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Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Nature Nanotechnology (2024)Cite this article

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Abstract

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging ‘dissipation dilution’—where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

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Fig. 1: Timeline of mechanical quality factors of dissipation-diluted resonators.
Fig. 2: Applications of dissipation-diluted nanomechanical resonators.
Fig. 3: Curvature at clamped boundaries and soft-clamping methods.
Fig. 4: Comparison of different dissipation-diluted resonator designs.

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References

  1. Huang, Y. L. & Saulson, P. R. Dissipation mechanisms in pendulums and their implications for gravitational wave interferometers. Rev. Sci. Instrum. 69, 544–553 (1998).

    Article  ADS  CAS  Google Scholar 

  2. González, G. I. & Saulson, P. R. Brownian motion of a mass suspended by an anelastic wire. J. Acoust. Soc. Am. 96, 207–212 (1994).

    Article  ADS  Google Scholar 

  3. Valette, C. & Cuesta, C. Mécanique de la Corde Vibrante (Hermes Science Publications, 1993).

  4. Unterreithmeier, Q. P., Faust, T. & Kotthaus, J. P. Damping of nanomechanical resonators. Phys. Rev. Lett. 105, 027205 (2010).

    Article  ADS  PubMed  Google Scholar 

  5. Fedorov, S. A. et al. Generalized dissipation dilution in strained mechanical resonators. Phys. Rev. B 99, 054107 (2019).

    Article  ADS  CAS  Google Scholar 

  6. Verbridge, S. S., Parpia, J. M., Reichenbach, R. B., Bellan, L. M. & Craighead, H. G. High quality factor resonance at room temperature with nanostrings under high tensile stress. J. Appl. Phys. 99, 124304 (2006).

    Article  ADS  Google Scholar 

  7. Verbridge, S. S., Craighead, H. G. & Parpia, J. M. A megahertz nanomechanical resonator with room temperature quality factor over a million. Appl. Phys. Lett. 92, 013112 (2008).

    Article  ADS  Google Scholar 

  8. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  9. Phillips, W. A. Two-level states in glasses. Rep. Prog. Phys. 50, 1657–1708 (1987).

    Article  ADS  CAS  Google Scholar 

  10. Ghani, T. et al. A 90nm high volume manufacturing logic technology featuring novel 45nm gate length strained silicon CMOS transistors. In IEEE International Electron Devices Meeting 2003 11.6.1–11.6.3 (IEEE, 2003); https://doi.org/10.1109/IEDM.2003.1269442

  11. Southworth, D. R. et al. Stress and silicon nitride: a crack in the universal dissipation of glasses. Phys. Rev. Lett. 102, 225503 (2009).

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Wu, J. & Yu, C. C. How stress can reduce dissipation in glasses. Phys. Rev. B 84, 174109 (2011).

    Article  ADS  Google Scholar 

  13. Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotechnol. 12, 776–783 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Ghadimi, A. H. et al. Elastic strain engineering for ultralow mechanical dissipation. Science 360, 764–768 (2018).

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  15. Bereyhi, M. J. et al. Hierarchical tensile structures with ultralow mechanical dissipation. Nat. Commun. 13, 3097 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  16. Shin, D. et al. Spiderweb nanomechanical resonators via Bayesian optimization: Inspired by nature and guided by machine learning. Adv. Mater. 34, 2106248 (2022).

    Article  CAS  Google Scholar 

  17. Bereyhi, M. J. et al. Perimeter modes of nanomechanical resonators exhibit quality factors exceeding 109 at room temperature. Phys. Rev. X 12, 021036 (2022).

    CAS  Google Scholar 

  18. Cupertino, A. et al. Centimeter-scale nanomechanical resonators with low dissipation. Preprint at https://arxiv.org/abs/2308.00611 (2023).

  19. Beccari, A. et al. Strained crystalline nanomechanical resonators with quality factors above 10 billion. Nat. Phys 18, 436–441 (2022).

