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arXiv:2507.23169 · Physical review. B./Physical review. B

Effect of quasiparticles on the parameters of a gap-engineered transmon

Daniil S. Antonenko, Pavel D. Kurilovich, Francisco J. Matute-Cañadas, L. I. Glazman

Published Dec 8, 2025• 2 citations
arXivHTMLPDF

Abstract

We evaluate the quasiparticle contribution to the frequency shift and relaxation rates of a transmon with the Josephson junctions connecting superconductors that have unequal energy gaps. The gap difference substantially affects the transmon characteristics. We investigate their dependence on the density and effective temperature of the quasiparticles, and on the nominal (unperturbed by the quasiparticles) transmon frequency. At temperatures low compared to the qubit frequency, the gap difference can induce an anomalous positive frequency shift, resulting in a non-monotonic temperature dependence of the transmon frequency. The qubit relaxation rate exhibits a resonance when the qubit frequency matches the gap difference; the shape of the resonance is strongly temperature-dependent. We propose to use these effects to access the details of the quasiparticle energy distribution.

DOI
10.1103/t448-147x

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We evaluate the quasiparticle contribution to the frequency shift and relaxation rates of a transmon with the Josephson junctions connecting superconductors that have unequal energy gaps. The gap difference substantially affects the transmon characteristics. We investigate their dependence on the density and effective temperature of the quasiparticles, and on the nominal (unperturbed by the quasiparticles) transmon frequency. At temperatures low compared to the qubit frequency, the gap difference can induce an anomalous positive frequency shift, resulting in a non-monotonic temperature dependence of the transmon frequency. The qubit relaxation rate exhibits a resonance when the qubit frequency matches the gap difference; the shape of the resonance is strongly temperature-dependent. We propose to use these effects to access the details of the quasiparticle energy distribution.
As low-loss nonlinear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represents an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and nonequilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible nonequilibrium quasiparticle distribution. We also derive expressions for the shift in qubit frequency in the presence of quasiparticles.
We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10 μs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100 μs.
Superconducting quantum circuits underpin large-scale quantum processors and are increasingly interfaced with optical systems, yet they are vulnerable to quasiparticle poisoning from high-energy radiation and optical fields. Gap engineering of Josephson junctions suppresses quasiparticle-induced relaxation, but quasiparticles near the junction can still shift the qubit frequency and cause phase errors. Here, we extend gap engineering beyond the junction using a flux-tunable transmon with a gold-on-niobium ground plane and island and strongly gap-engineered aluminum junctions designed to keep quasiparticles away from the junction leads. Compared with an all-aluminum transmon with nominally identical junctions, we demonstrate that the niobium device withstands more than an order of magnitude higher near-infrared optical power before excess relaxation appears. The Nb transmon shows no resolvable quasiparticle-induced frequency shift over the same power range. At the same time, we observe that dephasing and state-preparation-and-measurement infidelity increase with optical power even while relaxation remains protected. These results suggest that engineering the quasiparticle energy landscape beyond the junction can substantially increase qubit resilience, not only to radiation-induced error bursts, but also to nearby optical fields.
This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.
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.
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.