- 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

Accelerated state expansion of a nanoparticle in a dark inverted potential

Grégoire F. M. Tomassi1,2, Daniël Veldhuizen1,2, Bruno Melo1,2, Davide Candoli3, Andreu Riera-Campeny3,4, Oriol Romero-Isart3,5, Nadine Meyer1,2,*, and Romain Quidant1,2

  • *Contact author: nmeyer@ethz.ch
PDF

Phys. Rev. Research 8, L012026 – Published 26 January, 2026

DOI: https://doi.org/10.1103/r7t1-w311

Abstract

While the wave packet of a massive particle grows linearly under free dynamics, it grows exponentially in an inverted harmonic potential, offering a pathway to rapidly increase quantum fluctuations to macroscopic dimensions. In this work, we experimentally demonstrate this principle by expanding the center-of-mass thermal state of a 125nm silica nanoparticle to a position uncertainty of 43.4nm within 260µs. This expansion, achieved using an inverted dark potential to minimize decoherence from photon recoil, represents a 952-fold increase, reaching a scale comparable to the nanoparticle's physical size. This work represents a key advancement toward preparing macroscopic quantum superpositions at unprecedented mass and length scales.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (79)

  1. W. Heisenberg, Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik, Z. Phys. 43, 172 (1927).
  2. F. Diedrich, J. Bergquist, W. M. Itano, and D. Wineland, Laser cooling to the zero-point energy of motion, Phys. Rev. Lett. 62, 403 (1989).
  3. C. Monroe, D. Meekhof, B. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy, Phys. Rev. Lett. 75, 4011 (1995).
  4. C. Roos, T. Zeiger, H. Rohde, H. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, Quantum state engineering on an optical transition and decoherence in a Paul trap, Phys. Rev. Lett. 83, 4713 (1999).
  5. 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).
  6. L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature (London) 595, 373 (2021).
  7. F. Tebbenjohanns, M. L. Mattana, M. Rossi, M. Frimmer, and L. Novotny, Quantum control of a nanoparticle optically levitated in cryogenic free space, Nature (London) 595, 378 (2021).
  8. A. Ranfagni, P. Vezio, M. Calamai, A. Chowdhury, F. Marino, and F. Marin, Vectorial polaritons in the quantum motion of a levitated nanosphere, Nat. Phys. 17, 1120 (2021).
  9. M. Kamba, R. Shimizu, and K. Aikawa, Optical cold damping of neutral nanoparticles near the ground state in an optical lattice, Opt. Express 30, 26716 (2022).
  10. J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez-Ballestero, A. de los Ríos Sommer, N. Meyer, R. Quidant, O. Romero-Isart, R. Reimann, and L. Novotny, Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle, Nat. Phys. 19, 1009 (2023).
  11. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  12. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, et al., Quantum ground state and single-phonon control of a mechanical resonator, Nature (London) 464, 697 (2010).
  13. J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, Sideband cooling of micromechanical motion to the quantum ground state, Nature (London) 475, 359 (2011).
  14. J. Chan, T. 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).
  15. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode, Nature (London) 482, 63 (2012).
  16. M. Bild, M. Fadel, Y. Yang, U. von Lüpke, P. Martin, A. Bruno, and Y. Chu, Schrödinger cat states of a 16-microgram mechanical oscillator, Science 380, 274 (2023).
  17. C. Davisson and L. H. Germer, The scattering of electrons by a single crystal of nickel, Nature (London) 119, 558 (1927).