    Article  CAS  Google Scholar 

  20. Unterreithmeier, Q. P., Weig, E. M. & Kotthaus, J. P. Universal transduction scheme for nanomechanical systems based on dielectric forces. Nature 458, 1001–1004 (2009).

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Chien, M.-H., Brameshuber, M., Rossboth, B. K., Schütz, G. J. & Schmid, S. Single-molecule optical absorption imaging by nanomechanical photothermal sensing. Proc. Natl Acad. Sci. USA 115, 11150–11155 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Purdy, T. P., Yu, P.-L., Peterson, R. W., Kampel, N. S. & Regal, C. A. Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013).

    CAS  Google Scholar 

  26. Nielsen, W. H. P., Tsaturyan, Y., Møller, C. B., Polzik, E. S. & Schliesser, A. Multimode optomechanical system in the quantum regime. Proc. Natl Acad. Sci. USA 114, 62–66 (2017).

    Article  ADS  PubMed  Google Scholar 

  27. Peterson, R. W. et al. Laser cooling of a micromechanical membrane to the quantum backaction limit. Phys. Rev. Lett. 116, 063601 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Saarinen, S. A., Kralj, N., Langman, E. C., Tsaturyan, Y. & Schliesser, A. Laser cooling a membrane-in-the-middle system close to the quantum ground state from room temperature. Optica 10, 364–372 (2023).

    Article  ADS  CAS  Google Scholar 

  30. Seis, Y. et al. Ground state cooling of an ultracoherent electromechanical system. Nat. Commun. 13, 1507 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  31. Mason, D., Chen, J., Rossi, M., Tsaturyan, Y. & Schliesser, A. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).

    Article  CAS  Google Scholar 

  32. Jöckel, A. et al. Sympathetic cooling of a membrane oscillator in a hybrid mechanical–atomic system. Nat. Nanotechnol. 10, 55–59 (2015).

    Article  ADS  PubMed  Google Scholar 

  33. Møller, C. B. et al. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547, 191–195 (2017).

    Article  ADS  PubMed  Google Scholar 

  34. Karg, T. M. et al. Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart. Science 369, 174–179 (2020).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  35. Thomas, R. A. et al. Entanglement between distant macroscopic mechanical and spin systems. Nat. Phys. 17, 228–233 (2021).

    Article  CAS  Google Scholar 

  36. Schmid, G.-L. et al. Coherent feedback cooling of a nanomechanical membrane with atomic spins. Phys. Rev. X 12, 011020 (2022).

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  39. Delaney, R. D. et al. Superconducting-qubit readout via low-backaction electro-optic transduction. Nature 606, 489–493 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  40. Košata, J., Zilberberg, O., Degen, C. L., Chitra, R. & Eichler, A. Spin detection via parametric frequency conversion in a membrane resonator. Phys. Rev. Appl. 14, 014042 (2020).

    Article  ADS  Google Scholar 

  41. Hälg, D. et al. Membrane-based scanning force microscopy. Phys. Rev. Appl. 15, 021001 (2021).

    Article  ADS  Google Scholar 

  42. Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nat. Photon. 6, 768–772 (2012).

    Article  ADS  CAS  Google Scholar 

  43. Zhou, F. et al. Broadband thermomechanically limited sensing with an optomechanical accelerometer. Optica 8, 350–356 (2021).

    Article  ADS  Google Scholar 

  44. Pratt, J. R. et al. Nanoscale torsional dissipation dilution for quantum experiments and precision measurement. Phys. Rev. X 13, 011018 (2023).

    CAS  Google Scholar 

  45. Carney, D. et al. Mechanical quantum sensing in the search for dark matter. Quantum Sci. Technol. 6, 024002 (2021).

    Article  ADS  Google Scholar 

  46. Manley, J., Chowdhury, M. D., Grin, D., Singh, S. & Wilson, D. J. Searching for vector dark matter with an optomechanical accelerometer. Phys. Rev. Lett. 126, 061301 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Gillespie, D. T. Fluctuation and dissipation in Brownian motion. Am. J. Phys. 61, 1077–1083 (1993).

