- Letter
- Open Access
Sub-kHz mechanical resonator passively cooled to 6 mK
Phys. Rev. Research 8, L022004 – Published 1 April, 2026
DOI: https://doi.org/10.1103/jmyg-299x
Abstract
Highly coherent mechanical resonators are invaluable to ultrasensitive detection techniques by enabling detection of small forces. Studying mechanical resonators in a thermal equilibrium state at millikelvin temperatures provides a promising path to increase their coherence time. Here, we passively cool a massive mechanical cantilever down to by means of nuclear demagnetization, as confirmed by detecting its thermal motion via a lock-in-based detection scheme. At the lowest temperatures the thermal motion of the resonator is still clearly distinguishable from the background noise. Our data analysis confirms that at these temperatures, the motion is still thermally distributed. These results pave the way for passive cooling low-frequency resonators to the sub-millikelvin regime, which would enable tests of quantum mechanics and advances in ultrasensitive force detection.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (46)
- F. Fogliano, B. Besga, A. Reigue, L. M. de Lépinay, P. Heringlake, C. Gouriou, E. Eyraud, W. Wernsdorfer, B. Pigeau, and O. Arcizet, Ultrasensitive nano-optomechanical force sensor operated at dilution temperatures, Nat. Commun. 12, 4124 (2021).
- M. Héritier, A. Eichler, Y. Pan, U. Grob, I. Shorubalko, M. D. Krass, Y. Tao, and C. L. Degen, Nanoladder cantilevers made from diamond and silicon, Nano Lett. 18, 1814 (2018).
- F. Monteiro, W. Li, G. Afek, C.-L. Li, M. Mossman, and D. C. Moore, Force and acceleration sensing with optically levitated nanogram masses at microkelvin temperatures, Phys. Rev. A 101, 053835 (2020).
- D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, Single spin detection by magnetic resonance force microscopy, Nature (London) 430, 329 (2004).
- C. Degen, M. Poggio, H. Mamin, C. Rettner, and D. Rugar, Nanoscale magnetic resonance imaging, Proc. Natl. Acad. Sci. USA 106, 1313 (2009).
- U. Grob, M.-D. Krass, M. Héritier, R. Pachlatko, J. Rhensius, J. Kosata, B. Moores, H. Takahashi, A. Eichler, and C. L. Degen, Magnetic resonance force microscopy with a one-dimensional resolution of 0.9 nanometers, Nano Lett. 19, 7935 (2019).
- R. Fischer, D. P. McNally, C. Reetz, G. G. Assumpcao, T. Knief, Y. Lin, and C. A. Regal, Spin detection with a micromechanical trampoline: Towards magnetic resonance microscopy harnessing cavity optomechanics, New J. Phys. 21, 043049 (2019).
- L. Bossoni, P. Carretta, and M. Poggio, Vortex lattice melting of a single grain probed by ultrasensitive cantilever magnetometry, Appl. Phys. Lett. 104, 182601 (2014).
- Z. Wang, J. Wei, P. Morse, J. G. Dash, O. E. Vilches, and D. H. Cobden, Phase transitions of adsorbed atoms on the surface of a carbon nanotube, Science 327, 552 (2010).
- L. Sellies, R. Spachtholz, S. Bleher, J. Eckrich, P. Scheuerer, and J. Repp, Single-molecule electron spin resonance by means of atomic force microscopy, Nature (London) 624, 64 (2023).
- T. Westphal, H. Hepach, J. Pfaff, and M. Aspelmeyer, Measurement of gravitational coupling between millimetre-sized masses, Nature (London) 591, 225 (2021).
- T. M. Fuchs, D. G. Uitenbroek, J. Plugge, N. van Halteren, J.-P. van Soest, A. Vinante, H. Ulbricht, and T. H. Oosterkamp, Measuring gravity with milligram levitated masses, Sci. Adv. 10, eadk2949 (2024).
- M. Carlesso, S. Donadi, L. Ferialdi, M. Paternostro, H. Ulbricht, and A. Bassi, Present status and future challenges of non-interferometric tests of collapse models, Nat. Phys. 18, 243 (2022).
- A. Vinante, M. Bahrami, A. Bassi, O. Usenko, G. Wijts, and T. Oosterkamp, Upper bounds on spontaneous wave-function collapse models using millikelvin-cooled nanocantilevers, Phys. Rev. Lett. 116, 090402 (2016).
- 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).
- A. Eichler, Ultra-high-Q nanomechanical resonators for force sensing, Mater. Quantum Technol. 2, 043001 (2022).
- Y. Seis, T. Capelle, E. Langman, S. Saarinen, E. Planz, and A. Schliesser, Ground state cooling of an ultracoherent electromechanical system, Nat. Commun. 13, 1507 (2022).
- M. Janse, D. G. Uitenbroek, L. van Everdingen, J. Plugge, B. Hensen, and T. H. Oosterkamp, Current experimental upper bounds on spacetime diffusion, Phys. Rev. Res. 6, 033076 (2024).
- T. Gisler, M. Helal, D. Sabonis, U. Grob, M. Héritier, C. L. Degen, A. H. Ghadimi, and A. Eichler, Soft-clamped silicon nitride string resonators at millikelvin temperatures, Phys. Rev. Lett. 129, 104301 (2022).
