We report quantitative electrical admittance measurements of diffusive superconductor--normal-metal--superconductor (SNS) junctions at gigahertz frequencies and millikelvin temperatures. The gold-palladium-based SNS junctions are arranged into a chai
n of superconducting quantum interference devices. The chain is coupled strongly to a multimode microwave resonator with a mode spacing of approximately 0.6 GHz. By measuring the resonance frequencies and quality factors of the resonator modes, we extract the dissipative and reactive parts of the admittance of the chain. We compare the phase and temperature dependence of the admittance near 1 GHz to theory based on the time-dependent Usadel equations. This comparison allows us to identify important discrepancies between theory and experiment that are not resolved by including inelastic scattering or elastic spin-flip scattering in the theory.
The emerging quantum technological apparatuses [1,2], such as the quantum computer [3-5], call for extreme performance in thermal engineering at the nanoscale [6]. Importantly, quantum mechanics sets a fundamental upper limit for the flow of informat
ion and heat, which is quantified by the quantum of thermal conductance [7,8]. The physics of this kind of quantum-limited heat conduction has been experimentally studied for lattice vibrations, or phonons [9], for electromagnetic interactions [10], and for electrons [11]. However, the short distance between the heat-exchanging bodies in the previous experiments hinders the applicability of these systems in quantum technology. Here, we present experimental observations of quantum-limited heat conduction over macroscopic distances extending to a metre. We achieved this striking improvement of four orders of magnitude in the distance by utilizing microwave photons travelling in superconducting transmission lines. Thus it seems that quantum-limited heat conduction has no fundamental restriction in its distance. This work lays the foundation for the integration of normal-metal components into superconducting transmission lines, and hence provides an important tool for circuit quantum electrodynamics [12-14], which is the basis of the emerging superconducting quantum computer [15]. In particular, our results demonstrate that cooling of nanoelectronic devices can be carried out remotely with the help of a far-away engineered heat sink. In addition, quantum-limited heat conduction plays an important role in the contemporary studies of thermodynamics such as fluctuation relations and Maxwells demon [16,17]. Here, the long distance provided by our results may, for example, lead to an ultimate efficiency of mesoscopic heat engines with promising practical applications [18].
