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# Phonon heat transfer across a vacuum through quantum fluctuations

## Abstract

Heat transfer in solids is typically conducted through either electrons or atomic vibrations known as phonons. In a vacuum, heat has long been thought to be transferred by radiation but not by phonons because of the lack of a medium1. Recent theory, however, has predicted that quantum fluctuations of electromagnetic fields could induce phonon coupling across a vacuum and thereby facilitate heat transfer2,3,4. Revealing this unique quantum effect experimentally would bring fundamental insights to quantum thermodynamics5 and practical implications to thermal management in nanometre-scale technologies6. Here we experimentally demonstrate heat transfer induced by quantum fluctuations between two objects separated by a vacuum gap. We use nanomechanical systems to realize strong phonon coupling through vacuum fluctuations, and observe the exchange of thermal energy between individual phonon modes. The experimental observation agrees well with our theoretical calculations and is unambiguously distinguished from other effects such as near-field radiation and electrostatic interaction. Our discovery of phonon transport through quantum fluctuations represents a previously unknown mechanism of heat transfer in addition to the conventional conduction, convection and radiation. It paves the way for the exploitation of quantum vacuum in energy transport at the nanoscale.

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## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

The work was supported by the National Science Foundation (NSF) under grant number 1725335, the King Abdullah University of Science and Technology Office of Sponsored Research (OSR) (award numbers OSR-2016-CRG5-2950-03 and OSR-2016-CRG5-2996); and the Ernest S. Kuh Endowed Chair Professorship.

## Author information

Authors

### Contributions

R.Z., K.Y.F., H.-K.L. and X.Z. conceived the project. K.Y.F., H.-K.L. and R.Z. designed the experiment. K.Y.F. and H.-K.L. built the experimental setup, performed the measurement, and analysed the data. K.Y.F. and H.-K.L. fabricated the samples, with assistance from R.Z. and S.Y. R.Z. carried out numerical calculations of the Casimir force. K.Y.F., H.-K.L. and X.Z. wrote the manuscript with inputs from all authors. X.Z., Y.W. and S.Y. guided the research.

### Corresponding author

Correspondence to Xiang Zhang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

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

Peer review information Nature thanks Tal Carmon, Karthik Sasihithlu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Numerical calculations of the Casimir force and its heat transfer effect.

a, Cross-section of the layered structure used in the experiment. b, Calculated correction factor, η, plotted against distance, d. c, Calculated coupling rate, gC, plotted against d. d, Calculated mode temperatures, $${T}_{1}^{{}^{^{\prime} }}$$ and $${T}_{2}^{\text{'}}$$, plotted against d on the basis of experimental condition 1 in Extended Data Fig. 2a. e, Ratio between the Casimir pressures contributed from thermal fluctuations (Fth) and quantum vacuum fluctuations (FCas) plotted against d.

### Extended Data Fig. 2 Additional experimental results obtained from different samples and conditions.

a, Summary of different experimental conditions used. Condition 1 corresponds to the experimental results presented in the main text. bf, Measurement results obtained using conditions 2 and 3. In all cases, phonon mode splitting is examined and confirms that the Casimir force is dominant over the distance range concerned. b, Resonance frequencies versus bath temperature for sample set B (conditions 2 and 3). c, d, Mode temperatures as functions of distances under different resonance-matching conditions. Error bars represent the standard error obtained from three hours of continuous measurement. e, f, Heat flux transferred across thermal baths as functions of distances. The error bars originate from error propagation in the calculation.

### Extended Data Fig. 3 Electrostatic calibration of the absolute distance between membranes.

a, b, Dependence of electrostatic strength (a) and minimum splitting voltage V0 (b) on the distance between membranes. In b, the error bars represent the error of the parabolic fit to the frequency splitting versus voltage.

### Extended Data Fig. 4 Near-field thermal radiation effects.

a, Frequency shifts of the two modes plotted against membrane distance. b, Frequency shifts of the two modes with the contribution from the Casimir force excluded. Measurements were carried out at bath temperatures T1 = 287.0 K and T2 = 312.5 K. The frequencies of the modes are offset by 250 Hz.

### Extended Data Fig. 5 Device fabrication.

ah, Fabrication process flow for the left (ad) and right (eh) samples. i, j, The left (i) and right (j) samples are attached to a custom-made copper plate and a printed circuit board, respectively.

### Extended Data Fig. 6 Parallel alignment of the membranes.

a, Schematic showing the parallel alignment setup. DAQ, data acquisition system. b, c, Transmission optical images of aligned (b) and misaligned (c) membranes. d, e, Optical intensity at different locations on the membranes (marked in b, c) as a function of the change in separation. Solid lines are sinusoidal fits with an attenuation factor. The periodicity of around 230 nm matches well with the half-wavelength of the illumination light (460 nm). From the fitting, we find that the angle misalignments along the x and y directions are Δθx = 22 ± 25 μrad and Δθy = 43 ± 24 μrad for aligned membranes (d), and Δθx = 228 ± 33 μrad and Δθy = 179 ± 39 μrad for misaligned membranes (e).

### Extended Data Fig. 7 Experimental setup.

a, Schematic showing the experimental setup. APD, avalanche photodetector; BS, beam splitter; DC PD, DC photodetector; L, lens; M, mirror; ND, neutral density filter. b, Optical image of the sample mount assembly and control stages.

### Extended Data Fig. 8 Stability of mechanical frequency and temperature during thermal feedback.

a, Frequency stability during thermal feedback control. The shaded areas represent the linewidths of the mechanical modes. b, Bath temperatures read from the temperature controller during feedback control of the resonance frequencies.

### Extended Data Fig. 9 Characterization of mechanical damping rate.

a, b, Relative change in damping rate $$(\Delta {\gamma }_{i}/{\bar{\gamma }}_{i})$$ plotted against distance (a) and temperature change (b). Error bars represent the standard deviation of 100 measurements.

## Supplementary information

### Supplementary Information

This file contains supplementary text which includes supplementary figures S1-S5.

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### Cite this article

Fong, K.Y., Li, HK., Zhao, R. et al. Phonon heat transfer across a vacuum through quantum fluctuations. Nature 576, 243–247 (2019). https://doi.org/10.1038/s41586-019-1800-4

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