  18. D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, Diffraction of atoms by a transmission grating, Phys. Rev. Lett. 61, 1580 (1988).
  19. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, Wave–particle duality of C60 molecules, Nature (London) 401, 680 (1999).
  20. M. Arndt and K. Hornberger, Testing the limits of quantum mechanical superpositions, Nat. Phys. 10, 271 (2014).
  21. O. Romero-Isart, Quantum superposition of massive objects and collapse models, Phys. Rev. A 84, 052121 (2011).
  22. A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Models of wave-function collapse, underlying theories, and experimental tests, Rev. Mod. Phys. 85, 471 (2013).
  23. C. A. Rosiek, M. Rossi, A. Schliesser, and A. S. Sørensen, Quadrature squeezing enhances Wigner negativity in a mechanical Duffing oscillator, PRX Quantum 5, 030312 (2024).
  24. A. Riera-Campeny, M. Roda-Llordes, P. T. Grochowski, and O. Romero-Isart, Wigner analysis of particle dynamics and decoherence in wide nonharmonic potentials, Quantum 8, 1393 (2024).
  25. C. Lei, A. Weinstein, J. Suh, E. Wollman, A. Kronwald, F. Marquardt, A. Clerk, and K. Schwab, Quantum nondemolition measurement of a quantum squeezed state beyond the 3 dB limit, Phys. Rev. Lett. 117, 100801 (2016).
  26. T. Weiss, M. Roda-Llordes, E. Torrontegui, M. Aspelmeyer, and O. Romero-Isart, 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).
  27. F. Cosco, J. Pedernales, and M. B. Plenio, Enhanced force sensitivity and entanglement in periodically driven optomechanics, Phys. Rev. A 103, L061501 (2021).
  28. M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys. Rev. Lett. 132, 023601 (2024).
  29. L. Neumeier, M. A. Ciampini, O. Romero-Isart, M. Aspelmeyer, and N. Kiesel, Fast quantum interference of a nanoparticle via optical potential control, Proc. Natl. Acad. Sci. USA 121, e2306953121 (2024).
  30. H. Pino, J. Prat-Camps, K. Sinha, B. P. Venkatesh, and O. Romero-Isart, On-chip quantum interference of a superconducting microsphere, Quantum Sci. Technol. 3, 025001 (2018).
  31. O. Romero-Isart, Coherent inflation for large quantum superpositions of levitated microspheres, New J. Phys. 19, 123029 (2017).
  32. O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, Large quantum superpositions and interference of massive nanometer-sized objects, Phys. Rev. Lett. 107, 020405 (2011).
  33. M. Scala, M. Kim, G. Morley, P. Barker, and S. Bose, Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin, Phys. Rev. Lett. 111, 180403 (2013).
  34. B. A. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, Probing macroscopic quantum superpositions with nanorotors, New J. Phys. 20, 122001 (2018).
  35. A. Pontin, H. Fu, M. Toroš, T. S. Monteiro, and P. F. Barker, Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle, Nat. Phys. 19, 1003 (2023).
  36. A. Ranfagni, K. Børkje, F. Marino, and F. Marin, Two-dimensional quantum motion of a levitated nanosphere, Phys. Rev. Res. 4, 033051 (2022).
  37. M. Kamba, R. Shimizu, and K. Aikawa, Nanoscale feedback control of six degrees of freedom of a near-sphere, Nat. Commun. 14, 7943 (2023).
  38. M. Rossi, A. Militaru, N. Carlon Zambon, A. Riera-Campeny, O. Romero-Isart, M. Frimmer, and L. Novotny, Quantum delocalization of a levitated nanoparticle, Phys. Rev. Lett. 135, 083601 (2025).
  39. M. Kamba and K. Aikawa, Revealing the velocity uncertainties of a levitated particle in the quantum ground state, Phys. Rev. Lett. 131, 183602 (2023).
  40. R. Muffato, T. Georgescu, M. Carlesso, M. Paternostro, and H. Ulbricht, Coherent expansion of the motional state of a massive nanoparticle beyond its linear dimensions, arXiv:2408.09596.
