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REVIEW 4 major objections 5 minor 51 references

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

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read In a gap-engineered transmon, quasiparticles produce a resonant relaxation peak and a frequency-shift dip when the qubit frequency equals the gap difference, giving a spectroscopic window on the quasiparticle energy distribution.

desk verdict Genuinely new resonance physics in gap-engineered transmons, solidly derived, with an abstract overclaim and an unproven inversion step. read the letter →

arxiv 2507.23169 v1 pith:MEBXVJOS submitted 2025-07-31 cond-mat.supr-con cond-mat.mes-hall

Daniil S. Antonenko , Pavel D. Kurilovich , Francisco J. Matute-Cañadas , Leonid I. Glazman This is my paper
classification cond-mat.supr-concond-mat.mes-hall
keywords quasiparticlestransmongap-engineeredJosephsonjunctionqubitrelaxationfrequencyshiftadmittancesuperconductingspectroscopydensityofstatessingularity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper predicts that in a transmon—a superconducting qubit whose Josephson junction connects two superconductors with different gaps—quasiparticles create sharp, measurable features in the qubit's properties. When the qubit frequency $\omega_{10}$ matches the gap difference $\delta\Delta$, the quasiparticle-induced relaxation rate develops a logarithmic singularity and the frequency shift develops a narrow, temperature-dependent dip whose width is set by $T_* = |\delta\Delta - \omega_{10}|$. Near this resonance, both observables collapse onto universal functions of $T/T_*$. Because a split transmon's frequency is flux-tunable, the resonance can be swept experimentally and used to probe the low-energy part of the quasiparticle distribution, a quantity that is otherwise difficult to access.

What carries the argument

The machinery is the finite-frequency admittance $Y(\omega)$ of an asymmetric Josephson junction, obtained from a tunnel Hamiltonian with BCS quasiparticles and evaluated through the Kubo formalism and Fermi's golden rule. The load-bearing identity is the spectral density in Eq. (25), built from two square-root density-of-states factors $1/\sqrt{\varepsilon}$ at the gap edges; it produces a logarithmic divergence in $\mathrm{Re}\,Y$ and a step in $\mathrm{Im}\,Y$ at $\omega = \delta\Delta$. The paper then evaluates the split-transmon frequency shift and relaxation rate from this admittance, assuming a quasi-thermal Boltzmann distribution $f_{\Delta+\varepsilon} = f_0 e^{-\varepsilon/T}$ with fixed total density $x_{qp}$, giving closed forms in terms of $H(x) = e^{x/2}K_0(x/2)$ and $h(x) = e^{-x/2}I_0(x/2)$.

What would settle it

In a split transmon with a known gap difference $\delta\Delta$, sweep $\omega_{10}$ through $\delta\Delta$ by magnetic flux at fixed quasiparticle density and measure $\Gamma_{1\to 0}(T)$ and $\delta\omega_{10}(T)$. The paper's claim is a logarithmic divergence of the rate at $\omega_{10} = \delta\Delta$, an additional $e^{-T_*/T}$ suppression on the $\delta\Delta > \omega_{10}$ side, and a frequency-shift dip of width $T_*$ on that same side; observing none of these under quasi-thermal conditions would falsify the central resonance picture.

Watch

Extended reading notes

Core claim

The central claim is that a finite gap difference $\delta\Delta$ between the superconductors of a Josephson junction qualitatively changes the quasiparticle back-action on a transmon. The singular density of states at the two gap edges makes the dissipative part of the junction admittance diverge logarithmically at $\omega = \delta\Delta$ while the reactive part jumps, and this singularity propagates into the qubit observables: the relaxation rate $\Gamma_{1\to 0}$ is resonantly enhanced by a factor $\sqrt{\Delta/|\delta\Delta - \omega_{10}|}$ and the frequency shift develops a dip that is deeper and narrower than in a symmetric junction. The paper gives closed-form expressions for both effects under a quasi-thermal quasiparticle distribution—Eq. (60) for the rate and Eq. (48) for the shift—and shows that near resonance each has a universal temperature dependence, $G(T/T_*)$ for the rate and $F(T/T_*)$ for the shift. It argues that measuring these features, together with the quasi-elastic parity-switching rate, provides a practical spectroscopic method to probe the low-energy quasiparticle distribution.

Load-bearing premise

The quantitative formulas assume quasiparticles in both leads share a single quasi-thermal Boltzmann distribution with one effective temperature and that the total quasiparticle density stays fixed as temperature changes; if the real distribution is non-thermal or differs between the two leads, the predicted temperature curves and universal collapse change.