    Article  ADS  Google Scholar 

  48. Saulson, P. R. Thermal noise in mechanical experiments. Phys. Rev. D. 42, 2437 (1990).

    Article  ADS  CAS  Google Scholar 

  49. Wilson, D. J., Regal, C. A., Papp, S. B. & Kimble, H. J. Cavity optomechanics with stoichiometric SiN films. Phys. Rev. Lett. 103, 207204 (2009).

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Nowick, A. S. and Berry, B. S. Anelastic Relaxation In Crystalline Solids (Academic Press, 1972).

  51. Villanueva, L. G. & Schmid, S. Evidence of surface loss as ubiquitous limiting damping mechanism in SiN micro-and nanomechanical resonators. Phys. Rev. Lett. 113, 227201 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  52. Høj, D., Hoff, U. B. & Andersen, U. L. Ultra-coherent nanomechanical resonators based on density phononic crystal engineering. Preprint at https://arxiv.org/abs/2207.06703 (2022).

  53. Schmid, S., Villanueva, L. G. & Roukes, M. L. (eds) Fundamentals of Nanomechanical Resonators (Springer, 2023).

  54. Enns, C. & Hunklinger, S. Low-Temperature Physics (Springer, 2005).

  55. Kleiman, R. N., Agnolet, G. & Bishop, D. J. Two-level systems observed in the mechanical properties of single-crystal silicon at low temperatures. Phys. Rev. Lett. 59, 2079–2082 (1987).

    Article  ADS  CAS  PubMed  Google Scholar 

  56. Hauer, B. D., Kim, P. H., Doolin, C., Souris, F. & Davis, J. P. Two-level system damping in a quasi-one-dimensional optomechanical resonator. Phys. Rev. B 98, 214303 (2018).

    Article  ADS  CAS  Google Scholar 

  57. MacCabe, G. S. et al. Nano-acoustic resonator with ultralong phonon lifetime. Science 370, 840–843 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  58. Wollack, E. A. et al. Loss channels affecting lithium niobate phononic crystal resonators at cryogenic temperature. Appl. Phys. Lett. 118, 123501 (2021).

    Article  ADS  CAS  Google Scholar 

  59. Zener, C. Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev. 53, 90–99 (1938).

    Article  ADS  Google Scholar 

  60. Lifshitz, R. & Roukes, M. L. Thermoelastic damping in micro- and nanomechanical systems. Phys. Rev. B 61, 5600–5609 (2000).

    Article  ADS  CAS  Google Scholar 

  61. Kiselev, A. A. & Iafrate, G. J. Phonon dynamics and phonon assisted losses in Euler–Bernoulli nanobeams. Phys. Rev. B 77, 205436 (2008).

    Article  ADS  Google Scholar 

  62. Bao, M., Yang, H., Yin, H. & Sun, Y. Energy transfer model for squeeze-film air damping in low vacuum. J. Micromech. Microeng. 12, 341–346 (2002).

    Article  ADS  Google Scholar 

  63. Cross, M. C. & Lifshitz, R. Elastic wave transmission at an abrupt junction in a thin plate with application to heat transport and vibrations in mesoscopic systems. Phys. Rev. B 64, 085324 (2001).

    Article  ADS  Google Scholar 

  64. Cole, G. D., Wilson-Rae, I., Werbach, K., Vanner, M. R. & Aspelmeyer, M. Phonon-tunnelling dissipation in mechanical resonators. Nat. Commun. 2, 231 (2011).

    Article  ADS  PubMed  Google Scholar 

  65. Wilson-Rae, I. et al. High-Q nanomechanics via destructive interference of elastic waves. Phys. Rev. Lett. 106, 047205 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  66. Ghadimi, A. H., Wilson, D. J. & Kippenberg, T. J. Radiation and internal loss engineering of high-stress silicon nitride nanobeams. Nano Lett. 17, 3501–3505 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  67. Jöckel, A. et al. Spectroscopy of mechanical dissipation in micro-mechanical membranes. Appl. Phys. Lett. 99, 143109 (2011).

