Efficient Long-Distance Heat Transport by Microwave Photons
Authors: Matti Partanen and Mikko Möttönen
Affiliation: QCD Labs, Department of Applied Physics, Aalto University, Finland.
Link to the Quantum Computing and Devices (QCD) Group >>
Quantum computers are predicted to vastly speed up the computation for certain problems of great practical interest . One of the most promising architectures for quantum computing is based on superconducting quantum bits , or qubits, which are the key ingredients in circuit quantum electrodynamics . In such systems, the control of heat at the quantum level is extremely important, and remote cooling may turn out to be a viable option.
In one dimension, heat transport may be described by individual heat conduction channels -- each corresponding to a certain quantized profile of the heat carriers in the transverse direction. Importantly, the maximum heat power flowing in a single channel between bodies at given temperatures is fundamentally limited by quantum mechanics [4,5]. This quantum limit has previously been observed for phonons , sub-wavelength photons [7,8], and electrons . Among these, the longest distance of roughly 50 μm [7,8] was recorded in the photonic channel . Such short distance may be undesirable in cooling quantum devices which are sensitive to spurious dissipation.
In our recent work , we observe quantum-limited heat conduction by microwave photons flying in a superconducting transmission line of length 20 cm and 1 m. Thus we were able to extend the maximum distance 10,000 fold compared with the previous experiments.
Figure 1: (click on the figure to view with higher resolution) Sample structure and measurement scheme. The electron temperature of the right resistor is controlled with an external voltage while the temperatures of both resistors are measured. Microwave photons transport heat through the spiraling transmission line.
Our sample is shown in Figure 1. The heat is transferred between two normal-metal resistors functioning as black-body radiators to the transmission line [10,12]. To be able to fabricate the whole sample on a single relatively small chip, the transmission line has a double spiral structure. We have measured such spiraling transmission lines without resistors and confirmed that photons travel along the line; they do not jump through vacuum from one end to the other. Thus for heat transport, the distance should be measured along the line.
We measure the electron temperatures of both normal-metal resistors while we change the temperature of one of them . The obtained temperature data agrees well with our thermal model, according to which the heat conduction is very close to the quantum limit.
In contrast to subwavelength distances employed in References [7,8], we need to match the resistance of the normal-metal parts to the characteristic impedance of the transmission line to reach the quantum limit. Furthermore, the transmission line itself has to be so weakly dissipative that almost no photons are absorbed even over distances of about a meter. However, we managed to develop nanofabrication techniques which enabled us to satisfy these conditions well. In fact, the losses in the transmission line are so weak they allow a further increment of the distance by several orders of magnitude.
We consider that long-distance heat transport through transmission lines may be a useful tool for certain future applications in the quickly developing field of quantum technology. If the coupling of a quantum device to a low-temperature transmission line can be well controlled in situ, the device may be accurately initialized without disturbing its coherence properties when the coupling is turned off . Furthermore, the implementation of such in-situ-tunable environments opens an interesting avenue for the study of the detailed dynamics of open quantum systems and quantum fluctuation relations .
Acknowledgements: We thank M. Meschke, J. P. Pekola, D. S. Golubev, J. Kokkala, M. Kaivola and J. C. Cuevas for useful discussions, and L. Grönberg, E. Mykkänen, and A. Kemppinen for technical assistance. We acknowledge the provision of facilities and technical support by Aalto University at Micronova Nanofabrication Centre. We also acknowledge funding by the European Research Council under Starting Independent Researcher Grant No. 278117 (SINGLEOUT), the Academy of Finland through its Centres of Excellence Program (project nos 251748 and 284621) and grants (nos 138903, 135794, 265675, 272806 and 276528), the Emil Aaltonen Foundation, the Jenny and Antti Wihuri Foundation, and the Finnish Cultural Foundation.
 T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O'Brien, “Quantum computers”, Nature, 464, 45 (2010). Abstract.
 J. Kelly, R. Barends, A.G. Fowler, A. Megrant, E. Jeffrey, T.C. White, D. Sank, J.Y. Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P.J.J. O’Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, A.N. Cleland, John M. Martinis, “State preservation by repetitive error detection in a superconducting quantum circuit”, Nature, 519, 66 (2015). Abstract.
 A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum Electrodynamics”, Nature, 431, 162 (2004). Abstract.
 J.B. Pendry, “Quantum limits to the flow of information and entropy”, Journal of Physics A: Mathematical and General, 16, 2161 (1983). Abstract.
 Luis G. C. Rego, George Kirczenow, “Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach”, Physical Review B, 59, 13080 (1999). Abstract.
 K. Schwab, E.A. Henriksen, J.M.Worlock, M.L. Roukes, “Measurement of the quantum of thermal conductance”, Nature, 404, 974 (2000). Abstract.
 Matthias Meschke, Wiebke Guichard, Jukka P. Pekola, “Single-mode heat conduction by photons”, Nature, 444, 187 (2006). Abstract.
 Andrey V. Timofeev, Meri Helle, Matthias Meschke, Mikko Möttönen, Jukka P. Pekola, “Electronic refrigeration at the quantum limit”, Physical Review Letters, 102, 200801 (2009). Abstract.
 S. Jezouin, F.D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, Y. Jin, and F. Pierre, “Quantum limit of heat flow across a single electronic channel”, Science, 342, 601 (2013). Abstract.
 D.R. Schmidt, R.J. Schoelkopf, A.N. Cleland, “Photon-mediated thermal relaxation of electrons in nanostructures”, Physical Review Letters, 93, 045901 (2004). Abstract.
 Matti Partanen, Kuan Yen Tan, Joonas Govenius, Russell E. Lake, Miika K. Mäkelä, Tuomo Tanttu, Mikko Möttönen, “Quantum-limited heat conduction over macroscopic distances”, Nature Physics, Advance online publication, DOI:10.1038/nphys3642 (2016). Abstract.
 L.M.A. Pascal, H. Courtois, F.W.J. Hekking, “Circuit approach to photonic heat transport”, Physical Review B, 83, 125113 (2011). Abstract.
 Francesco Giazotto, Tero T. Heikkilä, Arttu Luukanen, Alexander M. Savin, Jukka P. Pekola, “Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications”, Reviews of Modern Physics, 78, 217 (2006). Abstract.
 P. J. Jones, J.A.M. Huhtamäki, J. Salmilehto, K.Y. Tan, M. Möttönen, “Tunable electromagnetic environment for superconducting quantum bits”, Scientific Reports, 3, 1987 (2013). Abstract.
 Jukka P. Pekola, “Towards quantum thermodynamics in electronic circuits”, Nature Physics, 11, 118 (2015). Abstract.