Editorial extensions

If this is right

  • Sweeping a split transmon's frequency through $\delta\Delta$ should reveal a resonant enhancement in $\Gamma_{1\to 0}$ whose height grows as $\sqrt{\Delta/|\delta\Delta - \omega_{10}|}$, making weak quasiparticle populations measurable.
  • Near resonance the temperature dependence of the relaxation rate has the universal form $G(T/T_*)$ on the $\omega_{10} > \delta\Delta$ side and $G(T/T_*)e^{-T_*/T}$ on the $\delta\Delta > \omega_{10}$ side, so a single experiment can separate quasiparticle density from spectral shape.
  • The frequency shift near $\delta\Delta > \omega_{10}$ develops a dip at $T \sim T_*$ with amplitude $x_{qp}\sqrt{\Delta/T_*}$, giving a second, independent observable for the same quasiparticle parameters.
  • At $T \ll \delta\Delta$ and $\omega_{10} \ll \delta\Delta$, dissipation is exponentially suppressed and the frequency shift varies on the temperature scale $\delta\Delta$ rather than $\omega_{10}$, confirming the gap-engineering strategy for protecting qubits from quasiparticles.
  • Parity-switching rates are exponentially suppressed at low temperature and show no resonance at $\omega_{10} = \delta\Delta$, so they can serve as a calibration reference for the resonant rates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The integral representations in Eqs. (23) and (29) relate the measured shift and rate directly to the distribution function $f_\varepsilon$; inverting them at several flux settings could recover a non-thermal $f_\varepsilon$ rather than merely fitting an effective temperature, extending the proposed spectroscopy beyond the quasi-thermal assumption.
  • A device with a small low-gap volume $V_L \ll V_R$ concentrates quasiparticles in the low-gap lead and amplifies the resonant signal by a factor $(V_L+V_R)/V_L$ up to a Saha-type ionization temperature $T_{\mathrm{Saha}}$; this trade-off suggests a design principle for quasiparticle sensors even though it worsens qubit coherence.
  • If the resident quasiparticle distribution is strongly non-thermal, the predicted collapse of the curves in the paper's Figs. 2 and 4 would fail, and the shape of that failure could itself diagnose the energy dependence of quasiparticle relaxation, a debated quantity the paper discusses.
  • A wording discrepancy: the abstract's phrase "anomalous positive frequency shift" does not match the main text, which states that the admittance-induced frequency shift is negative at all parameter values; the non-monotonic feature shown in the figures is a dip toward more negative values.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper develops a theory of quasiparticle-induced frequency shifts and relaxation rates in a gap-engineered transmon, i.e., a split transmon whose Josephson junctions connect superconductors with unequal gaps ΔL and ΔR. Using the tunnel Hamiltonian, Fermi's golden rule for the dissipative response, and Kramers-Kronig plus inductive matching for the reactive response, the authors derive closed-form expressions for the finite-frequency admittance (Eqs. (20)–(30)), the transmon frequency shift (Eqs. (45), (48), (52)), the downward relaxation rate (Eqs. (58), (60)), and the parity-switching rate (Eqs. (64), (67)). The central predictions are: (i) a resonant enhancement of the quasiparticle-induced relaxation rate when the qubit frequency ω10 matches the gap difference δΔ, with a logarithmic divergence and a temperature scale T* = |δΔ − ω10|; (ii) a correspondingly narrow and deep dip in the frequency shift on the δΔ > ω10 side; and (iii) universal scaling functions F(T/T*) and G(T/T*) in the quasi-thermal model. The paper also proposes that these effects could be used to probe the low-energy quasiparticle distribution. The derivation is analytic and detailed, with the full Kubo-formalism expression relegated to Appendix A.

Significance. If the quantitative predictions hold, this work provides a useful theoretical foundation for interpreting experiments on gap-engineered transmons and for designing spectroscopic probes of nonequilibrium quasiparticles. The paper's strengths include its transparent microscopic starting point, absence of fitted parameters in the final predictions (xqp and T are inputs), closed-form analytic results, reproduction of the symmetric-junction limit δΔ → 0, and explicit falsifiable predictions such as the resonance at ω10 = δΔ and the collapse of curves onto F(T/T*) and G(T/T*). The main caveat is that the quantitative lineshapes and the proposed distribution-extraction protocol are derived under a quasi-thermal Boltzmann distribution and a common distribution in both leads; this is acknowledged as an assumption but its consequences for the proposed spectroscopy are not fully explored.

major comments (4)
  1. [§VI A, Eq. (60)] The prefactor in Eq. (60) appears to be inconsistent with the low-temperature limit of Eq. (58). For T ≪ T* ≡ |δΔ − ω10|, Eq. (58) gives Γ1→0 ≈ (xqpζ/2π) F [sqrt(Δ/(2T*))] G(T/T*) with F = (ω10(0)^2 + ω10(Φ)^2)/ω10(Φ), i.e., the amplitude contains sqrt(Δ/(2T*)) = sqrt(πΔ/(2πT*)). Eq. (60) instead displays sqrt(Δ/(2πT*)), which is smaller by a factor sqrt(π). This affects the quantitative amplitude and the data collapse in Fig. 4. Please correct the prefactor or clarify the definition of G.
  2. [§V B, Eq. (48)] The resonant first term of Eq. (48) is a factor of 2 larger than the corresponding T ≪ T* limit of Eq. (45). Setting Φ = 0, so that ω10(0) = ω10(Φ) = ω, and using h(x) ≈ 1/sqrt(πx) for x ≫ 1, Eq. (45) yields δωY10 ≈ −(xqpζω/2π) sqrt(Δ/(2T*)), whereas Eq. (48) yields −(xqpζω/π) sqrt(Δ/(2T*)). The discrepancy apparently arises from the missing factor 1/2 in the flux factor (ω10(0)^2 + ω10(Φ)^2)/(2ω10(Φ)^2) when passing from Eq. (45) to Eq. (48). This changes the claimed resonant amplitude and the inset in Fig. 2; please verify the other regular terms in Eq. (48) as well.
  3. [§VII and Eqs. (23), (29)] The paper states that the integral representations, Eqs. (23) and (29), allow one to access the quasiparticle energy distribution function, but no inversion, uniqueness, or sensitivity analysis is provided. The extraction of an 'effective temperature' and the universal collapse onto F(T/T*) and G(T/T*) are consequences of the Boltzmann ansatz Eq. (24), not of a model-independent inversion. As written, the manuscript demonstrates a quasi-thermal model and its observable signatures, but it does not demonstrate that measurements of δω10 and Γ1→0 can reconstruct a general non-thermal distribution. Please either add such an analysis or explicitly limit the proposal to the quasi-thermal case.
  4. [§II, Eq. (5) and §V B, Eqs. (42)–(44)] The assumption that quasiparticles in both leads share the same distribution function, Eq. (5), together with the fixed-total-density condition Eq. (42), implies that the two leads are equilibrated with a common effective temperature and chemical potential on the relevant time scales. For weakly coupled leads with different gaps this is physically nontrivial; if the two leads instead support independent quasiparticle populations, the volume factor ζ(T) and the temperature dependencies of Eqs. (45), (58), and (64) would change. Please discuss the parameter regime in which this equilibration assumption is expected to hold, or present the two-population generalization.
minor comments (5)
  1. [§V B] The text refers to 'δωY01' in two places ('The temperature dependence of δωY01 in this case' and 'The resonant enhancement of the frequency shift δωY01'); both should read δωY10.
  2. [§I] There is a typo in the Introduction: 'gap-engieered devices' should be 'gap-engineered devices'.
  3. [§IV B, Eq. (29)] The notation in Eq. (29) is somewhat dense: the integration limits 'Z |ω−δ∆| 0' should be written as ∫_0^{|ω−δΔ|} for clarity, and the step-function arguments should be explicitly parenthesized.
  4. [§V B, Figs. 2 and 3] The figure captions state that ζ(T) = 1 in the limit VL ≫ VR; for Fig. 3, where VL/VR is varied, it would help to state explicitly that the plotted curves use the full ζ(T) of Eq. (44).
  5. [§VI A, Eq. (60)] The definition T* = |δΔ − ω10(Φ)| in Eq. (60) is said to 'extend' the earlier definition; for consistency with Eq. (48), where T* = δΔ − ω10, please state clearly that the absolute value is taken in Eq. (60).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: quasiparticle transmon predictions are derived from the tunnel Hamiltonian with explicit inputs; the quasi-thermal ansatz is a stated modeling assumption, not a fitted output.

