  24. C. Healey, H. Kaviani, M. Wu, B. Khanaliloo, M. Mitchell, A. C. Hryciw, and P. E. Barclay, Design and experimental demonstration of optomechanical paddle nanocavities, Appl. Phys. Lett. 107, 231107 (2015).
  25. P. Z. G. Fonseca, E. B. Aranas, J. Millen, T. S. Monteiro, and P. F. Barker, Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles, Phys. Rev. Lett. 117, 173602 (2016).
  26. U. Delić, M. Reisenbauer, D. Grass, N. Kiesel, V. Vuletic, and M. Aspelmeyer, Cavity Cooling of a Levitated Nanosphere by Coherent Scattering, Phys. Rev. Lett. 122, 123602 (2019).
  27. U. Delić, D. Grass, M. Reisenbauer, T. Damm, M. Weitz, N. Kiesel, and M. Aspelmeyer, Levitated cavity optomechanics in high vacuum, Quantum Sci. Technol. 5, 025006 (2020).
  28. J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, Subkelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle, Phys. Rev. Lett. 109, 103603 (2012).
  29. J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state, Nat. Nanotechnol. 9, 358 (2014).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032022 for a complete description of the model and additional details on the experimental setup and calibrations.
  31. N. P. Bullier, A. Pontin, and P. F. Barker, Characterisation of a charged particle levitated nano-oscillator, J. Phys. D 53, 175302 (2020).
  32. A. C. Pflanzer, O. Romero-Isart, and J. I. Cirac, Master-equation approach to optomechanics with arbitrary dielectrics, Phys. Rev. A 86, 013802 (2012).
  33. F. Ricci, M. T. Cuairan, G. P. Conangla, A. W. Schell, and R. Quidant, Accurate mass measurement of a levitated nanomechanical resonator for precision force-sensing, Nano Lett. 19, 6711 (2019).
  34. F. García-Santamaría, H. Míguez, M. Ibisate, F. Meseguer, and C. López, Refractive index properties of calcined silica submicrometer spheres, Langmuir 18, 1942 (2002).
  35. J. Millen, T. Deesuwan, P. Barker, and J. Anders, Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere, Nat. Nanotechnol. 9, 425 (2014).
  36. E. Hebestreit, R. Reimann, M. Frimmer, and L. Novotny, Measuring the internal temperature of a levitated nanoparticle in high vacuum, Phys. Rev. A 97, 043803 (2018).
  37. N. P. Bullier, A. Pontin, and P. F. Barker, Super-resolution imaging of a low frequency levitated oscillator, Rev. Sci. Instrum. 90, 093201 (2019).
  38. N. Kiesel, F. Blaser, U. Delić, D. Grass, R. Kaltenbaek, and M. Aspelmeyer, Cavity cooling of an optically levitated submicron particle, Proc. Natl. Acad. Sci. USA 110, 14180 (2013).
  39. J. Millen, P. Z. G. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, Cavity Cooling a Single Charged Levitated Nanosphere, Phys. Rev. Lett. 114, 123602 (2015).
  40. T. S. Monteiro, J. Millen, G. A. T. Pender, F. Marquardt, D. Chang, and P. F. Barker, Dynamics of levitated nanospheres: Towards the strong coupling regime, New J. Phys. 15, 015001 (2013).
  41. E. B. Aranas, P. Z. G. Fonseca, P. F. Barker, and T. S. Monteiro, Split-sideband spectroscopy in slowly modulated optomechanics, New J. Phys. 18, 113021 (2016).
  42. C. Jiang, Y. Cui, and G. Chen, Dynamics of an optomechanical system with quadratic coupling: Effect of first order correction to adiabatic elimination, Sci. Rep. 6, 35583 (2016).
  43. R. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1967), Vol. 2.
  44. J. Roberts and P. Spanos, Stochastic averaging: An approximate method of solving random vibration problems, Int. J. Non Linear Mech. 21, 111 (1986).
  45. E. Boujo and N. Noiray, Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation, Proc. R. Soc. A 473, 20160894 (2017).
  46. J. Bendat and A. Piersol, Random Data: Analysis and Measurement Procedures, 4th ed. (Wiley, Hoboken, NJ, 2011).
  47. A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Cooling and squeezing via quadratic optomechanical coupling, Phys. Rev. A 82, 021806(R) (2010).
  48. A. Pontin, N. P. Bullier, M. Toroš, and P. F. Barker, Ultranarrow-linewidth levitated nano-oscillator for testing dissipative wave-function collapse, Phys. Rev. Research 2, 023349 (2020).
  49. D. Zheng, Y. Leng, X. Kong et al., Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator, Phys. Rev. Research 2, 013057 (2020).
  50. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Probability of Second Law Violations in Shearing Steady States, Phys. Rev. Lett. 71, 2401 (1993).
  51. D. J. Evans and D. J. Searles, Equilibrium microstates which generate second law violating steady states, Phys. Rev. E 50, 1645 (1994).
  52. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in stationary states, J. Stat. Phys. 80, 931 (1995).

Outline

Information

Phys. Rev. Research 3, L032022– Published 28 July, 2021
  • Received 30 June 2020
  • Accepted 16 June 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation