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Casimir spring and dilution in macroscopic cavity optomechanics


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.

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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.

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.


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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




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.

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The authors declare no competing interests.

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

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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.

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

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