The presence of quasiparticles typically degrades the performance of superconducting microwave circuits. The readout signal can generate nonequilibrium quasiparticles, which lead to excess microwave loss and decoherence. To understand this effect quantitatively, we measure quasiparticle fluctuations and extract the quasiparticle density across different temperatures, readout powers, and resonator volumes. We find that microwave power generates a higher quasiparticle density as the active resonator volume is reduced and show that this effect sets a sensitivity limit on kinetic inductance detectors. We compare our results with theoretical models of direct microwave photon absorption by quasiparticles and conclude that an unknown, indirect mechanism plays a dominant role in quasiparticle generation. These results provide a route to mitigate quasiparticle generation due to readout power in superconducting devices.

Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits, and can improve superconducting detectors due to their high kinetic inductance and sheet resistance. The performance of these devices can be limited, however, by quasiparticles—the fundamental excitations of a superconductor. While experiments have shown that disorder affects the relaxation of quasiparticles drastically, the microscopic mechanisms are still not understood. We address this issue by measuring quasiparticle relaxation in a disordered β-Ta film, which we pattern as the inductor of a microwave resonator. We observe that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. We interpret the results as recombination of localized quasiparticles, induced by disorder, which first delocalize via phonon absorption. We analyze quasiparticle relaxation measurements on superconductors with different degrees of disorder and conclude that this phenomenon is inherent to disordered superconductors.

Parallel-plate capacitors (PPC) significantly reduce the size of superconducting microwave resonators, reducing the pixel pitch for arrays of single-photon energy-resolving kinetic inductance detectors (KIDs). The frequency noise of KIDs is typically limited by tunneling two-level systems (TLS), which originate from lattice defects in the dielectric materials required for PPCs. How the frequency noise level depends on the PPC's dimensions has not been experimentally addressed. We measure the frequency noise of 56 resonators with a-SiC:H PPCs, which cover a factor of 44 in PPC area and a factor of 4 in dielectric thickness. To support the noise analysis, we measure the resonators' TLS-induced power-dependent intrinsic loss and temperature-dependent resonance frequency shift. From the TLS models, we expect a geometry-independent microwave loss and resonance frequency shift, which is set by the TLS properties of the dielectric. However, we observe a thickness-dependent microwave loss and resonance frequency shift; this is explained by surface layers that limit the performance of PPC-based resonators. For a uniform dielectric, the frequency noise level should scale directly inversely with the PPC area and thickness. We observe that an increase in PPC size reduces the frequency noise, but the exact scaling is, in some cases, weaker than expected. Finally, we derive engineering guidelines for the design of KIDs based on PPC-based resonators.

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 β-phase tantalum (β-Ta) inductor and a Nb-Ti-N interdigitated capacitor. The devices show an average intrinsic quality factor Qi of 4.3×105±1.3×105. To increase the power captured by the light-sensitive inductor, we 3D print an array of 150×150μm resin microlenses on the backside of the sapphire substrate. The shape deviation between design and printed lenses is smaller than 1μm, and the alignment accuracy of this process is δx=+5.8±0.5μm and δy=+8.3±3.3μm. 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.

Aims. Future actively cooled space-borne observatories for the far-infrared, loosely defined as a 1-10 THz band, can potentially reach a sensitivity limited only by background radiation from the Universe. This will result in an increase in observing speed of many orders of magnitude. A spectroscopic instrument on such an observatory requires large arrays of detectors with a sensitivity expressed as a noise equivalent power NEP = 3 × 10-20 W√ p Hz. Methods. We present the design, fabrication, and characterisation of microwave kinetic inductance detectors (MKIDs) for this frequency range reaching the required sensitivity. The devices are based on thin-film NbTiN resonators which use lens-antenna coupling to a submicron-width aluminium transmission line at the shorted end of the resonator where the radiation is absorbed. We optimised the MKID geometry for a low NEP by using a small aluminium volume of ≈1 μm3 and fabricating the aluminium section on a very thin (100 nm) SiN membrane. Both methods of optimisation also reduce the effect of excess noise by increasing the responsivity of the device, which is further increased by reducing the parasitic geometrical inductance of the resonator. Results. We measure the sensitivity of eight MKIDs with respect to the power absorbed in the detector using a thermal calibration source filtered in a narrow band around 1.5 THz. We obtain a NEPexp(Pabs) = 3:1 ± 0:9 × 10-20 W√ p Hz at a modulation frequency of 200 Hz averaged over all measured MKIDs. The NEP is limited by quasiparticle trapping. Conclusions. The measured sensitivity is sufficient for spectroscopic observations from future, actively cooled space-based observatories. Moreover, the presented device design and assembly can be adapted for frequencies up to ≈10 THz and can be readily implemented in kilopixel arrays.

Typical materials for optical Microwave Kinetic Inductance Detetectors (MKIDs) are metals with a natural absorption of ∼ 30–50% in the visible and near-infrared. To reach high absorption efficiencies (90–100%) the KID must be embedded in an optical stack. We show an optical stack design for a 60 nm TiN film. The optical stack is modeled as sections of transmission lines, where the parameters for each section are related to the optical properties of each layer. We derive the complex permittivity of the TiN film from a spectral ellipsometry measurement. The designed optical stack is optimised for broadband absorption and consists of, from top (illumination side) to bottom: 85 nm SiO₂, 60 nm TiN, 23 nm of SiO₂, and a 100 nm thick Al mirror. We show the modeled absorption and reflection of this stack, which has >80% absorption from 400 to 1550 nm and near-unity absorption for 500–800 nm. We measure transmission and reflection of this stack with a commercial spectrophotometer. The results are in good agreement with the model.

