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Normal-Metal Quasiparticle Traps For Superconducting Qubits: Modeling, Optimization, and Proximity Effect

Amin Hosseinkhani

Published Jan 1, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.18154/rwth-2018-226909

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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.
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.
In many superconducting devices, including qubits, quasiparticle excitations are detrimental. A normal metal (N)(N)(N) in contact with a superconductor (S)(S)(S) can trap these excitations; therefore, such a trap can potentially improve the device's performances. The two materials influence each other, a phenomenon known as proximity effect which has drawn attention since the 1960's. Here, we study whether this mutual influence places a limitation on the possible performance improvement in superconducting qubits. We first revisit the proximity effect in uniform NSNSNS bilayers; we show that the density of states is of the Dynes type above the minigap. We then extend our results to describe a nonuniform system in the vicinity of a trap edge. Using these results together with a phenomenological 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.
Quasiparticles are an intrinsic source of relaxation and decoherence for superconducting qubits. Recent works have shown that normal-metal traps may be used to evacuate quasiparticles, and potentially improve the qubit lifetime. Here, we investigate how far the normal metals themselves may introduce qubit relaxation. We identify the Ohmic losses inside the normal metal and the tunneling current through the normal-metal--superconductor interface as the relevant relaxation mechanisms. We show that the Ohmic loss contribution depends strongly on the device and trap geometry, as a result of the inhomogeneous electric fields in the qubit. The correction of the quality factor due to the tunneling current on the other hand is highly sensitive to the nonequilibrium distribution function of the quasiparticles. Overall, we show that even when choosing less than optimal parameters, the presence of normal-metal traps does not affect the quality factor of state-of-the-art qubits.
The performance of many superconducting devices is degraded in presence of non-equilibrium quasiparticles in the superconducting part. One promising approach towards their evacuation is the use of normal-metal quasiparticle traps, where normal metal is brought into good metallic contact with the superconductor. A voltage biased normal-metal--insulator--superconductor junction equipped with such a trap is used to investigate on the trapping performance and the part played by the superconducting proximity effect therein. This involves an appropriate one-dimensional model of the junction and the numerical solution of Usadel equations describing the non-equilibrium state of the superconductor. The functionality of the trap is determined by the density of states (DOS) at the tunnel barrier. Herein, the proximity effect leads to two antagonistic characteristics affecting the trapping performance: the beneficial reduction of the DOS at an energy ∣E∣=ΔBCS|E| = Δ_{\text{BCS}}∣E∣=ΔBCS​ versus the contraction of the spectral energy gap causing quasiparticle poisoning. For both effects the trap position is decisive, which needs to be taken into account for optimizing the trapping performance. In addition, the conversion between dissipative normal and supercurrent inside the superconducting part with its impact on the quasiparticle density is studied.
In quantum information processing, long qubit coherence times are crucial. In a superconducting qubit, quasiparticles set fundamental limits on coherence, and are generated not just predictably in the course of operation, but also sporadically by unknown sources. While prevent their random appearance is difficult, their number may be controlled and adverse effects mitigated by incorporating normal-metal islands (traps) into the qubit. For the technologically important transmon configuration, the authors provide strategies to optimize such traps by varying their number, size, and location, to evacuate quasiparticles rapidly, and suppress population fluctuations.
Superconducting resonators with high quality factors are of great interest in many areas. However, the quality factor of the resonator can be weakened by many dissipation channels including trapped magnetic flux vortices and nonequilibrium quasiparticles which can significantly impact the performance of superconducting microwave resonant circuits and qubits at millikelvin temperatures. Quasiparticles result in excess loss, reducing resonator quality factors and qubit lifetimes. Vortices trapped near regions of large microwave currents also contribute excess loss. However, vortices located in current-free areas in the resonator or in the ground plane of a device can actually trap quasiparticles and lead to a reduction in the quasiparticle loss. In this thesis, we will describe experiments involving the controlled trapping of vortices for reducing quasiparticle density in the superconducting resonators. We provide a model for the simulation of reduction of nonequilibrium quasiparticles by vortices. In our experiments, quasiparticles are generated either by stray pair-breaking radiation or by direct injection using normal-insulator-superconductor (NIS)-tunnel junctions.