  41. E. Hebestreit, M. Frimmer, R. Reimann, and L. Novotny, Sensing static forces with free-falling nanoparticles, Phys. Rev. Lett. 121, 063602 (2018).
  42. M. Duchaň, M. Šiler, P. Jákl, O. Brzobohatý, A. Rakhubovsky, R. Filip, and P. Zemánek, Nanomechanical state amplifier based on optical inverted pendulum, Commun. Phys. 8, 276 (2025).
  43. V. Jain, J. Gieseler, C. Moritz, C. Dellago, R. Quidant, and L. Novotny, Direct measurement of photon recoil from a levitated nanoparticle, Phys. Rev. Lett. 116, 243601 (2016).
  44. D. E. Chang, C. Regal, S. Papp, D. 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).
  45. P. Maurer, C. Gonzalez-Ballestero, and O. Romero-Isart, Quantum theory of light interaction with a Lorenz-Mie particle: Optical detection and three-dimensional ground-state cooling, Phys. Rev. A 108, 033714 (2023).
  46. G. P. Conangla, R. A. Rica, and R. Quidant, Extending vacuum trapping to absorbing objects with hybrid Paul-optical traps, Nano Lett. 20, 6018 (2020).
  47. D. S. Bykov, M. Meusburger, L. Dania, and T. E. Northup, Hybrid electro-optical trap for experiments with levitated particles in vacuum, Rev. Sci. Instrum. 93, 073201 (2022).
  48. E. Bonvin, L. Devaud, M. Rossi, A. Militaru, L. Dania, D. S. Bykov, M. Teller, T. E. Northup, L. Novotny, and M. Frimmer, Hybrid Paul-optical trap with large optical access for levitated optomechanics, Phys. Rev. Res. 6, 043129 (2024).
  49. E. Bonvin, L. Devaud, M. Rossi, A. Militaru, L. Dania, D. S. Bykov, O. Romero-Isart, T. E. Northup, L. Novotny, and M. Frimmer, State expansion of a levitated nanoparticle in a dark harmonic potential, Phys. Rev. Lett. 132, 253602 (2024).
  50. B. Melo, M. T. Cuairan, G. F. M. Tomassi, N. Meyer, and R. Quidant, Vacuum levitation and motion control on chip, Nat. Nanotechnol. 19, 1270 (2024).
  51. F. G. Major, V. N. Gheorghe, and G. Werth, Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement (Springer, Berlin, Heidelberg, 2005).
  52. R. Graham, Squeezing and frequency changes in harmonic oscillations, J. Mod. Opt. 34, 873 (1987).
  53. J. Janszky and Y. Y. Yushin, Squeezing via frequency jump, Opt. Commun. 59, 151 (1986).
  54. J.-S. Chen, Ticking near the zero-point energy: Towards 1×10−18 accuracy in Al+ optical clocks, Ph.D. thesis, University of Colorado, Boulder, CO, 2017.
  55. J.-S. Chen, S. Brewer, C. Chou, D. Wineland, D. Leibrandt, and D. Hume, Sympathetic ground state cooling and time-dilation shifts in an Al+27 optical clock, Phys. Rev. Lett. 118, 053002 (2017).
  56. S. Brewer, J.-S. Chen, A. Hankin, E. Clements, C. Chou, D. Wineland, D. Hume, and D. Leibrandt, Al+27 quantum-logic clock with a systematic uncertainty below 10−18, Phys. Rev. Lett. 123, 033201 (2019).
  57. M. Teller, V. Messerer, K. Schüppert, Y. Zou, D. A. Fioretto, M. Galli, P. C. Holz, J. Reichel, and T. E. Northup, Integrating a fiber cavity into a wheel trap for strong ion–cavity coupling, AVS Quantum Sci. 5, 012001 (2023).
  58. M. Poggio, C. Degen, H. Mamin, and D. Rugar, Feedback cooling of a cantilever's fundamental mode below 5 mK, Phys. Rev. Lett. 99, 017201 (2007).
  59. G. P. Conangla, F. Ricci, M. T. Cuairan, A. W. Schell, N. Meyer, and R. Quidant, Optimal feedback cooling of a charged levitated nanoparticle with adaptive control, Phys. Rev. Lett. 122, 223602 (2019).
  60. F. Tebbenjohanns, M. Frimmer, A. Militaru, V. Jain, and L. Novotny, Cold damping of an optically levitated nanoparticle to microkelvin temperatures, Phys. Rev. Lett. 122, 223601 (2019).