    Article  ADS  Google Scholar 

  68. Borrielli, A. et al. Control of recoil losses in nanomechanical SiN membrane resonators. Phys. Rev. B 94, 121403 (2016).

    Article  ADS  Google Scholar 

  69. Schmid, S., Jensen, K. D., Nielsen, K. H. & Boisen, A. Damping mechanisms in high-Q micro and nanomechanical string resonators. Phys. Rev. B 84, 165307 (2011).

    Article  ADS  Google Scholar 

  70. Yu, P.-L., Purdy, T. P. & Regal, C. A. Control of material damping in high-Q membrane microresonators. Phys. Rev. Lett. 108, 083603 (2012).

    Article  ADS  PubMed  Google Scholar 

  71. Landau, L. D., Lifshitz, E. M., Pitaevskii, L. P. & Kosevich, A. M. Theory of Elasticity. Course of Theoretical Physics Vol. 7 (Pergamon, 1986).

  72. Catalini, L., Rossi, M., Langman, E. C. & Schliesser, A. Modeling and observation of nonlinear damping in dissipation-diluted nanomechanical resonators. Phys. Rev. Lett. 126, 174101 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  73. Bachtold, A., Moser, J. & Dykman, M. I. Mesoscopic physics of nanomechanical systems. Rev. Mod. Phys. 94, 045005 (2022).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  74. Bereyhi, M. J. et al. Clamp-tapering increases the quality factor of stressed nanobeams. Nano Lett. 19, 2329–2333 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  75. Sadeghi, P., Tanzer, M., Christensen, S. L. & Schmid, S. Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators. J. Appl. Phys. 126, 165108 (2019).

    Article  ADS  Google Scholar 

  76. Reinhardt, C., Müller, T., Bourassa, A. & Sankey, J. C. Ultralow-noise SiN trampoline resonators for sensing and optomechanics. Phys. Rev. X 6, 021001 (2016).

  77. Norte, R. A., Moura, J. P. & Gröblacher, S. Mechanical resonators for quantum optomechanics experiments at room temperature. Phys. Rev. Lett. 116, 147202 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

  78. Wilson, D. J. Cavity Optomechanics with High Stress Silicon Nitride Films. PhD thesis, California Institute of Technology (2012); https://doi.org/10.7907/VB3C-1G76

  79. Chakram, S., Patil, Y. S., Chang, L. & Vengalattore, M. Dissipation in ultrahigh quality factor SiN membrane resonators. Phys. Rev. Lett. 112, 127201 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  80. Yu, P.-L. et al. A phononic bandgap shield for high-Q membrane microresonators. Appl. Phys. Lett. 104, 023510 (2014).

    Article  ADS  Google Scholar 

  81. Tsaturyan, Y. et al. Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics. Opt. Express 22, 6810–6821 (2014).

    Article  ADS  PubMed  Google Scholar 

  82. Weaver, M. J. et al. Nested trampoline resonators for optomechanics. Appl. Phys. Lett. 108, 033501 (2016).

    Article  ADS  Google Scholar 

  83. Serra, E. et al. Silicon nitride MOMS oscillator for room temperature quantum optomechanics. J. Microelectromech. Syst. 27, 1193–1203 (2018).

    Article  CAS  Google Scholar 

  84. Reetz, C. et al. Analysis of membrane phononic crystals with wide band gaps and low-mass defects. Phys. Rev. Appl. 12, 044027 (2019).

    Article  ADS  CAS  Google Scholar 

  85. Fedorov, S. A. et al. Thermal intermodulation noise in cavity-based measurements. Optica 7, 1609–1616 (2020).

    Article  ADS  Google Scholar 

  86. Guo, J., Norte, R. & Gröblacher, S. Feedback cooling of a room temperature mechanical oscillator close to its motional ground state. Phys. Rev. Lett. 123, 223602 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  87. Fedorov, S. Mechanical Resonators with High Dissipation Dilution in Precision and Quantum Measurements. PhD thesis, EPFL, Lausanne (2021); https://doi.org/10.5075/epfl-thesis-10421

  88. Fedorov, S. A., Beccari, A., Engelsen, N. J. & Kippenberg, T. J. Fractal-like mechanical resonators with a soft-clamped fundamental mode. Phys. Rev. Lett. 124, 025502 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  89. Høj, D. et al. Ultra-coherent nanomechanical resonators based on inverse design. Nat. Commun. 12, 5766 (2021).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  90. Davenport, W. B. & Root, W. L. An Introduction to the Theory of Random Signals and Noise (Wiley-IEEE, 1987).

