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Applied Sciences

Measurement of Quasiparticle Diffusion in a Superconducting Transmon Qubit

Yuqian Dong, Yong Li, Wen Zheng, Yu Zhang, Zhuang Ma, Xinsheng Tan, Yang Yu

Published Aug 24, 2022• 6 citations
Publisher

Abstract

Quasiparticles, especially the ones near the Josephson junctions in the superconducting qubits, are known as an important source of decoherence. By injecting quasiparticles into a quantum chip, we characterized the diffusion feature by measuring the energy relaxation time and the residual excited-state population of a transmon qubit. From the extracted transition rates, we phenomenologically modeled the quasiparticle diffusion in a superconducting circuit that contained “hot” nonequilibrium quasiparticles in addition to low-energy ones.

DOI
10.3390/app12178461

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Quasiparticles, especially the ones near the Josephson junctions in the superconducting qubits, are known as an important source of decoherence. By injecting quasiparticles into a quantum chip, we characterized the diffusion feature by measuring the energy relaxation time and the residual excited-state population of a transmon qubit. From the extracted transition rates, we phenomenologically modeled the quasiparticle diffusion in a superconducting circuit that contained “hot” nonequilibrium quasiparticles in addition to low-energy ones.
Nonequilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit T_{1} to ≈200 μs, which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density.
Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike the transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection and isolating the quasiparticle-induced contribution by subtracting the background transition rates. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle densities in the small junction and the junction array and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.
We calculate the energy decay rate of Josephson qubits and superconducting resonators from nonequilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n(qp) = 10/microm(3), which suggests that nonequilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators-a small reduction in decay rate with increasing temperature.
The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions is recognized as one of the main loss and decoherence mechanisms in superconducting qubits. Here we present a unified impedance theory that accounts for quasiparticle energy loss in circuit regions both far from and near to (across) junctions. Our theory leverages the recent experimental demonstration that the excess quasiparticles are in quasiequilibrium [Connolly et al., Phys. Rev. Lett. 132, 217001 (2024)] and uses a generalized fluctuation-dissipation theorem to predict the amount of charge and flux noise generated by them. We compute the resulting energy relaxation time T1{T}_{1}T1​ in transmon qubits with and without junction asymmetric gap engineering, and show that quasiparticles residing away from junctions can play a dominant role in the former case. They also may provide an upper limit for resonator quality factors if the density of amorphous two-level systems is reduced. In addition, we show that charge noise from quasiparticles leads to flux noise that is logarithmic in frequency, giving rise to a ``nearly white'' contribution that is comparable to the flux noise observed in flux qubits. This contrasts with amorphous two-level systems, whose associated flux noise is shown to be super-Ohmic. We discuss how this quasiparticle flux noise can limit ${T}_{2}^{\ensuremath{\ast}}$ coherence times in flux-tunable qubits. The final conclusion is that asymmetric gap engineering can greatly reduce noise and increase coherence times in superconducting qubits.
Quasiparticles are an important decoherence mechanism in superconducting qubits, and can be described with a complex admittance that is a generalization of the Mattis-Bardeen theory. By injecting nonequilibrium quasiparticles with a tunnel junction, we verify qualitatively the expected change of the decay rate and transition frequency in a phase qubit. With their relative change in agreement to within 4 % of prediction, the theory can be reliably used to infer quasiparticle density. We describe how settling of the decay rate may allow determination of whether qubit energy relaxation is limited by nonequilibrium quasiparticles.
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.