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Single-mode heat conduction by photons

Abstract

The thermal conductance of a single channel is limited by its unique quantum value GQ, as was shown theoretically1 in 1983. This result closely resembles the well-known quantization of electrical conductance in ballistic one-dimensional conductors2,3. Interestingly, all particles—irrespective of whether they are bosons or fermions—have the same quantized thermal conductance4,5 when they are confined within dimensions that are small compared to their characteristic wavelength. The single-mode heat conductance is particularly relevant in nanostructures. Quantized heat transport through submicrometre dielectric wires by phonons has been observed6, and it has been predicted to influence cooling of electrons in metals at very low temperatures due to electromagnetic radiation7. Here we report experimental results showing that at low temperatures heat is transferred by photon radiation, when electron–phonon8 as well as normal electronic heat conduction is frozen out. We study heat exchange between two small pieces of normal metal, connected to each other only via superconducting leads, which are ideal insulators against conventional thermal conduction. Each superconducting lead is interrupted by a switch of electromagnetic (photon) radiation in the form of a DC-SQUID (a superconducting loop with two Josephson tunnel junctions). We find that the thermal conductance between the two metal islands mediated by photons indeed approaches the expected quantum limit of GQ at low temperatures. Our observation has practical implications—for example, for the performance and design of ultra-sensitive bolometers (detectors of far-infrared light) and electronic micro-refrigerators9, whose operation is largely dependent on weak thermal coupling between the device and its environment.

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Figure 1: The system under investigation.
Figure 2: Results of the measurements in the absence of extra heating.
Figure 3: Results of the measurement of Δ T with variable amounts of Joule heating applied to resistor 1.

References

  1. Pendry, J. B. Quantum limits to flow of information and entropy. J. Phys. A 16, 2161–2171 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  2. van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron-gas. Phys. Rev. Lett. 60, 848–850 (1988)

    ADS  CAS  Article  Google Scholar 

  3. Wharam, D. A. et al. One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. C 21, L209–L214 (1988)

    Article  Google Scholar 

  4. Rego, L. G. C. & Kirczenow, G. Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach. Phys. Rev. B 59, 13080–13086 (1999)

    ADS  CAS  Article  Google Scholar 

  5. Blencowe, M. P. & Vitelli, V. Universal quantum limits on single-channel information, entropy, and heat flow. Phys. Rev. B 62, 052104 (2000)

    ADS  Article  Google Scholar 

  6. Schwab, K., Henriksen, E. A., Worlock, J. M. & Roukes, M. L. Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000)

    ADS  CAS  Article  Google Scholar 

  7. Schmidt, D. R., Schoelkopf, R. J. & Cleland, A. N. Photon-mediated thermal relaxation of electrons in nanostructures. Phys. Rev. Lett. 93, 045901 (2004)

    ADS  CAS  Article  Google Scholar 

  8. Roukes, M. L., Freeman, M. R., Germain, R. S., Richardson, R. C. & Ketchen, M. B. Hot electrons and energy transport in metals at millikelvin temperatures. Phys. Rev. Lett. 55, 422–425 (1985)

    ADS  CAS  Article  Google Scholar 

  9. Giazotto, F., Heikkilä, T. T., Luukanen, A., Savin, A. M. & Pekola, J. P. Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications. Rev. Mod. Phys. 78, 217–274 (2006)

    ADS  CAS  Article  Google Scholar 

  10. Wilczek, F. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. Haldane, F. D. M. “Fractional statistics” in arbitrary dimensions: A generalization of the Pauli principle. Phys. Rev. Lett. 67, 937–940 (1991)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  12. Kane, C. L. & Fisher, M. P. A. Thermal transport in a Luttinger liquid. Phys. Rev. Lett. 76, 3192–3195 (1996)

    ADS  CAS  Article  Google Scholar 

  13. Kane, C. L. & Fisher, M. P. A. Quantized thermal transport in the fractional quantum Hall effect. Phys. Rev. B 55, 15832–15837 (1997)

    ADS  CAS  Article  Google Scholar 

  14. Greiner, A., Reggiani, L., Kuhn, T. & Varani, L. Thermal conductivity and Lorenz number for one-dimensional ballistic transport. Phys. Rev. Lett. 78, 1114–1117 (1997)

    ADS  CAS  Article  Google Scholar 

  15. Pashkin, A., Nakamura, Y. & Tsai, J. S. Room-temperature Al single-electron transistor made by electron-beam lithography. Appl. Phys. Lett. 76, 2256–2258 (2000)

    ADS  CAS  Article  Google Scholar 

  16. Nahum, M. & Martinis, J. M. Ultrasensitive-hot-electron microbolometer. Appl. Phys. Lett. 63, 3075–3077 (1993)

    ADS  CAS  Article  Google Scholar 

  17. Ambegaokar, V. & Baratoff, A. Tunneling between superconductors. Phys. Rev. Lett. 10, 486–489 (1963)

    ADS  Article  Google Scholar 

  18. Savin, A. M., Pekola, J. P., Averin, D. V. & Semenov, V. K. Thermal budget of superconducting digital circuits at subkelvin temperatures. J. Appl. Phys. 99, 084501 (2006)

    ADS  Article  Google Scholar 

  19. Clark, A. M., Williams, A., Ruggiero, S. T., van den Berg, M. L. & Ullom, J. N. Practical electron-tunneling refrigerator. Appl. Phys. Lett. 84, 625–627 (2004)

    ADS  CAS  Article  Google Scholar 

  20. Makhlin, Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001)

    ADS  Article  Google Scholar 

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Acknowledgements

We thank M. Paalanen, D. Averin, A. Luukanen, H. Pothier, F. Hekking and G. Schön for comments, and the Academy of Finland (TULE) and the EC-funded ULTI project for financial support.

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Correspondence to Jukka P. Pekola.

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Meschke, M., Guichard, W. & Pekola, J. Single-mode heat conduction by photons. Nature 444, 187–190 (2006). https://doi.org/10.1038/nature05276

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