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.

Casimir spring and dilution in macroscopic cavity optomechanics

An Author Correction to this article was published on 01 December 2021

This article has been updated


The Casimir force was predicted in 1948 as a force arising between macroscopic bodies from the zero-point energy. At finite temperatures, it has been shown that a thermal Casimir force exists due to thermal rather than zero-point energy and there are a growing number of experiments that characterize the effect at a range of temperatures and distances. In addition, in the rapidly evolving field of cavity optomechanics, there is an endeavour to manipulate phonons and enhance coherence. We demonstrate a way to realize a Casimir spring and engineer dilution in macroscopic optomechanics, by coupling a metallic SiN membrane to a photonic re-entrant cavity. The attraction of the spatially localized Casimir spring mimics a non-contacting boundary condition, giving rise to increased strain and acoustic coherence through dissipation dilution. This provides a way to manipulate phonons via thermal photons leading to ‘in situ’ reconfigurable mechanical states, to reduce loss mechanisms and to create additional types of acoustic nonlinearity—all at room temperature.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental design and influence of the Casimir force.
Fig. 2: Power law of the thermal Casimir force.
Fig. 3: The driven membrane and microwave modulation.
Fig. 4: The effect of Casimir pinning and dilution on the (0, 2) and (0, 3) niobium membrane modes.

Similar content being viewed by others

Data availability

All the data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

Finite-element analysis was undertaken using COMSOL; implemented meshes and data output may be requested from the corresponding authors.

Change history


  1. Casimir, H. B. On the attraction between two perfectly conducting plates. Front. Phys. 100, 61–63 (1948).

    MATH  Google Scholar 

  2. Sushkov, A., Kim, W., Dalvit, D. & Lamoreaux, S. Observation of the thermal Casimir force. Nat. Phys. 7, 230–233 (2011).

    Google Scholar 

  3. Bressi, G., Carugno, G., Onofrio, R. & Ruoso, G. Measurement of the Casimir force between parallel metallic surfaces. Phys. Rev. Lett. 88, 041804 (2002).

    ADS  Google Scholar 

  4. Klimchitskaya, G., Mohideen, U. & Mostepanenko, V. Casimir force between real materials: experiment and theory. Rev. Mod. 81, 1827–1885 (2009).

    ADS  Google Scholar 

  5. Obrecht, J. M. et al. Measurement of the temperature dependence of the Casimir–Polder force. Phys. Rev. Lett. 98, 063201 (2007).

    ADS  Google Scholar 

  6. Rodriguez, A. W., Capasso, F. & Johnson, S. G. The Casimir effect in microstructured geometries. Nat. Photon. 5, 211–221 (2011).

    ADS  Google Scholar 

  7. Zou, J. et al. Casimir forces on a silicon micromechanical chip. Nat. Commun. 4, 1845 (2013).

    ADS  Google Scholar 

  8. Wilson, C. M. et al. Observation of the dynamical Casimir effect in a superconducting circuit. Nature 479, 376–379 (2011).

    ADS  Google Scholar 

  9. Somers, D. A., Garrett, J. L., Palm, K. J. & Munday, J. N. Measurement of the Casimir torque. Nature 564, 386–389 (2018).

    ADS  Google Scholar 

  10. Wang, X., Qin, W., Miranowicz, A., Savasta, S. & Nori, F. Unconventional cavity optomechanics: nonlinear control of phonons in the acoustic quantum vacuum. Phys. Rev. A 100, 063827 (2019).

    ADS  Google Scholar 

  11. Stange, A., Imboden, M., Javor, J., Barrett, L. K. & Bishop, D. J. Building a Casimir metrology platform with a commercial MEMs sensor. Microsyst. Nanoeng. 5, 14 (2019).

    ADS  Google Scholar 

  12. Lamoreaux, S. K. The Casimir force: background, experiments, and applications. Rep. Prog. Phys. 68, 201 (2004).

    ADS  Google Scholar 

  13. Liu, X.-f, Li, Y. & Jing, H. Casimir switch: steering optical transparency with vacuum forces. Sci. Rep. 6, 27102 (2016).

