- Article
- Published:
- Yichi Zhang1,2,3,
- Hui Zhang ORCID: orcid.org/0000-0001-9749-25551,2,4,
- Xiuxia Wang5,
- Yiheng Wang ORCID: orcid.org/0009-0002-0840-03941,2,3,
- Yuchen Liu1,2,3,
- Shu Li1,2,3,
- Tianyi Zhang1,2,
- Chuang Fan1,2,3 &
- …
- Changgan Zeng ORCID: orcid.org/0000-0001-8630-845X1,2,4
Nature Physics (2024)Cite this article
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Subjects
- Characterization and analytical techniques
- Quantum mechanics
Abstract
The quantum fluctuation-induced Casimir force can be either attractive or repulsive, depending on the dielectric permittivities and magnetic permeabilities of the materials involved. However, it is challenging to manipulate the dielectric permittivities of most materials using external fields. In contrast, the magnetic permeabilities of ferrofluids can be readily tuned by magnetic fields, which opens up the possibility of magnetic-field tuning of the Casimir force. Here, we demonstrate that this tuning can be achieved for a gold sphere and a silica plate immersed in water-based ferrofluids. Our theoretical calculations predict that, by varying the magnetic field, separation distance and ferrofluid volume fraction, the Casimir force can be tuned from attractive to repulsive over a wide range of parameters in this system. Experimentally, we develop a cantilever designed to conduct measurements within water-based ferrofluids. Using this setup, we observe the predicted transitions. These findings may lead to the development of switchable micromechanical devices based on the Casimir effect.
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Data availability
Further data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
Codes for reproducing the calculation results are available from the corresponding author upon reasonable request.
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Acknowledgements
Y.Z., H.Z., X.W., Y.W., Y.L., S.L., T.Z., C.F. and C.Z. were supported by the National Key Research and Development Program of China (grant no. 2023YFA1406300), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302800), the National Natural Science Foundation of China (grant nos. 92165201, 92265201 and 12074357), Anhui Provincial Key Research and Development Project (grant no. 2023z04020008), the CAS Project for Young Scientists in Basic Research (grant no. YSBR-046), the Geek Center Project of USTC and the Fundamental Research Funds for the Central Universities (grant nos. WK9990000118 and WK2310000104). Part of this work was carried out at the USTC Center for Micro and Nanoscale Research and Fabrication.
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Authors and Affiliations
CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics and Department of Physics, University of Science and Technology of China, Hefei, China
Yichi Zhang,Hui Zhang,Yiheng Wang,Yuchen Liu,Shu Li,Tianyi Zhang,Chuang Fan&Changgan Zeng
International Center for Quantum Design of Functional Materials (ICQD), Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, China
Yichi Zhang,Hui Zhang,Yiheng Wang,Yuchen Liu,Shu Li,Tianyi Zhang,Chuang Fan&Changgan Zeng
School of the Gifted Young, University of Science and Technology of China, Hefei, China
Yichi Zhang,Yiheng Wang,Yuchen Liu,Shu Li&Chuang Fan
Hefei National Laboratory, Hefei, China
Hui Zhang&Changgan Zeng
Center for Micro- and Nanoscale Research and Fabrication, University of Science and Technology of China, Hefei, China
Xiuxia Wang
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Contributions
C.Z. and H.Z. designed and supervised the work. Y.Z. and H.Z. performed the experiments with assistance from X.W., Y.L., S.L., T.Z. and C.F. Y.Z. performed the theoretical calculation and analysis. C.Z., Y.Z. and H.Z. analysed the data and wrote the manuscript with assistance from Y.W. and C.F. All authors contributed to the scientific discussion and manuscript revisions.
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Correspondence to Hui Zhang or Changgan Zeng.
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Extended data
Extended Data Fig. 1 Calculated dielectric permittivities of materials used in this work.
a, Calculated dielectric permittivities of Au, SiO2, H2O, Fe3O4 and kerosene respectively. The inset is a zoom-in plot of the dielectric permittivities with the Matsubara energy in the range between 100 eV and 500 eV. b, Calculated dielectric permittivities of water-based ferrofluids with different volume fractions. The dielectric permittivities of Au and SiO2 are also shown for comparison.
Extended Data Fig. 2 Magnetization curve of 4.9% ferrofluid measured by vibrating sample magnetometer.
The square dots are the measured results. The orange line is the theoretical fitting by first-order modified mean-field model (see Supplementary Note 3). No apparent hysteresis is observed.
Extended Data Fig. 3 Calculated Casimir force between a gold sphere and a silica plate in ferrofluid as a function of separation distance and magnetic field.
a-d, 3.5%, 4.9%, 5.5% and 9% volume fractions, respectively. Iso-lines are plotted in bright dashed lines to show the magnitude of the Casimir force.
Source data
Extended Data Fig. 4 Measured Casimir force in 5.5% water-based ferrofluid between gold-coated sphere and SiO2 plate.
Measurements data at μ0H = 0 and 8.6 mT are averaged from eleven and six measurements respectively, with error bars indicating the standard deviation. The fitting results according to the Lifsh*tz theory are presented by solid lines.
Source data
Supplementary information
Supplementary Information
Supplementary Sections 1–6 and Figs. 1–5.
Source data
Source Data Fig. 2
Statistical source data.
Source Data Fig. 3
Statistical source data.
Source Data Fig. 4
Statistical source data.
Source Data Extended Data Fig./Table 3
Statistical source data.
Source Data Extended Data Fig./Table 4
Statistical source data.
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Zhang, Y., Zhang, H., Wang, X. et al. Magnetic-field tuning of the Casimir force. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02521-0
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DOI: https://doi.org/10.1038/s41567-024-02521-0
