We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators in either hanger- or necklace-type, and reve
al interesting transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together form a solid basis for analyzing the decoherence effect in a general microwave resonator. These results pave the way for designing and applying superconducting microwave resonators in complex circuits, and should stimulate the interest of distinguishing different decoherence mechanisms of a resonator mode beyond free energy relaxation.
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit a
symmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the electrical properties of a microwave resonator in a single measurement. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.
Superconducting microwave circuits show great potential for practical quantum technological applications such as quantum information processing. However, fast and on-demand initialization of the quantum degrees of freedom in these devices remains a c
hallenge. Here, we experimentally implement a tunable heat sink that is potentially suitable for the initialization of superconducting qubits. Our device consists of two coupled resonators. The first resonator has a high quality factor and a fixed frequency whereas the second resonator is designed to have a low quality factor and a tunable resonance frequency. We engineer the low quality factor using an on-chip resistor and the frequency tunability using a superconducting quantum interference device. When the two resonators are in resonance, the photons in the high-quality resonator can be efficiently dissipated. We show that the corresponding loaded quality factor can be tuned from above $10^5$ down to a few thousand at 10 GHz in good quantitative agreement with our theoretical model.
Quantum technology promises revolutionizing applications in information processing, communications, sensing, and modelling. However, efficient on-demand cooling of the functional quantum degrees of freedom remains a major challenge in many solid-stat
e implementations, such as superconducting circuits. Here, we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable quantum tunneling of electrons in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even when the electrons in the refrigerator itself are at an elevated temperature. Our conclusions are verified by control experiments and by a good quantitative agreement between a detailed theoretical model and the direct experimental observations in a broad range of operation voltages and phonon bath temperatures. In the future, the introduced refrigerator can be integrated with different quantum electric devices, potentially enhancing their performance. For the superconducting quantum computer, for example, it may provide an efficient way of initializing the quantum bits.
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].