    ADS  Google Scholar 

  14. Imboden, M., Morrison, J., Campbell, D. & Bishop, D. Design of a Casimir-driven parametric amplifier. J. Appl. Phys. 116, 134504 (2014).

    ADS  Google Scholar 

  15. Rivera, N., Wong, L. J., Joannopoulos, J. D., Soljačić, M. & Kaminer, I. Light emission based on nanophotonic vacuum forces. Nat. Phys. 15, 1284–1289 (2019).

  16. Corbitt, T. et al. Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK. Phys. Rev. Lett. 99, 160801 (2007).

    ADS  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  19. Kalaee, M. et al. Quantum electromechanics of a hypersonic crystal. Nat. Nanotechnol. 14, 334–339 (2019).

    ADS  Google Scholar 

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

    Google Scholar 

  21. Han, X., Fong, K. Y. & Tang, H. X. A 10-GHz film-thickness-mode cavity optomechanical resonator. Appl. Phys. Lett. 106, 161108 (2015).

    ADS  Google Scholar 

  22. Macrì, V. et al. Nonperturbative dynamical Casimir effect in optomechanical systems: vacuum Casimir–Rabi splittings. Phys. Rev. X 8, 011031 (2018).

    Google Scholar 

  23. Settineri, A. et al. Conversion of mechanical noise into correlated photon pairs: dynamical Casimir effect from an incoherent mechanical drive. Phys. Rev. A 100, 022501 (2019).

    ADS  Google Scholar 

  24. Ashkin, A. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl Acad. Sci. USA 94, 4853–4860 (1997).

    ADS  Google Scholar 

  25. Süsstrunk, R. & Huber, S. D. Topological mechanical metamaterials. Proc. Natl Acad. Sci. USA 113, E4767–E4775 (2016).

    ADS  Google Scholar 

  26. Fujisawa, K. General treatment of klystron resonant cavities. IEEE Trans. Microw. Theory Tech. 6, 344–358 (1958).

    ADS  Google Scholar 

  27. Le Floch, J.-M. et al. Rigorous analysis of highly tunable cylindrical transverse magnetic mode re-entrant cavities. Rev. Sci. Instrum. 84, 125114 (2013).

    ADS  Google Scholar 

  28. Tobar, M. E., Locke, C. R., Ivanov, E. N., Heng, I. S. & Blair, D. G. Accurate calibration technique for a resonant-mass gravitational wave detector. Rev. Sci. Instrum. 71, 4282–4285 (2000).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  30. Blair, D. G. et al. High sensitivity gravitational wave antenna with parametric transducer readout. Phys. Rev. Lett. 74, 1908–1911 (1995).

    ADS  Google Scholar 

  31. Barroso, J. J., Castro, P. J., Aguiar, O. D. & Carneiro, L. A. Reentrant cavities as electromechanical transducers. Rev. Sci. Instrum. 75, 1000–1005 (2004).

    ADS  Google Scholar 

  32. Carvalho, N. C., Fan, Y., Le Floch, J.-M. & Tobar, M. E. Piezoelectric voltage coupled reentrant cavity resonator. Rev. Sci. Instrum. 85, 104705 (2014).

    ADS  Google Scholar 

  33. Goryachev, M. & Tobar, M. E. The 3D split-ring cavity lattice: a new metastructure for engineering arrays of coupled microwave harmonic oscillators. New J. Phys. 17, 023003 (2015).

    ADS  Google Scholar 

  34. Carvalho, N. C., Fan, Y. & Tobar, M. E. Piezoelectric tunable microwave superconducting cavity. Rev. Sci. Instrum. 87, 094702 (2016).

    ADS  Google Scholar 

  35. Clark, T. J., Vadakkumbatt, V., Souris, F., Ramp, H. & Davis, J. P. Cryogenic microwave filter cavity with a tunability greater than 5 GHz. Rev. Sci. Instrum. 89, 114704 (2018).

    ADS  Google Scholar 

  36. Pate, J. M., Martinez, L. A., Thompson, J. J., Chiao, R. Y. & Sharping, J. E. Electrostatic tuning of mechanical and microwave resonances in 3D superconducting radio frequency cavities. AIP Adv. 8, 115223 (2018).