  91. Zwickl, B. M. et al. High quality mechanical and optical properties of commercial silicon nitride membranes. Appl. Phys. Lett. 92, 103125 (2008).

    Article  ADS  Google Scholar 

  92. Renninger, W. H., Kharel, P., Behunin, R. O. & Rakich, P. T. Bulk crystalline optomechanics. Nat. Phys. 14, 601–607 (2018).

    Article  CAS  Google Scholar 

  93. Sementilli, L., Romero, E. & Bowen, W. P. Nanomechanical dissipation and strain engineering. Adv. Funct. Mater. 32, 2105247 (2022).

    Article  CAS  Google Scholar 

  94. Kermany, A. R. et al. Microresonators with Q-factors over a million from highly stressed epitaxial silicon carbide on silicon. Appl. Phys. Lett. 104, 081901 (2014).

    Article  ADS  Google Scholar 

  95. Romero, E. et al. Engineering the dissipation of crystalline micromechanical resonators. Phys. Rev. Appl. 13, 044007 (2020).

    Article  ADS  CAS  Google Scholar 

  96. Cole, G. D. et al. Tensile-strained InxGa1−xP membranes for cavity optomechanics. Appl. Phys. Lett. 104, 201908 (2014).

    Article  ADS  Google Scholar 

  97. Bückle, M. et al. Stress control of tensile-strained In1−xGaxP nanomechanical string resonators. Appl. Phys. Lett. 113, 201903 (2018).

    Article  ADS  Google Scholar 

  98. Manjeshwar, S. K. et al. High-Q trampoline resonators from strained crystalline InGaP for integrated free-space optomechanics. Nano Lett. 23, 5076–5082 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  99. Liu, J. et al. High-Q optomechanical GaAs nanomembranes. Appl. Phys. Lett. 99, 243102 (2011).

    Article  ADS  Google Scholar 

  100. Minamisawa, R. A. et al. Top-down fabricated silicon nanowires under tensile elastic strain up to 4.5%. Nat. Commun. 3, 1096 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  101. Dang, C. et al. Achieving large uniform tensile elasticity in microfabricated diamond. Science 371, 76–78 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  102. Xu, M. et al. High-strength amorphous silicon carbide for nanomechanics. Adv. Mater. 36, 2306513 (2023).

    Article  Google Scholar 

  103. Tao, Y., Boss, J. M., Moores, B. A. & Degen, C. L. Single-crystal diamond nanomechanical resonators with quality factors exceeding one million. Nat. Commun. 5, 3638 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  104. Yuan, M., Cohen, M. A. & Steele, G. A. Silicon nitride membrane resonators at millikelvin temperatures with quality factors exceeding 108. Appl. Phys. Lett. 107, 263501 (2015).

    Article  ADS  Google Scholar 

  105. Manjeshwar, S. K. et al. Suspended photonic crystal membranes in AlGaAs heterostructures for integrated multi-element optomechanics. Appl. Phys. Lett. 116, 264001 (2020).

    Article  ADS  Google Scholar 

  106. Fitzgerald, J. M., Manjeshwar, S. K., Wieczorek, W. & Tassin, P. Cavity optomechanics with photonic bound states in the continuum. Phys. Rev. Res. 3, 013131 (2021).

    Article  CAS  Google Scholar 

  107. Manjeshwar, S. K. et al. Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector. Opt. Express 31, 30212–30226 (2023).

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  109. Kampel, N. S. et al. Improving broadband displacement detection with quantum correlations. Phys. Rev. X 7, 021008 (2017).

    Google Scholar 

  110. Brubaker, B. M. et al. Optomechanical ground-state cooling in a continuous and efficient electro-optic transducer. Phys. Rev. X 12, 021062 (2022).

    CAS  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  112. 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 

  113. Guo, J. & Gröblacher, S. Integrated optical-readout of a high-Q mechanical out-of-plane mode. Light Sci. Appl. 11, 282 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  114. Guo, J., Chang, J., Yao, X. & Gröblacher, S. Active-feedback quantum control of an integrated low-frequency mechanical resonator. Nat. Commun. 14, 4721 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  115. Anetsberger, G. et al. Near-field cavity optomechanics with nanomechanical oscillators. Nat. Phys. 5, 909–914 (2009).

    Article  CAS  Google Scholar 

  116. Anetsberger, G. et al. Measuring nanomechanical motion with an imprecision below the standard quantum limit. Phys. Rev. A 82, 061804 (2010).

    Article  ADS  Google Scholar 

  117. Galinskiy, I., Tsaturyan, Y., Parniak, M. & Polzik, E. S. Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state. Optica 7, 718–725 (2020).

    Article  ADS  CAS  Google Scholar 

  118. Shaniv, R., Kumar Keshava, S., Reetz, C. & Regal, C. A. Understanding the quality factor of mass-loaded tensioned resonators. Phys. Rev. Appl. 19, 031006 (2023).

    Article  ADS  Google Scholar 

  119. Kuehn, S., Loring, R. F. & Marohn, J. A. Dielectric fluctuations and the origins of noncontact friction. Phys. Rev. Lett. 96, 156103 (2006).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  120. Fischer, R. et al. Spin detection with a micromechanical trampoline: towards magnetic resonance microscopy harnessing cavity optomechanics. New J. Phys. 21, 043049 (2019).

    Article  ADS  CAS  Google Scholar 

  121. Zhang, C., Giroux, M., Nour, T. A. & St-Gelais, R. Thermal radiation sensing using high mechanical Q-factor silicon nitride membranes. In 2019 IEEE SENSORS 1–4 (IEEE, 2019); https://doi.org/10.1109/SENSORS43011.2019.8956551

  122. Piller, M. et al. Thermal IR detection with nanoelectromechanical silicon nitride trampoline resonators. IEEE Sens. J. 23, 1066–1071 (2023).

    Article  ADS  CAS  Google Scholar 

  123. Fong, K. Y., Pernice, W. H. P. & Tang, H. X. Frequency and phase noise of ultrahigh Q silicon nitride nanomechanical resonators. Phys. Rev. B 85, 161410 (2012).

    Article  ADS  Google Scholar 

  124. Gavartin, E., Verlot, P. & Kippenberg, T. J. Stabilization of a linear nanomechanical oscillator to its thermodynamic limit. Nat. Commun. 4, 2860 (2013).

    Article  ADS  PubMed  Google Scholar 

  125. Liu, Y. et al. Materials, design, and characteristics of bulk acoustic wave resonator: a review. Micromachines 11, 630 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. Tu, C., Lee, J. E.-Y. & Zhang, X.-S. Dissipation analysis methods and Q-enhancement strategies in piezoelectric MEMS laterally vibrating resonators: a review. Sensors 20, 4978 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  127. Hopcroft, M. A., Nix, W. D. & Kenny, T. W. What is the Young’s modulus of silicon?. J. Microelectromech. Syst. 19, 229–238 (2010).

    Article  CAS  Google Scholar 

  128. Zhang, H. et al. Approaching the ideal elastic strain limit in silicon nanowires. Sci. Adv. 2, 1501382 (2016).

    Article  ADS  Google Scholar 

  129. Tao, Y. et al. Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection. Nanotechnology 26, 465501 (2015).

    Article  CAS  PubMed  Google Scholar 

  130. Klaß, Y. S., Doster, J., Bückle, M., Braive, R. & Weig, E. M. Determining Young’s modulus via the eigenmode spectrum of a nanomechanical string resonator. Appl. Phys. Lett. 121, 083501 (2022).

