Material inhomogeneities in a superconductor generically lead to broadening of the density of states and to subgap states. The latter are associated with spatial fluctuations of the gap in which quasiparticles can be trapped. Recombination between such localized quasiparticles is hindered by their spatial separation and hence their density could be higher than expectations based on the recombination between mobile quasiparticles. We show here that the recombination between localized and mobile excitations can be efficient at limiting the quasiparticle density. We comment on the significance of our findings for devices such as superconducting resonators and qubits. We find that for typical aluminum devices, the subgap states do not significantly influence the quasiparticle density.
Material inhomogeneities in a superconductor generically lead to broadening of the density of states and to subgap states. The latter are associated with spatial fluctuations of the gap in which quasiparticles can be trapped. Recombination between such localized quasiparticles is hindered by their spatial separation and hence their density could be higher than expectations based on the recombination between mobile quasiparticles. We show here that the recombination between localized and mobile excitations can be efficient at limiting the quasiparticle density. We comment on the significance of our findings for devices such as superconducting resonators and qubits. We find that for typical aluminum devices, the subgap states do not significantly influence the quasiparticle density.
An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of Bespalov [] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in subgap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the subgap states and gap smearing. With these parameters, we evaluate the density-dependent recombination times calculated by Bespalov and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminum- and niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to nonthermal sources of quasiparticle generation and not slow recombination.
An excess density of quasiparticles is widely observed in superconducting films. This excess causes performance degradation in a variety of superconducting devices, including decoherence in qubits. In this Letter, we evaluate the hypothesis of [1] that the quasiparticle excess is caused by anomalously slow recombination at low quasiparticle densities due to localization in sub-gap states. We probe the density of states in aluminum and niobium films using current-voltage measurements of tunnel junctions and extract upper bounds on the energy scales of the sub-gap states and gap smearing. With these parameters, we evaluate the recombination times predicted by [1] and find that slow recombination is not predicted to occur at observed quasiparticle densities in aluminumand niobium-based superconducting devices. These results suggest that the quasiparticle excess in ordered superconductors is primarily due to non-thermal sources of quasiparticle generation and not slow recombination.
At low temperature, the concentration of quasiparticles observed in superconducting circuits far exceeds the predictions of microscopic BCS theory at equilibrium. As a source of dissipation, these excess quasiparticles degrade the performance of various devices. Therefore, understanding their dynamics, especially their recombination into Cooper pairs, is an active topic of current research. In disordered superconductors, spatial fluctuations in the superconducting gap can trap quasiparticles and modify their eigenspectrum. Since this spectrum plays a key role in quasiparticle dynamics, it must be carefully investigated. To this end, we introduce a toy model of a single trap. Specifically, we consider a shallow disk-shaped gap variation in a clean superconductor. Using a semiclassical approximation, we demonstrate the existence of multiple bound states and give the dependence of their number on the size and depth of the gap suppression. Extending our analysis beyond the semiclassical regime, in dimensions larger than one, we observe an infinite number of bound states very close to the gap edge, even for an arbitrarily small trap. These results deepen our understanding of trapped quasiparticles and may have important implications for their recombination in disordered superconductors.
Superconducting materials are useful for a wide range of applications, ranging from particle detectors to quantum computing. The presence of excitations (quasiparticles) in the superconductor can be a resource in some devices and a disturbance in others - in kinetic inductance detectors, the generation of quasiparticles by an incoming photon can be read out and used to calculate the energy of the photon, while the tunnelling of quasiparticles is a cause of decoherence in quantum computing. While early research mostly focused on superconductors close to the critical temperature, temperatures that are far below the critical temperatures are often used for current applications. At these low temperatures, the energy exchange between quasiparticles and phonons becomes slow, and even small disturbances may drive the energy distribution of the quasiparticles out of thermal equilibrium. In fact, experiments usually show a residual number of quasiparticles even at milikelvin temperatures, for which the thermal density of quasiparticles would be negligible. This thesis consists of two parts: In the first part, I model the energy distribution of quasiparticles in superconducting resonators: Quasiparticles absorb energy by absorbing photons and release it as phonons, which drives the superconductor out of thermal equilibrium. I solve a set of rate equations, both numerical and analytical, to calculate the energy distribution of the quasiparticles. For parameters typically used in kinetic inductance detectors made of aluminum, the microwave signal used to read out the resonator dominates the energy distribution of the quasiparticles, while their density is determined by other processes. At not too low temperatures, quasiparticles are mainly produced by thermal phonons, and my calculations reproduce recently measured quality factors of resonators at temperatures above 250 mK without free parameters. I show that even a very small number of photons of higher energy, which I ascribe to noise from the microwave generator, would dominate the quasiparticle density at lower temperatures. Under this assumption, my calculations also reproduce the quality factors at lower temperatures. In the second part of this thesis, I investigate the effects of spatial fluctuations of the superconducting energy gap on the dynamics of quasiparticles. Recently, it has been proposed that such fluctuations may lead to the localization of quasiparticles in states below the energy gap, which could cause a finite quasiparticle density even at very low temperatures. Using the Keldysh-Usadel formalism, I derive rates for the different processes (recombination/(de-) localization/generation) of quasiparticles in such systems. Using these rate equations I derive new upper limits for the quasiparticle density that could result from these localized states. These upper limits show that localization caused by weak magnetic impurities in typical aluminum systems does not lead to a relevant quasiparticle density. This contradicts previous theories, which only consider the recombination between two localized quasiparticles without examining their dynamics in detail.
Designing the spatial profile of the superconducting gap-gap engineering-has long been recognized as an effective way of controlling quasiparticles in superconducting devices.In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlO x /Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices.Here, we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction.We find that different regimes can be encountered in which the quasiparticles have either similar densities in the two junction leads or are largely confined to the lower-gap lead.Qualitatively, for similar densities the qubit excited-state population is lower but its relaxation rate is higher than when the quasiparticles are confined; therefore, there is a potential trade-off between two desirable properties in a qubit.
Superconducting qubits are among the most promising elements for the implementation of the concept of quantum computing. Quasiparticles are an intrinsic sources of qubit decoherence, and are more generally detrimental to the operation of superconducting devices, e.g., Cooper pair pumps. Experiments reveal that quasiparticles fail to equilibrate and their density remains high even at low temperatures. Planting normal-metal traps on a superconducting device offers a way to reduce the quasiparticle density: once a quasiparticle tunnels into the normal metal and relaxes to subgap energy via inelastic processes, it cannot return to the superconductor. This paper presents a theoretical model for the time-resolved dynamics of quasiparticles injected into a qubit, and experiments with transmon qubits validating the model. The authors show that, contrary to expectations, the effective trapping rate depends on temperature, which is a consequence of the strong energy dependence of the quasiparticle density of states in the superconductor. At low temperatures, the relaxation process in the normal metal is the bottleneck limiting the effectiveness of traps. The authors also show that the trapping rate saturates for larger traps. At saturation, the rate is limited by the inverse of the time it takes for quasiparticles to diffuse across the device.