Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum control of a nanoparticle optically levitated in cryogenic free space


Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1,2,3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4,5,6,7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Experimental setup.
Fig. 2: Quantum ground-state verification via out-of-loop measurements.
Fig. 3: In-loop analysis of the feedback system.

Data availability

Source data for Figs. 1b, 2, 3 and for Extended Data Figs. 27 are available in the ETH Zurich Research Collection (


  1. 1.

    Zurek, W. H. Decoherence and the transition from quantum to classical — revisited. In Quantum Decoherence: Poincaré Seminar 2005 (eds Duplantier, B. et al.) 1–31 (Birkhäuser, 2007).

  2. 2.

    Chen, Y. Macroscopic quantum mechanics: theory and experimental concepts of optomechanics. J. Phys. B 46, 104001 (2013).

    ADS  CAS  Google Scholar 

  3. 3.

    Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S. & Arndt, M. Colloquium: Quantum interference of clusters and molecules. Rev. Mod. Phys. 84, 157–173 (2012).

    ADS  CAS  Google Scholar 

  4. 4.

    Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).

    ADS  CAS  Google Scholar 

  5. 5.

    Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    ADS  CAS  Google Scholar 

  6. 6.

    Qiu, L., Shomroni, I., Seidler, P. & Kippenberg, T. J. Laser cooling of a nanomechanical oscillator to its zero-point energy. Phys. Rev. Lett. 124, 173601 (2020).

    ADS  CAS  Google Scholar 

  7. 7.

    Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

  8. 8.

    Rossi, M., Mason, D., Chen, J., Tsaturyan, Y. & Schliesser, A. Measurement-based quantum control of mechanical motion. Nature 563, 53–58 (2018).

    ADS  CAS  Google Scholar 

  9. 9.

    Chang, D. E. et al. Cavity opto-mechanics using an optically levitated nanosphere. Proc. Natl Acad. Sci. USA 107, 1005–1010 (2010).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  10. 10.

    Romero-Isart, O., Juan, M. L., Quidant, R. & Cirac, J. I. Toward quantum superposition of living organisms. New J. Phys. 12, 033015 (2010).

    ADS  Google Scholar 

  11. 11.

    Leggett, A. J. Testing the limits of quantum mechanics: motivation, state of play, prospects. J. Phys. Condens. Matter 14, R415 (2002).

    ADS  CAS  Google Scholar 

  12. 12.

    Braginskii, V. B. & Manukin, A. B. Measurement of Weak Forces in Physics Experiments (Univ. of Chicago Press, 1977).

  13. 13.

    Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014).

    CAS  Google Scholar 

  14. 14.

    Bagci, T. et al. Optical detection of radio waves through a nanomechanical transducer. Nature 507, 81–85 (2014).

    Google Scholar 

  15. 15.

    Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599–603 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Cirac, J. I., Lewenstein, M., Mølmer, K. & Zoller, P. Quantum superposition states of Bose-Einstein condensates. Phys. Rev. A 57, 1208–1218 (1998).

    ADS  Google Scholar 

  17. 17.

    Bose, S., Jacobs, K. & Knight, P. L. Scheme to probe the decoherence of a macroscopic object. Phys. Rev. A 59, 3204–3210 (1999).

    ADS  CAS  Google Scholar 

  18. 18.

    Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Romero-Isart, O. Quantum superposition of massive objects and collapse models. Phys. Rev. A 84, 052121 (2011).

    ADS  Google Scholar 

  20. 20.

    Ashkin, A. & Dziedzic, J. M. Feedback stabilization of optically levitated particles. Appl. Phys. Lett. 30, 202 (1977).

    ADS  Google Scholar 

  21. 21.

    Hebestreit, E., Frimmer, M., Reimann, R. & Novotny, L. Sensing Static forces with free-falling nanoparticles. Phys. Rev. Lett. 121, 063602 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

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

    ADS  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Kaltenbaek, R. et al. Macroscopic quantum resonators (MAQRO). Exp. Astron. 34, 123–164 (2012).

    ADS  Google Scholar 

  25. 25.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. 26.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  27. 27.

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

    ADS  PubMed  PubMed Central  Google Scholar 

  28. 28.

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

    ADS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Li, T., Kheifets, S. & Raizen, M. G. Millikelvin cooling of an optically trapped microsphere in vacuum. Nat. Phys. 7, 527–530 (2011).

    CAS  Google Scholar 

  30. 30.

    Gieseler, J., Deutsch, B., Quidant, R. & Novotny, L. Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. Phys. Rev. Lett. 109, 103603 (2012).

    ADS  Google Scholar 

  31. 31.

    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).

    ADS  CAS  Google Scholar 

  32. 32.

    Mancini, S., Vitali, D. & Tombesi, P. Optomechanical cooling of a macroscopic oscillator by homodyne feedback. Phys. Rev. Lett. 80, 688 (1998).