    ADS  Google Scholar 

  37. Bagheri, M., Poot, M., Li, M., Pernice, W. P. & Tang, H. X. Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation. Nat. Nanotechnol. 6, 726–732 (2011).

    ADS  Google Scholar 

  38. Shoaib, M., Hisham, N., Basheer, N. & Tariq, M. Frequency and displacement analysis of electrostatic cantilever-based MEMs sensor. Analog Integr. Circuits Signal Process. 88, 1–11 (2016).

    Google Scholar 

  39. Chan, H., Aksyuk, V., Kleiman, R., Bishop, D. & Capasso, F. Nonlinear micromechanical Casimir oscillator. Phys. Rev. Lett. 87, 211801 (2001).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  41. Polzik, E. S. et al. Optical detector and amplifier for RF-detection having a position dependent capacitor with a displaceable membrane. US patent 9,660,721 (2017).

  42. Fan, Y. et al. Investigation of higher order reentrant modes of a cylindrical reentrant-ring cavity resonator. IEEE Trans. Microw. Theory Tech. 62, 1657–1662 (2014).

    ADS  Google Scholar 

  43. Goryachev, M. & Tobar, M. Microwave frequency magnetic field manipulation systems and methods and associated application instruments, apparatus and system. AU patent 2014903143 (2014).

  44. Goryachev, M. et al. High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev. Appl. 2, 054002 (2014).

    ADS  Google Scholar 

  45. Kostylev, N., Goryachev, M. & Tobar, M. E. Superstrong coupling of a microwave cavity to yttrium iron garnet magnons. Appl. Phys. Lett. 108, 062402 (2016).

    ADS  Google Scholar 

  46. Creedon, D. L. et al. Strong coupling between P1 diamond impurity centers and a three-dimensional lumped photonic microwave cavity. Phys. Rev. B 91, 140408 (2015).

    ADS  Google Scholar 

  47. Rhoads, J. F., Shaw, S. W. & Turner, K. L. Nonlinear dynamics and its applications in micro-and nanoresonators. In ASME 2008 Dynamic Systems and Control Conference 1509–1538 (American Society of Mechanical Engineers Digital Collection, 2009).

  48. Huang, P. et al. Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond. Nat. Commun. 7, 11517 (2016).

    ADS  Google Scholar 

  49. Pirkkalainen, J.-M., Damskägg, E., Brandt, M., Massel, F. & Sillanpää, M. A. Squeezing of quantum noise of motion in a micromechanical resonator. Phys. Rev. Lett. 115, 243601 (2015).

    ADS  Google Scholar 

  50. Rabl, P. Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011).

    ADS  Google Scholar 

  51. Huang, R., Miranowicz, A., Liao, J.-Q., Nori, F. & Jing, H. Nonreciprocal photon blockade. Phys. Rev. Lett. 121, 153601 (2018).

    ADS  Google Scholar 

Download references


J.M.P. thanks E. Ivanov for his help with the development and analysis of the microwave phase-bridge circuit. J.M.P. also thanks K. Blackburn for his help with machining the vacuum testbed. This research was supported by the Australian Research Council grant number CE170100009 and DARPA through grant W911NF1510557.

Author information

Authors and Affiliations



The experimental work was carried out by J.M.P. The manuscript and theoretical work was done by J.M.P, M.G., R.Y.C., J.E.S. and M.E.T.

Corresponding authors

Correspondence to J. M. Pate or M. E. Tobar.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Hui Jing and Salvatore Savasta for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary methods, additional measurements (mechanical bistability, and niobium membranes and acoustic response) and Supplementary Figs. 1–8.

Source data

Source Data Fig. 1

Processed data from raw measurements used to create the figure.

Source Data Fig. 2

Processed data from raw measurements used to create the figure.

Source Data Fig. 3

Processed data from raw measurements used to create the figure.

Source Data Fig. 4

Experimental and simulated processed data from experiment and COMSOL modelling.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pate, J.M., Goryachev, M., Chiao, R.Y. et al. Casimir spring and dilution in macroscopic cavity optomechanics. Nat. Phys. 16, 1117–1122 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing