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Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits and improve superconducting single photon detectors due to their high kinetic inductance and sheet resistance. However, the relaxation of quasiparticles, which cause decoherence and microwave loss, is drastically affected by disorder, which is still not understood. We address this issue by measuring the quasiparticle relaxation time in a disordered $\beta$-Ta film, which we pattern as the inductor of a microwave resonator. We observe that the quasiparticle relaxation time is governed by the phonon scattering time and is independent on the phononic environment, which is in stark contrast to the relaxation of quasiparticles in ordered superconductors. We explain these observations in terms of the recombination of localized quasiparticles that first delocalize via phonon scattering. We analyse quasiparticle relaxation measurements on superconductors with different degrees of disorder and conclude that this phenomenon is inherent to disordered superconductors., Comment: 8 pages main text, including 3 figures

Kinetic Inductance Detectors (KIDs) are superconducting energy-resolving detectors, sensitive to single photons from the near-infrared to ultraviolet. We study a hybrid KID design consisting of a beta phase tantalum ($\beta$-Ta) inductor and a NbTiN interdigitated capacitor (IDC). The devices show an average intrinsic quality factor $Q_i$ of 4.3$\times10^5$ $\pm$ 1.3 $\times10^5$. To increase the power captured by the light sensitive inductor, we 3D-print an array of 150$\times$150 $\mu$m resin micro lenses on the backside of the sapphire substrate. The shape deviation between design and printed lenses is smaller than 1$\mu$m, and the alignment accuracy of this process is $\delta_x = +5.8 \pm 0.5$ $\mu$m and $\delta_y = +8.3 \pm 3.3$ $\mu$m. We measure a resolving power for 1545-402 nm that is limited to 4.9 by saturation in the KID's phase response. We can model the saturation in the phase response with the evolution of the number of quasiparticles generated by a photon event. An alternative coordinate system that has a linear response raises the resolving power to 5.9 at 402 nm. We verify the measured resolving power with a two-line measurement using a laser source and a monochromator. We discuss several improvements that can be made to the devices on a route towards KID arrays with high resolving powers., Comment: 13 pages, 11 Figures, Journal Paper

A noiseless, photon counting detector, which resolves the energy of each photon, could radically change astronomy, biophysics and quantum optics. Superconducting detectors promise an intrinsic resolving power at visible wavelengths of $R=E/\delta E\approx100$ due to their low excitation energy. We study superconducting energy-resolving Microwave Kinetic Inductance Detectors (MKIDs), which hold particular promise for larger cameras. A visible/near-infrared photon absorbed in the superconductor creates a few thousand quasiparticles through several stages of electron-phonon interaction. Here we demonstrate experimentally that the resolving power of MKIDs at visible to near-infrared wavelengths is limited by the loss of hot phonons during this process. We measure the resolving power of our aluminum-based detector as a function of photon energy using four lasers with wavelengths between $1545-402$ nm. For detectors on thick SiN/Si and sapphire substrates the resolving power is limited to $10-21$ for the respective wavelengths, consistent with the loss of hot phonons. When we suspend the sensitive part of the detector on a 110 nm thick SiN membrane, the measured resolving power improves to $19-52$ respectively. The improvement is equivalent to a factor $8\pm2$ stronger phonon trapping on the membrane, which is consistent with a geometrical phonon propagation model for these hot phonons. We discuss a route towards the Fano limit by phonon engineering., Comment: 14 pages, 8 figures, including appendices

We measure temperature dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for read-out close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces a factor $\sim$100. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between quasiparticle number and recombination time is invalid in this experiment. This is consistent with quasiparticle trapping, where on-trap recombination limits the observed quasiparticle lifetime., Comment: Main text: 5 pages, 3 figures; Supplemental material: 11 pages, 8 figures

Superconducting resonators used in millimeter-submillimeter astronomy would greatly benefit from deposited dielectrics with a small dielectric loss. We deposited hydrogenated amorphous silicon films using plasma-enhanced chemical vapor deposition, at substrate temperatures of 100\deg C, 250\deg C and 350\deg C. The measured void volume fraction, hydrogen content, microstructure parameter, and bond-angle disorder are negatively correlated with the substrate temperature. All three films have a loss tangent below $10^{-5}$ for a resonator energy of $10^5$ photons, at 120 mK and 4-7 GHz. This makes these films promising for microwave kinetic inductance detectors and on-chip millimeter-submilimeter filters., Comment: Presented at the SPIE Astronomical Telescopes + Instrumentation 2020. Full published paper, poster and video available at https://doi.org/10.1117/12.2562233

Superconducting resonators and transmission lines are fundamental building blocks of integrated circuits for millimeter-submillimeter astronomy. Accurate simulation of radiation loss from the circuit is crucial for the design of these circuits because radiation loss increases with frequency, and can thereby deteriorate the system performance. Here we show a stratification for a 2.5-dimensional method-of-moment simulator Sonnet EM that enables accurate simulations of the radiative resonant behavior of submillimeter-wave coplanar resonators and straight coplanar waveguides (CPWs). The Sonnet simulation agrees well with the measurement of the transmission through a coplanar resonant filter at 374.6 GHz. Our Sonnet stratification utilizes artificial lossy layers below the lossless substrate to absorb the radiation, and we use co-calibrated internal ports for de-embedding. With this type of stratification, Sonnet can be used to model superconducting millimeter-submillimeter wave circuits even when radiation loss is a potential concern., Comment: Presented at the SPIE Astronomical Telescopes + Instrumentation 2020. Full published paper, poster and video available at https://doi.org/10.1117/12.2560458