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Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the $N\times N\times 2$overlapping metamaterial array, where we develop an understanding of the many ( $8N^2-8N+3$) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials. 

Abstract Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two‐level systems (TLS) which become the dominant source of loss in the few‐photon and low temperature regime. In this study, capacitively‐coupled aluminum half‐wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters. 

Abstract Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe₂with surface normal fluid response. The microwave surface impedance of the UTe₂crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe₂can be a new platform to study exotic topological excitations in higher dimension. 

We give a broad overview of the history of microwave superconductivity and explore the technological developments that have followed from the unique electrodynamic properties of superconductors. Their low loss properties enable resonators with high quality factors that can nevertheless handle extremely high current densities. This in turn enables superconducting particle accelerators, high-performance filters and analog electronics, including metamaterials, with extreme performance. The macroscopic quantum properties have enabled new generations of ultra-high-speed digital computing and extraordinarily sensitive detectors. The microscopic quantum properties have enabled large-scale quantum computers, which at their heart are essentially microwave-fueled quantum engines. We celebrate the rich history of microwave superconductivity and look to the promising future of this exciting branch of microwave technology.