full rationale

The paper's central claims—the resonant relaxation rate near ω10=δΔ and the temperature-dependent frequency shift near T*=δΔ−ω10—are obtained by substituting the quasi-thermal distribution ansatz of Eq. (24) and the fixed-density normalization of Eq. (44) into spectral functions derived from the tunnel Hamiltonian via Fermi's golden rule and Kubo/Kramers-Kronig response theory (Eqs. (20), (23), (25), (29), (30)). The quasiparticle density xqp and effective temperature T are inputs, not parameters fitted to the target observables δω10 or Γ1→0; the resulting formulas (45), (48), (58), and (60) are explicit closed forms of the model, not tautological restatements of the inputs. The paper checks limiting cases against independently published results: Eq. (15) matches the symmetric-junction result of Ref. 33, Eq. (47) reproduces the symmetric-junction high-temperature asymptote, and Eq. (53) agrees with Ref. 26. These are external benchmarks rather than load-bearing self-citations. The quasi-thermal Boltzmann assumption (24) is openly declared as an assumption, not justified by a self-citation, and the paper even acknowledges that the problem of the detailed distribution function is open (Refs. 35, 36). The proposed spectroscopy based on the integral representations (23) and (29) is not demonstrated with an inversion or uniqueness proof, but that is a limitation of the proposal, not a circular reduction: those representations are derived functionals of f, not definitions that assume the conclusion. Therefore no circular step can be identified; the derivation is self-contained from standard microscopic input.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central results rest on the BCS tunneling model, the small-xqp linearization, and, for the quantitative temperature dependencies, the quasi-thermal Boltzmann distribution (Eq. 24). No new physical entities are introduced. The free inputs are the quasiparticle density and effective temperature; device parameters (Δ, δΔ, ω10, EC/EJ, volumes) are given by the experiment.

free parameters (2)
  • xqp (system-averaged quasiparticle density)
    Explicitly treated as a free parameter in Eq. (42) and the text following Eq. (7); represents the combined thermal and resident quasiparticle density. All final results are linear in xqp.
  • T (effective quasiparticle temperature)
    Input parameter characterizing the assumed Boltzmann distribution (Eq. 24). The paper treats T as a variable; no data fitting is used to set it.
assumptions (6)
  • domain assumption Both leads are described by BCS mean-field theory with gap parameters ΔL and ΔR (Eq. 4).
    Standard model for superconducting leads; used throughout to define quasiparticle energies and Bogoliubov amplitudes.
  • domain assumption Quasiparticles in both leads share the same energy-dependent distribution function fε (Eq. 5).
    Assumed in Section II. If the two leads are not in mutual equilibrium, the nonequilibrium factor would differ.
  • domain assumption Quasiparticle density is small, xqp ≪ 1, allowing linearization in xqp and neglect of f^2 terms (Eqs. 7, 23).
    Used throughout; valid for resident quasiparticle densities in practical devices.
  • ad hoc to paper The quasiparticle distribution is quasi-thermal and Boltzmann: f_{Δ+ε} = f0 e^{-ε/T} (Eq. 24).
    This is the key modeling assumption for the closed-form results (Eqs. 45, 58). The paper also gives integral representations (Eqs. 23, 29) valid for arbitrary fε, but the quantitative temperature dependencies and the proposed extraction method rely on this parameterization.
  • domain assumption Gap difference and energy scales are small relative to the gap: δΔ ≪ Δ, ω, T, δΔ ≪ Δ (Eq. 18 and Section IV).
    Used to simplify density-of-states factors and to replace Bogoliubov amplitudes by 1/√2. Appendix A provides the full expressions without this simplification.
  • domain assumption The system-averaged quasiparticle density xqp remains fixed as T varies; the chemical potential adjusts (Eq. 42 and footnote 42).
    Needed for the temperature dependence of ζ(T) in Eq. (44). Justified only for spatially uniform sources of non-equilibrium quasiparticles.

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Pith. "Pith review of Effect of quasiparticles on the parameters of a gap-engineered transmon." pith.science (2026). https://pith.science/paper/MEBXVJOS

@misc{pith2026250723169,
  author       = {Pith},
  title        = {Pith review of: Effect of quasiparticles on the parameters of a gap-engineered transmon},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MEBXVJOS}},
  note         = {Machine review of arXiv:2507.23169}
}
read the original 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.

Figures

Figures reproduced from arXiv: 2507.23169 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Split-transmon effective circuit; (b) Josephson [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Temperature dependence of the relative frequency [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Frequency shift of a split-transmon at Φ = 0 (or [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the transition rate Γ [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.