- D. Lee, S. Jahanbani, J. Kramer, R. Lu, and K. Lai, Nanoscale imaging of super-high-frequency microelectromechanical resonators with femtometer sensitivity, Nat. Commun. 14, 1188 (2023).
- S. De Bonis, C. Urgell, W. Yang, C. Samanta, A. Noury, J. Vergara-Cruz, Q. Dong, Y. Jin, and A. Bachtold, Ultrasensitive displacement noise measurement of carbon nanotube mechanical resonators, Nano Lett. 18, 5324 (2018).
- T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, Attonewton force detection using ultrathin silicon cantilevers, Appl. Phys. Lett. 71, 288 (1997).
- D. Zoepfl, M. Juan, N. Diaz-Naufal, C. Schneider, L. Deeg, A. Sharafiev, A. Metelmann, and G. Kirchmair, Kerr enhanced backaction cooling in magnetomechanics, Phys. Rev. Lett. 130, 033601 (2023).
- A. Youssefi, S. Kono, M. Chegnizadeh, and T. J. Kippenberg, A squeezed mechanical oscillator with millisecond quantum decoherence, Nat. Phys. 19, 1697 (2023).
- 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).
- 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).
- J. Guo, R. Norte, and S. Gröblacher, Feedback cooling of a room temperature mechanical oscillator close to its motional ground state, Phys. Rev. Lett. 123, 223602 (2019).
- 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).
- M. Sarsby, N. Yurttagül, and A. Geresdi, 500 microkelvin nanoelectronics, Nat. Commun. 11, 1492 (2020).
- G. Batey, A. Casey, M. Cuthbert, A. Matthews, J. Saunders, and A. Shibahara, A microkelvin cryogen-free experimental platform with integrated noise thermometry, New J. Phys. 15, 113034 (2013).
- D. Cattiaux, I. Golokolenov, S. Kumar, M. Sillanpää, L. Mercier de Lépinay, R. Gazizulin, X. Zhou, A. Armour, O. Bourgeois, A. Fefferman, et al., A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling, Nat. Commun. 12, 6182 (2021).
- G. Pickett and C. Enss, The European microkelvin platform, Nat. Rev. Mater. 3, 18012 (2018).
- O. Maillet, D. Cattiaux, X. Zhou, R. R. Gazizulin, O. Bourgeois, A. D. Fefferman, and E. Collin, Nanomechanical damping via electron-assisted relaxation of two-level systems, Phys. Rev. B 107, 064104 (2023).
- B. van Heck, T. M. Fuchs, J. Plugge, W. A. Bosch, and T. H. Oosterkamp, Magnetic cooling and vibration isolation of a sub-kHz mechanical resonator, J Low Temp. Phys. 210, 588 (2023).
- B. W. Chui, Y. Hishinuma, R. Budakian, H. J. Mamin, T. W. Kenny, and D. Rugar, Mass-loaded cantilevers with suppressed higher-order modes for magnetic resonance force microscopy, in TRANSDUCERS'03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No. 03TH8664) (IEEE, 2003), Vol. 2, pp. 1120–1123.
- A. Fleischmann, A. Reiser, and C. Enss, Noise thermometry for ultralow temperatures, J. Low Temp. Phys. 201, 803 (2020).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/jmyg-299x for details on experimental setup, the displacement calibration, and MFFT thermometry, which also includes Refs. [45, 46].
- O. Usenko, A. Vinante, G. Wijts, and T. Oosterkamp, A superconducting quantum interference device based read-out of a subattoNewton force sensor operating at millikelvin temperatures, Appl. Phys. Lett. 98, 133105 (2011).
- I. Golokolenov, A. Ranadive, L. Planat, M. Esposito, N. Roch, X. Zhou, A. Fefferman, and E. Collin, Thermodynamics of a single mesoscopic phononic mode, Phys. Rev. Res. 5, 013046 (2023).
- J. Wagenaar, Magnetic resonance force microscopy for condensed matter, Ph.D. thesis, Leiden University, 2017, https://hdl.handle.net/1887/50492.
- A. M. J. den Haan, J. J. T. Wagenaar, J. M. de Voogd, G. Koning, and T. H. Oosterkamp, Spin-mediated dissipation and frequency shifts of a cantilever at millikelvin temperatures, Phys. Rev. B 92, 235441 (2015).
- F. Pobell, Matter and Methods at Low Temperatures (Springer, Berlin, 2007), Vol. 2.
- G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, Zeptonewton force sensing with nanospheres in an optical lattice, Phys. Rev. A 93, 053801 (2016).
- H. Mamin and D. Rugar, Sub-attonewton force detection at millikelvin temperatures, Appl. Phys. Lett. 79, 3358 (2001).
- J. Chawner, A. Jones, M. Noble, G. Pickett, V. Tsepelin, and D. Zmeev, LEGO® block structures as a sub-kelvin thermal insulator, Sci. Rep. 9, 19642 (2019).
- A. L. Woodcraft and A. Gray, A low temperature thermal conductivity database, AIP Conf. Proc. 1185, 681 (2009).