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arXiv:2302.12330 · Physical Review Letters

Coexistence of Nonequilibrium Density and Equilibrium Energy Distribution of Quasiparticles in a Superconducting Qubit

Thomas Connolly, Pavel D. Kurilovich, Spencer Diamond, Heekun Nho, C. G. L. Bøttcher, L. I. Glazman, Valla Fatemi, Michel Devoret

Published May 20, 2024• 54 citations
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Abstract

The density of quasiparticles typically observed in superconducting qubits exceeds the value expected in equilibrium by many orders of magnitude. Can this out-of-equilibrium quasiparticle density still possess an energy distribution in equilibrium with the phonon bath? Here, we answer this question affirmatively by measuring the thermal activation of charge-parity switching in a transmon qubit with a difference in superconducting gap on the two sides of the Josephson junction. We then demonstrate how the gap asymmetry of the device can be exploited to manipulate its parity.

DOI
10.1103/physrevlett.132.217001

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The density of quasiparticles typically observed in superconducting qubits exceeds the value expected in equilibrium by many orders of magnitude. Can this out-of-equilibrium quasiparticle density still possess an energy distribution in equilibrium with the phonon bath? Here, we answer this question affirmatively by measuring the thermal activation of charge-parity switching in a transmon qubit with a difference in superconducting gap on the two sides of the Josephson junction. We then demonstrate how the gap asymmetry of the device can be exploited to manipulate its parity.
Superconducting qubits hold promise for quantum computing, but their operation is challenged by various sources of noise, including excitations known as quasiparticles. Qubits with gap asymmetry larger than their transition energy are less susceptible to quasiparticle decoherence as the quasiparticles are mostly trapped in the low-gap side of the junction. Because of this trapping, the gap asymmetry can contribute to maintaining the quasiparticles out of equilibrium. Here we address the temperature dependence of the quasiparticle densities in the two sides of the junction. We show that four qualitatively different regimes are possible with increasing temperature: (i) nonequilibrium, (ii) local quasiequilibrium, (iii) global quasiequilibrium, and (iv) full equilibrium. We identify shortcomings in assuming global quasiequilibrium when interpreting experimental data, highlighting how measurements in the presence of magnetic field can aid the accurate determination of the junction parameters, and hence the identification of the nonequilibrium regimes. Quasiparticle poisoning challenges the operation of superconducting qubits, but errors can be suppressed by engineering gap asymmetry between the electrodes of the qubit’s Josephson junction. The authors present a model of the qubit-quasiparticle system valid beyond the low-temperature limit and identify different nonequilibrium regimes, which can affect the interpretation of experimental data.
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.
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.
Phonon-induced Cooper pair breaking, inciting nonequilibrium quasiparticle (QP) bursts, is known to deteriorate the performance of superconducting devices. However, a detailed understanding of QP-phonon dynamics is lacking due to the absence of a well-established theoretical framework. This paper presents a fully ab initio scheme of calculating nonequilibrium, polarization-dependent QP-phonon dynamics in superconductors. The authors find that with only an 8% deviation from the equilibrium phonon Bose–Einstein distribution, the resulting nonequilibrium QP population is 83 times larger than the equilibrium Fermi–Dirac distribution, and the longitudinal acoustic (LA) phonon polarization is most responsible for QP generation. The authors demonstrated that the qubit transition rate in Josephson junction-based transmon qubits is increased by orders of magnitude when taking these nonequilibrium distributions into account, compared to equilibrium distributions. This framework allows an in-depth exploration of nonequilibrium QP-phonon dynamics in various Josephson-junction-based superconducting devices. It paves the way for formulating advanced phonon shielding strategies to target the LA polarization, potentially leading to enhanced device performance, such as increased coherence time of transmon qubits or reduced thermal noise in cryogenics.
Designing the spatial profile of the superconducting gap-gap engineering-has long been recognized as an effective way of controlling quasiparticles in superconducting devices.In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlO x /Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices.Here, we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction.We find that different regimes can be encountered in which the quasiparticles have either similar densities in the two junction leads or are largely confined to the lower-gap lead.Qualitatively, for similar densities the qubit excited-state population is lower but its relaxation rate is higher than when the quasiparticles are confined; therefore, there is a potential trade-off between two desirable properties in a qubit.
Abstract Non-equilibrium quasiparticles are possible sources for decoherence in superconducting qubits because they can lead to energy decay or dephasing upon tunneling across Josephson junctions (JJs). Here, we investigate the impact of the intrinsic properties of two-dimensional transmon qubits on quasiparticle tunneling (QPT) and discuss how we can use quasiparticle dynamics to gain critical information about the quality of JJ barrier. We find the tunneling rate of the non-equilibrium quasiparticles to be sensitive to the choice of the shunting capacitor material and their geometry in qubits. In some devices, we observe an anomalous temperature dependence of the QPT rate below 100 mK that deviates from a constant background associated with non-equilibrium quasiparticles. We speculate that this behavior is caused by high transmission sites/defects within the oxide barriers of the JJs, leading to spatially localized subgap states. We model this by assuming that such defects generate regions with a smaller effective gap. Our results present a unique in situ characterization tool to assess the uniformity of tunnel barriers in qubit junctions and shed light on how quasiparticles can interact with various elements of the qubit circuit.