Phonon traps reduce the quasiparticle density in superconducting circuits
Fábio Henriques, Francesco Valenti, Thibault Charpentier, Marc Lagoin, Clement Gouriou, M. Martínez, L. Cardani, M. Vignati, Lukas Grünhaupt, Daria Gusenkova, Julian Ferrero, Sebastian T. Skacel, Wolfgang Wernsdorfer, Alexey Vladimirovich Ustinov, Gianluigi Catelani, Oliver Sander, Ioan M. Pop
Out of equilibrium quasiparticles (QPs) are one of the main sources of decoherence in superconducting quantum circuits and one that is particularly detrimental in devices with high kinetic inductance, such as high impedance resonators, qubits, and detectors. Despite significant progress in the understanding of QP dynamics, pinpointing their origin and decreasing their density remain outstanding tasks. The cyclic process of recombination and generation of QPs implies the exchange of phonons between the superconducting thin film and the underlying substrate. Reducing the number of substrate phonons with frequencies exceeding the spectral gap of the superconductor should result in a reduction of QPs. Indeed, we demonstrate that surrounding high impedance resonators made of granular aluminum (grAl) with lower gapped thin film aluminum islands increases the internal quality factors of the resonators in the single photon regime, suppresses the noise, and reduces the rate of observed QP bursts. The aluminum islands are positioned far enough from the resonators to be electromagnetically decoupled, thus not changing the resonator frequency nor the loading. We therefore attribute the improvements observed in grAl resonators to phonon trapping at frequencies close to the spectral gap of aluminum, well below the grAl gap.
Out of equilibrium quasiparticles (QPs) are one of the main sources of decoherence in superconducting quantum circuits and one that is particularly detrimental in devices with high kinetic inductance, such as high impedance resonators, qubits, and detectors. Despite significant progress in the understanding of QP dynamics, pinpointing their origin and decreasing their density remain outstanding tasks. The cyclic process of recombination and generation of QPs implies the exchange of phonons between the superconducting thin film and the underlying substrate. Reducing the number of substrate phonons with frequencies exceeding the spectral gap of the superconductor should result in a reduction of QPs. Indeed, we demonstrate that surrounding high impedance resonators made of granular aluminum (grAl) with lower gapped thin film aluminum islands increases the internal quality factors of the resonators in the single photon regime, suppresses the noise, and reduces the rate of observed QP bursts. The aluminum islands are positioned far enough from the resonators to be electromagnetically decoupled, thus not changing the resonator frequency nor the loading. We therefore attribute the improvements observed in grAl resonators to phonon trapping at frequencies close to the spectral gap of aluminum, well below the grAl gap.
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (grAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/□ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from grAl with a room temperature resistivity of 4×10^{3} μΩ cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Q_{i}=10^{5} in the single photon regime, and we demonstrate that nonequilibrium quasiparticles (QPs) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20 s. The current level of coherence of grAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of nonequilibrium QPs.
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/□ range, with proven applicability in superconducting quantum bits and microwave detectors. Here, we show that the single photon internal quality factor Qi of grAl microwave resonators exceeds 105 in magnetic fields up to 1 T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5 mT, enhance Qi by approximately 15%, possibly due to the introduction of quasiparticle traps in the form of fluxons. Further increasing the perpendicular field deteriorates the resonators' quality factor. These results open the door for the use of high kinetic inductance grAl structures in circuit quantum electrodynamics and hybrid architectures with magnetic field requirements.
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.
Quasiparticle (QP) effects play a significant role in the coherence and fidelity of superconducting quantum circuits.The Andreev bound states of high-transparency Josephson junctions can act as low-energy traps for QPs, providing a mechanism for studying the dynamics and properties of both the QPs and the junction.Using locally injected and thermal QPs, we study QP loss and QP poisoning in epitaxial Al-InAs Josephson junctions incorporated in a superconducting quantum interference device (SQUID) galvanically shorting a superconducting resonator to ground.We observe changes in the resonance line shape and frequency shifts consistent with QP trapping into and clearing out of the ABSs of the junctions when the junctions are phase biased.By monitoring the QP trapping and clearing mechanisms in time, we find a time scale of O(1 µs) for these QP dynamics, consistent with the presence of phonon-mediated QP-QP interactions.Our measurements suggest that electron-phonon interactions play a significant role in the relaxation mechanisms of our system, while electron-photon interactions and electron-phonon interactions govern the clearing mechanisms.Our results highlight the QP-induced dissipation and complex QP dynamics in superconducting quantum circuits fabricated on superconductor-semiconductor heterostructures.
We study single-Cooper-pair-transistors in which the island is made from an ultra-thin (10nm) aluminum film. The value of the superconducting gap (2Delta) changes dramatically with film thickness therefore allowing different superconducting gaps for the islands and leads simply by using different film thicknesses. Devices engineered in this way can be made less susceptible to having a single quasiparticle trapped on the island (often known as the quasiparticle poisoning problem). This is an advantage for charge-based superconducting qubits where quasiparticle poisoning is a source of decoherence. We perform radio-frequency measurements and observe 2e-periodic supercurrent peaks as a function of gate charge. With the device biased on a supercurrent oscillation, a fast random-telegraph signal due to individual quasiparticle poisoning events is observed. By analyzing the statistics of the poisoning and un-poisoning events we determine the energetics and thermal activation of these processes
Superconducting circuits based on high kinetic inductance materials are promising candidates for future quantum technologies, owing to their magnetic field resilience, low microwave losses, and lithographic scalability. In this thesis, we explore the properties of granular aluminum (grAl) resonators in two distinct geometries, using the nonlinear kinetic inductance of grAl for applications in superconducting quantum circuits. In the first part, we present compact meandered ring resonators fabricated using a single-step electron-beam lithography and lift-off process. By optimizing film resistivity and geometry, we achieve superinductors with characteristic impedances exceeding 100kΩ, corresponding to total inductances of several microhenries, while maintaining internal quality factors on the order of 105 in the single-photon regime. In the second part, we investigate DC-tunable resonators based on a 3λ/4 fractal geometry that allows direct current injection for in-situ tuning of the resonance frequency. We achieve frequency tunability up to 4.5% and analyze the nonlinear kinetic inductance using models based on Ginzburg-Landau, Mattis-Bardeen-BCS, and an effective Josephson-junction-array model. This work establishes granular aluminum as a material for realizing high-impedance and frequency-tunable superconducting circuits, offering new opportunities for advanced applications in protected qubits, hybrid quantum systems, broadband phase shifters, and three-wave mixing parametric amplifiers.