  61. O. Kremer, I. Califrer, D. Tandeitnik, J. P. von der Weid, G. Temporão, and T. Guerreiro, All-electrical cooling of an optically levitated nanoparticle, Phys. Rev. Appl. 22, 024010 (2024).
  62. See Supplemental Material at http://link.aps.org/supplemental/10.1103/r7t1-w311 for more details on the experimental setup, characterization of the inverted harmonic, data evaluation, and decoherences, which includes Refs. [68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79].
  63. J. Gieseler, Dynamics of optically levitated nanoparticles in high vacuum, Ph.D. thesis, ICFO, 2014.
  64. S. Lindner, P. Juschitz, J. Rieser, Y. Y. Fein, M. Debiossac, M. A. Ciampini, M. Aspelmeyer, and N. Kiesel, Hollow-core fiber loading of nanoparticles into ultra-high vacuum, Appl. Phys. Lett. 124, 143501 (2024).
  65. L. Dania, D. S. Bykov, F. Goschin, M. Teller, A. Kassid, and T. E. Northup, Ultrahigh quality factor of a levitated nanomechanical oscillator, Phys. Rev. Lett. 132, 133602 (2024).
  66. J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Near-field interferometry of a free-falling nanoparticle from a point-like source, Nat. Commun. 5, 4788 (2014).
  67. G. F. M. Tomassi, D. Veldhuizen, B. Melo, D. Candoli, A. Riera-Campeny, O. Romero-Isart, N. Meyer, and R. Quidant, Dataset for “Accelerated state expansion of a nanoparticle in a dark inverted potential” (2024), https://doi.org/10.3929/ethz-c-000790706.
  68. E. Hebestreit, M. Frimmer, R. Reimann, C. Dellago, F. Ricci, and L. Novotny, Calibration and energy measurement of optically levitated nanoparticle sensors, Rev. Sci. Instrum. 89, 033111 (2018).
  69. B. D. Hauer, C. Doolin, K. S. D. Beach, and J. P. Davis, A general procedure for thermomechanical calibration of nano/micro-mechanical resonators, Ann. Phys. 339, 181 (2013).
  70. B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Stat. 7, 1 (1979).
  71. F. Tebbenjohanns, M. Frimmer, and L. Novotny, Optimal position detection of a dipolar scatterer in a focused field, Phys. Rev. A 100, 043821 (2019).
  72. P. Jones, O. Marago, and G. Volpe, Optical tweezers: Principles and applications, in Optical Tweezers: Principles and Applications, edited by P. H. Jones, O. M. Maragò, and G. Volpe (Cambridge University Press, Cambridge, 2015), pp. 1–16.
  73. M. G. Paris, F. Illuminati, A. Serafini, and S. De Siena, Purity of Gaussian states: Measurement schemes and time evolution in noisy channels, Phys. Rev. A 68, 012314 (2003).
  74. E. Joos and A. Lindner, Langevin equation for the parametric oscillator: A model for ion confinement in a radio frequency trap, Z. Phys. D: At. Mol. Clusters 11, 295 (1989).
  75. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (US Government Printing Office, Washington, DC, 1968), Vol. 55.
  76. C. Gonzalez-Ballestero, P. Maurer, D. Windey, L. Novotny, R. Reimann, and O. Romero-Isart, Theory for cavity cooling of levitated nanoparticles via coherent scattering: Master equation approach, Phys. Rev. A 100, 013805 (2019).
  77. M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion-trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87, 1419 (2015).
  78. M. Kumph, C. Henkel, P. Rabl, M. Brownnutt, and R. Blatt, Electric-field noise above a thin dielectric layer on metal electrodes, New J. Phys. 18, 023020 (2016).
  79. M. Teller, D. A. Fioretto, P. C. Holz, P. Schindler, V. Messerer, K. Schüppert, Y. Zou, R. Blatt, J. Chiaverini, J. Sage, et al., Heating of a trapped ion induced by dielectric materials, Phys. Rev. Lett. 126, 230505 (2021).

Outline

Information

Phys. Rev. Research 8, L012026– Published 26 January, 2026
  • Received 27 March 2025
  • Accepted 17 December 2025
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