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Local Density of States of the Quasiparticles in the Superconducting States of the Non-Uniform t-J Model

Yasunari Tanuma, Yukio Tanaka, Masao Ogata, Satoshi Kashiwaya

Published Jan 1, 1998• 0 citations
Publisher
DOI
10.1007/978-4-431-66879-4_62

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

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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.

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We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles.
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.