The idea that preformed Cooper pairs could exist in a superconductor at temperatures higher than its zero-resistance critical temperature (T_c) has been explored for unconventional, interfacial, and disordered superconductors, but direct experimental evidence is lacking. We used scanning tunneling noise spectroscopy to show that preformed Cooper pairs exist up to temperatures much higher than T_c in the disordered superconductor titanium nitride by observing an enhancement in the shot noise that is equivalent to a change of the effective charge from one to two electron charges. We further show that the spectroscopic gap fills up rather than closes with increasing temperature. Our results demonstrate the existence of a state above T_c that, much like an ordinary metal, has no (pseudo)gap but carries charge through paired electrons.

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/δE≈100 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 and 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 1545-402nm. 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±2 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.

We measure temperature-dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for readout close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle effects from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces by a factor ∼100. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between the 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.

We trace the historical fate of experiment and theory of microwave-stimulated superconductivity as originally reported for constriction-type superconducting weak links. It is shown that the observed effect disappeared by improving weak links to obtain the desired Josephson properties. Separate experiments were carried out to evaluate the validity of the proposed theory of Eliash'berg for energy-gap-enhancement in superconducting films in a microwave field, without reaching a full quantitatively reliable measurement of the stimulated energy gap in a microwave field, but convincing enough to understand the earlier deviations from the Josephson-effect. Over the same time period microwave-stimulated superconductivity continued to be present in superconductor-normal metal-superconductor Josephson weak links. This experimental body of work was left unexplained for several decades and could only be understood properly after the microscopic theory of the proximity-effect had matured enough, including its non-equilibrium aspects. It implies that the increase in critical current in weak-link Josephson-junctions is due to an enhancement of the phase-coherence rather than to an enhancement of the energy-gap as proposed by Eliash'berg. The complex interplay between proximity-effect and the occupation of states continues to be, in a variety of ways, at the core of the ongoing research on hybrid Josephson-junctions. The subject of radiation-enhanced superconductivity has re-emerged in the study of the power-dependence of superconducting microwave resonators, but also in the light-induced emergence of superconductivity in complex materials.

For space observatories, the glitches caused by high energy phonons created by the interaction of cosmic ray particles with a detector substrate lead to dead time during observation. Mitigating the impact of cosmic rays is therefore an important requirement for detectors to be used in future space missions. In order to investigate possible solutions, we carry out a systematic study by testing four large arrays of Microwave Kinetic Inductance Detectors (MKIDs), each consisting of ∼960 pixels and fabricated on monolithic 55 mm × 55 mm × 0.35 mm Si substrates. We compare the response to cosmic ray interactions in our laboratory for different detector arrays: A standard array with only the MKID array as reference, an array with a low T_c superconducting film as a phonon absorber on the opposite side of the substrate, and arrays with MKIDs on membranes. The idea is that the low T_c layer down converts the phonon energy to values below the pair breaking threshold of the MKIDs, and the membranes isolate the sensitive part of the MKIDs from phonons created in the substrate. We find that the dead time can be reduced up to a factor of 40 when compared to the reference array. Simulations show that the dead time can be reduced to below 1% for the tested detector arrays when operated in a spacecraft in an L2 or a similar far-Earth orbit. The technique described here is also applicable and important for large superconducting qubit arrays for future quantum computers.

Ultra-wideband, three-dimensional (3D) imaging spectrometry in the millimeter–submillimeter (mm–submm) band is an essential tool for uncovering the dust-enshrouded portion of the cosmic history of star formation and galaxy evolution^1–3. However, it is challenging to scale up conventional coherent heterodyne receivers⁴ or free-space diffraction techniques⁵ to sufficient bandwidths (≥1 octave) and numbers of spatial pixels^2,3 (>10²). Here, we present the design and astronomical spectra of an intrinsically scalable, integrated superconducting spectrometer⁶, which covers 332–377 GHz with a spectral resolution of F/ΔF ~ 380. It combines the multiplexing advantage of microwave kinetic inductance detectors (MKIDs)⁷ with planar superconducting filters for dispersing the signal in a single, small superconducting integrated circuit. We demonstrate the two key applications for an instrument of this type: as an efficient redshift machine and as a fast multi-line spectral mapper of extended areas. The line detection sensitivity is in excellent agreement with the instrument design and laboratory performance, reaching the atmospheric foreground photon noise limit on-sky. The design can be scaled to bandwidths in excess of an octave, spectral resolution up to a few thousand and frequencies up to ~1.1 THz. The miniature chip footprint of a few cm² allows for compact multi-pixel spectral imagers, which would enable spectroscopic direct imaging and large-volume spectroscopic surveys that are several orders of magnitude faster than what is currently possible^1–3.

We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc depairing, the density of states acquires, for microwaves with frequency ω0, steps at multiples of the photon energy Δ±n ω0 and shows an exponential-like tail in the subgap regime. We show that this ac depairing explains the measured frequency shift of a superconducting resonator with microwave power at low temperatures.

Thin layers of black phosphorus present an ideal combination of a 2Dmaterial with a tunable direct bandgap and high carrier mobility. However the material suffers from degradation in ambient conditions due to an oxidation reaction which involves water, oxygen and light. Wehave measured the spatial profile of the conductivity on flakes of black phosphorus as a function of time using scanning microwave impedance microscopy. Amicrowave excitation (3 GHz) allows to image a conducting sample even when covered with a dielectric layer. Weobserve that on bare black phosphorus, the conductivity changes drastically over the whole surface within a day. Wedemonstrate that the degradation process is slowed down considerably by covering the material with a 10 nmlayer of hafnium oxide. It is stable for more than a week, opening up a route towards stable black phosphorus devices in which the high dielectric constant of hafnium oxide can be exploited. Covering black phosphorus with a 15 nmboron nitride flake changes the degradation process qualitatively, it is dominated by the edges of the flake indicating a diffusive process and happens on the scale of days.