    ADS  CAS  Google Scholar 

  33. 33.

    Wilson, D. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015).

    ADS  CAS  Google Scholar 

  34. 34.

    Cohadon, P. F., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83, 3174–3177 (1999).

    ADS  CAS  Google Scholar 

  35. 35.

    Poggio, M., Degen, C. L., Mamin, H. J. & Rugar, D. Feedback cooling of a cantilever’s fundamental mode below 5 mK. Phys. Rev. Lett. 99, 017201 (2007).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  36. 36.

    Tebbenjohanns, F., Frimmer, M., Jain, V., Windey, D. & Novotny, L. Motional sideband asymmetry of a nanoparticle optically levitated in free space. Phys. Rev. Lett. 124, 013603 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Tebbenjohanns, F., Frimmer, M. & Novotny, L. Optimal position detection of a dipolar scatterer in a focused field. Phys. Rev. A 100, 043821 (2019).

    ADS  CAS  Google Scholar 

  38. 38.

    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).

    ADS  CAS  Google Scholar 

  39. 39.

    Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).

    ADS  MathSciNet  MATH  Google Scholar 

  40. 40.

    Safavi-Naeini, A. H. et al. Observation of quantum motion of a nanomechanical resonator. Phys. Rev. Lett. 108, 033602 (2012).

    ADS  PubMed  PubMed Central  Google Scholar 

  41. 41.

    Purdy, T. P., Grutter, K. E., Srinivasan, K. & Taylor, J. M. Quantum correlations from a room-temperature optomechanical cavity. Science 356, 1265–1268 (2017).

    ADS  MathSciNet  CAS  PubMed  PubMed Central  MATH  Google Scholar 

  42. 42.

    Shkarin, A. B. et al. Quantum optomechanics in a liquid. Phys. Rev. Lett. 122, 153601 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  43. 43.

    Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2010).

  44. 44.

    Sudhir, V. et al. Appearance and disappearance of quantum correlations in measurement-based feedback control of a mechanical oscillator. Phys. Rev. X 7, 011001 (2017).

    Google Scholar 

  45. 45.

    Sayrin, C. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  46. 46.

    Vijay, R. et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77–80 (2012).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

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

  48. 48.

    Meng, C., Brawley, G. A., Bennett, J. S., Vanner, M. R. & Bowen, W. P. Mechanical squeezing via fast continuous measurement. Phys. Rev. Lett. 125, 043604 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  49. 49.

    Vanner, M. R. et al. Pulsed quantum optomechanics. Proc. Natl Acad. Sci. USA 108, 16182 (2011).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Gabrielse, G. et al. Thousandfold improvement in the measured antiproton mass. Phys. Rev. Lett. 65, 1317–1320 (1990).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  51. 51.

    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).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  52. 52.

    Doherty, A. C., Tan, S. M., Parkins, A. S. & Walls, D. F. State determination in continuous measurement. Phys. Rev. A 60, 2380–2392 (1999).

    ADS  CAS  Google Scholar 

  53. 53.

    Micke, P. et al. Closed-cycle, low-vibration 4 K cryostat for ion traps and other applications. Rev. Sci. Instrum. 90, 065104 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  54. 54.

    Frimmer, M. et al. Controlling the net charge on a nanoparticle optically levitated in vacuum. Phys. Rev. A 95, 061801 (2017).

    ADS  Google Scholar 

  55. 55.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  56. 56.

    Hebestreit, E. et al. Calibration and energy measurement of optically levitated nanoparticle sensors. Rev. Sci. Instrum. 89, 033111 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  57. 57.

    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 

  58. 58.

    Underwood, M. et al. Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime. Phys. Rev. A 92, 061801(R) (2015).

    ADS  Google Scholar 

  59. 59.

    Doherty, A. C. & Jacobs, K. Feedback control of quantum systems using continuous state estimation. Phys. Rev. A 60, 2700–2711 (1999).

    ADS  CAS  Google Scholar 

  60. 60.

    Genes, C., Vitali, D., Tombesi, P., Gigan, S. & Aspelmeyer, M. Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes. Phys. Rev. A 77, 033804 (2008).

    ADS  Google Scholar 

  61. 61.

    Pluchar, C. M., Agrawal, A. R., Schenk, E. & Wilson, D. J. Towards cavity-free ground-state cooling of an acoustic-frequency silicon nitride membrane. Appl. Opt. 59, G107–G111 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  62. 62.

    Iwasaki, M. et al. Electric feedback cooling of single charged nanoparticles in an optical trap. Phys. Rev. A 99, 051401 (2019).

    ADS  CAS  Google Scholar 

  63. 63.

    Conangla, G. P. et al. Optimal feedback cooling of a charged levitated nanoparticle with adaptive control. Phys. Rev. Lett. 122, 223602 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  64. 64.

