Abstract The fundamental excitations in superconductors—Bogoliubov quasiparticles—can be either a resource or a liability in superconducting devices: they are what enables photon detection in microwave kinetic inductance detectors, but they are a source of errors in qubits and electron pumps. To improve operation of the latter devices, ways to mitigate quasiparticle effects have been devised; in particular, combining different materials quasiparticles can be trapped where they do no harm and their generation can be impeded. We review recent developments in these mitigation efforts and discuss open questions.
Abstract The fundamental excitations in superconductors—Bogoliubov quasiparticles—can be either a resource or a liability in superconducting devices: they are what enables photon detection in microwave kinetic inductance detectors, but they are a source of errors in qubits and electron pumps. To improve operation of the latter devices, ways to mitigate quasiparticle effects have been devised; in particular, combining different materials quasiparticles can be trapped where they do no harm and their generation can be impeded. We review recent developments in these mitigation efforts and discuss open questions.
hen a photon strikes a superconductor, its energy cascades through the material via electron-phonon interactions, generating thousands of excitations called quasiparticles.Before this energy dissipates, these quasiparticles measurably change the kinetic inductance of the material, a property that researchers have used to make superconducting single-photon detectors (see Synopsis: Direct Detection of Quasiparticles).Now, Pieter de Visser at the Netherlands Institute for Space Research and colleagues have modified the design of such a detector to achieve a 2.5-fold increase in the precision with which the device can measure photon frequency [1].That precision increase could improve spectroscopy measurements of exoplanet atmospheres and fluorescence measurements of biological samples.Currently, operational superconductor-based photon detectors are made as follows: A series of superconducting circuits is deposited on a thick (> 300 µm) silicon or sapphire substrate, with each circuit making up one pixel.The frequency resolution
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.
Extending the qubit coherence times is a crucial task in building quantum information processing devices. In the three-dimensional cavity implementations of circuit QED, the coherence of superconducting qubits was improved dramatically due to cutting the losses associated with the photon emission. Next frontier in improving the coherence includes the mitigation of the adverse effects of superconducting quasiparticles. In these lectures, we review the basics of the quasiparticles dynamics, their interaction with the qubit degree of freedom, their contribution to the qubit relaxation rates, and approaches to control their effect.
Bogoliubov quasiparticle excitations are detrimental for the operation of many superconducting devices. In superconducting qubits, quasiparticles interact with the qubit degree of freedom when tunneling through a Josephson junction, and this interaction can lead to qubit relaxation. At millikelvin temperatures, there is substantial evidence of nonequilibrium quasi- particles. While there is no agreed upon explanation for the origin of these excess quasiparticles, it is nevertheless possible to limit the quasiparticle-induced relaxation by steering quasiparticles away from qubit active elements. In this thesis, we study quasiparticle traps that are formed by a normal-metal in tunnel contact with the superconducting electrode of a qubit. We develop a model to explain how a trap can influence the dynamics of the excess quasiparticles injected in a transmontype qubit. This model makes it possible to find the time it takes to evacuate the injected quasiparticles from the transmon as a function of trap parameters. We show when the trap size is increased, the evacuation time decreases monotonically and saturates at a level that depends on the quasiparticles diffusion constant and the qubit geometry. We find the characteristic trap size needed for the evacuation time to approach the saturation value. It turns out that the bottleneck limiting the trapping rate is the slow quasiparticle energy relaxation inside the normal-metal trap, a quantity that is very hard to control. In order to optimize normal-metal quasiparticle trapping, we study the effects of trap size, number, and placement. These factors become important when the trap size increases beyond the characteristic length. We discuss for some experimentally relevant examples how to shorten the evacuation time of the excess quasiparticle density. Moreover, we show that a trap in the vicinity of a Josephson junction can significantly suppress the steady-state quasiparticle density near that junction and reduce the impact of fluctuations in the generation rate of quasiparticles. When such normal-metal elements are connected to a superconducting material, Cooper- pairs can leak into the normal-metal trap. This modifies the superconductor properties and, in turn, affects the qubit coherence. Using the Usadel formalism, we first revisit the proximity effect in uniform NS bilayers; despite the long history of this problem, we present novel findings for the density of states. We then extend our results to describe a non-uniform system in the vicinity of a trap edge. Using these results together with the previously developed model for the suppression of the quasiparticle density due to the trap, we find in a transmon qubit an optimum trap-junction distance at which the qubit relaxation rate is minimized. This optimum distance, of the order of 4 to 20 coherence lengths, originates from the competition between proximity effect and quasiparticle density suppression. We conclude that the harmful influence of the proximity effect can be avoided so long as the trap is farther away from the junction than this optimum.
Nonequilibrium quasiparticle and phonon dynamics are central to the operation of superconducting devices. Superconducting detectors, such as superconducting nanowire single-photon detectors, transition-edge sensors, or microwave kinetic inductance detectors, perform best when a large quasiparticle population is generated in response to small perturbations. Conversely, for superconducting qubits and topologically protected Majorana fermions, even relatively small quasiparticle densities can lead to significant performance degradation. Hence, ideal materials for these devices would be less susceptible to quasiparticle poisoning. However, existing models of these devices often rely on approximations and phenomenology. Therefore, they lack a rigorous description of the underlying quasiparticle and phonon dynamics that are responsible for device performance. In this article, we combine kinetic equations with density functional theory to model the nonequilibrium quasiparticle and phonon dynamics of a thin superconducting film ab initio. To demonstrate the universality of our model, we illustrate two independent example applications: (1) we develop a theoretical model describing the detection of single photons in superconducting nanowires, and (2) we calculate the energy-relaxation rate of a transmon qubit due to the presence of excess quasiparticles. Our examples demonstrate from first principles that niobium nitride is well suited to be used for single-photon detection and that tantalum transmon qubits possess reduced sensitivity to quasiparticle poisoning relative to other materials, which is likely in part responsible for their longer coherence times. In contrast to previous models of superconducting devices, our ab initio approach makes predictions of device performance without experimental input and thus can be used to accelerate progress in device development. Moreover, by considering the full-bandwidth electron-phonon coupling, our approach can incorporate strong-coupling effects. Our methods effectively integrate ab initio materials modeling with nonequilibrium theory of superconductivity to perform practical modeling of superconducting devices, providing a comprehensive approach that connects fundamental theory with device-level applications.
Quasiparticles represent an intrinsic source of perturbation for superconducting qubits, leading to both dissipation of the qubit energy and dephasing. Recently, it has been shown that normal-metal traps may efficiently reduce the quasiparticle population and improve the qubit lifetime, provided the trap surpasses a certain characteristic size. Moreover, while the trap itself introduces new relaxation mechanisms, they are not expected to harm state-of-the-art transmon qubits under the condition that the traps are not placed too close to extremal positions where electric fields are high. Here we study a different type of trap, realized through gap engineering. We find that gap-engineered traps relax the remaining constraints imposed on normal metal traps. First, the characteristic trap size, above which the trap is efficient, is reduced with respect to normal metal traps, such that here, strong traps are possible in smaller devices. Second, the losses caused by the trap are now greatly reduced, providing more flexibility in trap placement. The latter point is of particular importance, since for efficient protection from quasiparticles, the traps ideally should be placed close to the active parts of the qubit device, where electric fields are typically high.