    Article  ADS  Google Scholar 

  131. Petersen, K. E. Silicon as a mechanical material. Proc. IEEE 70, 420–457 (1982).

    Article  ADS  CAS  Google Scholar 

  132. Bückle, M. Nanomechanical Systems Based on Tensile-stressed Crystalline Indium Gallium Phosphide. PhD thesis, Univ. Konstanz (2020).

  133. Hjort, K., Söderkvist, J. & Schweitz, J.-Å. Gallium arsenide as a mechanical material. J. Micromech. Microeng. 4, 1–13 (1994).

    Article  ADS  CAS  Google Scholar 

  134. Smith, R. T. & Welsh, F. S. Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate. J. Appl. Phys. 42, 2219–2230 (1971).

    Article  ADS  CAS  Google Scholar 

  135. Gruber, M. et al. Strength distribution and fracture analyses of LiNbO3 and LiTaO3 single crystals under biaxial loading. J. Eur. Ceram. Soc. 37, 4397–4406 (2017).

    Article  CAS  Google Scholar 

  136. Österlund, E., Kinnunen, J., Rontu, V., Torkkeli, A. & Paulasto-Kröckel, M. Mechanical properties and reliability of aluminum nitride thin films. J. Alloys Compd 772, 306–313 (2019).

    Article  Google Scholar 

  137. Cleland, A. N., Pophristic, M. & Ferguson, I. Single-crystal aluminum nitride nanomechanical resonators. Appl. Phys. Lett. 79, 2070–2072 (2001).

    Article  ADS  CAS  Google Scholar 

  138. Wu, H. et al. Reducing intrinsic energy dissipation in diamond-on-diamond mechanical resonators toward one million quality factor. Phys. Rev. Mater. 2, 090601 (2018).

    Article  CAS  Google Scholar 

  139. Falin, A. et al. Mechanical properties of atomically thin boron nitride and the role of interlayer interactions. Nat. Commun. 8, 15815 (2017).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  140. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  141. Cleland, A. N. & Roukes, M. L. Noise processes in nanomechanical resonators. J. Appl. Phys. 92, 2758–2769 (2002).

    Article  ADS  CAS  Google Scholar 

  142. Gely, M. F. & Steele, G. A. Superconducting electro-mechanics to test Diósi–Penrose effects of general relativity in massive superpositions. AVS Quantum Sci. 3, 035601 (2021).

    Article  ADS  CAS  Google Scholar 

  143. Lubensky, T. C., Kane, C. L., Mao, X., Souslov, A. & Sun, K. Phonons and elasticity in critically coordinated lattices. Rep. Prog. Phys. 78, 073901 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  144. González, G. Suspensions thermal noise in the LIGO gravitational wave detector. Class. Quantum Gravity 17, 4409–4435 (2000).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank A. Arabmoheghi, M. J. Bereyhi and S. A. Fedorov for insightful exchanges and assistance with figure preparation. We are also grateful to S. Schmid for multiple relevant discussions. This work was supported by funding from the Swiss National Science Foundation under grant agreement no. 185870 (Ambizione) and grant agreement no. 204927 (Cavity Quantum Electro-optomechanics). We further acknowledge funding from the European Research Council (ERC) under the EU H2020 Research and Innovation programme, grant agreement no. 835329 (ExCOM-cCEO).

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Authors and Affiliations

  1. Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, Gothenburg, Sweden

    Nils Johan Engelsen

  2. Instutute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland

    Alberto Beccari & Tobias Jan Kippenberg

  3. Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland

    Alberto Beccari & Tobias Jan Kippenberg

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  1. Nils Johan Engelsen
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N.J.E., A.B. and T.J.K. wrote the paper and prepared the figures.

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Correspondence to Nils Johan Engelsen, Alberto Beccari or Tobias Jan Kippenberg.

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Engelsen, N.J., Beccari, A. & Kippenberg, T.J. Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution. Nat. Nanotechnol. (2024). https://doi.org/10.1038/s41565-023-01597-8

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