    Kamba, M., Kiuchi, H., Yotsuya, T. & Aikawa, K. Recoil-limited feedback cooling of single nanoparticles near the ground state in an optical lattice. Phys. Rev. A 103, L051701 (2021).

    ADS  CAS  Google Scholar 

  65. 65.

    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).

    ADS  CAS  Google Scholar 

  66. 66.

    Wieczorek, W. et al. Optimal state estimation for cavity optomechanical systems. Phys. Rev. Lett. 114, 223601 (2015).

    ADS  PubMed  PubMed Central  Google Scholar 

  67. 67.

    Garbini, J. L., Bruland, K. J., Dougherty, W. M. & Sidles, J. A. Optimal control of force microscope cantilevers. I. Controller design. J. Appl. Phys. 80, 1951–1958 (1996).

    ADS  CAS  Google Scholar 

Download references


This research was supported by the Swiss National Science Foundation (SNF) through the NCCR-QSIT programme (grant no. 51NF40-160591) and the R’Equip programme (grant no. 206021-189605), and by the European Union’s Horizon 2020 research and innovation programme under grant no. 863132 (iQLev). We are grateful to F. van der Laan for his contributions to the particle characterization procedure. We thank O. Wipfli and C. Fischer for their suggestions in designing the cryogenic vacuum chamber, J. Piotrowski and D. Windey for their advice with the trap assembly, and Y. Li for her work on the control software. We thank our colleagues P. Back, E. Bonvin, J. Gao, A. Militaru, R. Reimann, J. Vijayan and J. Zielinska for input and discussions.

Author information




F.T., M.L.M. and M.R. conducted the experiments and co-wrote the manuscript with M.F., who directed the project with L.N.

Corresponding author

Correspondence to Lukas Novotny.

Additional information

Competing interests The authors declare no competing interests.

Peer review information Nature thanks Dalziel Wilson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Experimental setup.

We optically trap a nanoparticle inside a cryogenic vacuum chamber using a telecom laser. In the forwards direction, we employ a libration and position detection system. In the backwards direction, we place both a homodyne and a heterodyne photodetector. AOM, acousto-optic modulator; DAQ, data acquisition card; EOM, electro-optic modulator; λ/2, half-wave plate; LO, local oscillator; PBS, polarizing beam-splitter; R, reflection; T, transmission.

Extended Data Fig. 2 Postselecting the data.

The compression cycles of the cryocooler are visible in our interferometric signal at baseband (idc[t] in grey). We identify the cycles (red dotted lines) and postselect 300-ms-long intervals (indicator function in orange) of the time traces containing the particle motion (exemplary for ihom[t] in blue).

Extended Data Fig. 3 Transfer function of the electronic feedback chain.

a, b, Measured magnitude (a) and phase (b) response of the experimentally used delay filter. The dotted, dashed, and dot-dashed vertical lines mark the location of the resonance frequency of motion along the z, x, and y axes, respectively.

Extended Data Fig. 4 Detection noise characterization.

Variance of the laser noise as a function of local oscillator power in homodyne detection. The variance, expressed in dB, is normalized to the variance of the electronic noise floor of the detector (grey). The dotted blue line provides a guide for the eye for the linear dependence between variance and power of the beam.

Extended Data Fig. 5 Sideband asymmetry in out-of-loop heterodyne measurements.

a, b, Stokes (a) and anti-Stokes (b) sidebands, at different electronic feedback gains, normalized to the estimated background level (grey line). Each sideband pair is simultaneously fitted to a theoretical model. c, Mechanical occupations (green squares) at different feedback gains. The black solid line is a theoretical model based on an ideal delay filter with parameters estimated from the in-loop spectra. The error bars are obtained by propagating the fit uncertainties (1 s.d.) of the areas.

Extended Data Fig. 6 Sideband cross-correlations in out-of-loop heterodyne measurements.

a, b, Real (a) and imaginary (b) parts of cross-spectra, at different electronic feedback gains. Each pair is simultaneously fitted to a theoretical model and the results are shown as black lines. The grey line marks the zero as a reference. c, d, Fitted mechanical resonance frequency (c) and effective linewidth (d) at different electronic gains. e, Extracted mechanical occupations as a function of fitted effective linewidths. The black line is a theoretical model based on an ideal delay filter and on parameters estimated from the in-loop spectra. The error bars are obtained by the fit uncertainties (1 s.d.).

Extended Data Fig. 7 Fit results.

a, Reference displacement spectrum measured by the homodyne detector at the smallest feedback gain, with a fit to a model (black line). In light red we show the spectral features excluded from the fits. b, Fitted feedback gain, γeff, as a function of the experimentally tunable electronic gain gel. Coloured dots come from fitting the corresponding spectra shown in Fig. 3a. The black squares are the full-width at half-maximum extracted from the computed actual displacement spectra. The grey line is a guide for the eye, and represents the expected linear relation.

Extended Data Table 1 Notation

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links