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REVIEW 4 major objections 5 minor 42 references

On-chip microwave sensing of quasiparticles in tantalum superconducting circuits on silicon for scalable quantum technologies

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read α-tantalum superconducting resonators show measurable non-equilibrium quasiparticle loss at millikelvin temperatures, and the quasiparticle density is roughly one-third that of NbN at equivalent normalized temperatures.

desk verdict Solid raw data on Ta resonators, but the central quasiparticle-density claim lacks the parameters and error bars needed to support it. read the letter →

arxiv 2509.07669 v1 pith:U5A2PB7K submitted 2025-09-09 quant-ph cond-mat.supr-concs.ETcs.SYeess.SYphysics.app-ph

Shima Poorgholam-Khanjari , Paniz Foshat , Mingqi Zhang , Valentino Seferai , Martin Weides , Kaveh Delfanazari This is my paper · ORCID
classification quant-phcond-mat.supr-concs.ETcs.SYeess.SYphysics.app-ph
keywords superconductingmicrowaveresonatorsalpha-tantalumquasiparticlesinternalqualityfactorsingle-photonregimeMattis-Bardeentheorytwo-levelsystemscryogenicspectroscopy
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

The paper reports single-photon microwave measurements of α-tantalum coplanar waveguide resonators on silicon, at temperatures from 77 mK to 1 K. It aims to establish that non-equilibrium quasiparticles persist at millikelvin temperatures and that their density can be read out from the suppression of the internal quality factor relative to theoretical expectation. Using Mattis–Bardeen complex-conductivity theory together with a two-level-system loss model, the authors extract quasiparticle densities and find that α-Ta carries about one-third the quasiparticle density of NbN at equivalent normalized temperatures. Since non-equilibrium quasiparticles are a leading coherence limiter in superconducting qubits, this materials comparison at thermodynamically matched operating points matters directly for scalable quantum circuits.

What carries the argument

The carrying mechanism is on-chip microwave spectroscopy of quarter-wavelength coplanar waveguide resonators operated in the single-photon regime. The temperature- and power-dependent internal quality factor $Q_i$ is decomposed into two-level-system loss, quasiparticle loss, and residual loss, using the TLS model of Eq. (9) and the quasiparticle loss of Eq. (5). Quasiparticle dissipation is modelled through the Mattis–Bardeen complex conductivity $\sigma = \sigma_1 - j\sigma_2$, which converts low-temperature loss into a quasiparticle density $n_\mathrm{qp} \propto \sigma_1 \propto e^{-\Delta/k_B T}$. The material benchmark compares different superconductors at equal $T/T_c$, which is what allows the α-Ta versus NbN comparison to be stated independently of each film's critical temperature.

What would settle it

Perform the same microwave loss measurement on a second resonator from the same film while deliberately varying the quasiparticle population with a known pair-breaking source, such as a small heater or an above-gap photon pulse; if the extracted $n_\mathrm{qp}$ does not track the injected quasiparticle rate, the attribution of residual loss to non-equilibrium quasiparticles fails. Alternatively, characterise the two-level-system loss on the identical 40 nm film and geometry; if the TLS fit does not account for the full zero-quasiparticle loss, the reported densities are overestimated.

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Extended reading notes

Core claim

In the paper's own terms, the central discovery is that high-Q α-Ta microwave resonators host a finite quasiparticle population even at millikelvin temperatures. This shows up as a persistent gap between the measured internal quality factor and the value predicted from thermal quasiparticles plus two-level-system loss, across the whole 0.77–1 K range. When the residual loss is converted to a quasiparticle density through the Mattis–Bardeen relations, the density stays finite at low temperature instead of falling to zero as the thermal formula predicts. The material benchmark is placed on a thermodynamic footing by comparing at the same fractional distance from each film's transition temperature, $T/T_c$: α-Ta reaches a quasiparticle density around $0.3\times 10^3\ \mu\mathrm{m}^{-3}$, about one-third of the $1\times 10^3\ \mu\mathrm{m}^{-3}$ reported for NbN, and the normalized conductivity traces agree with Mattis–Bardeen theory over the measured range.

Load-bearing premise

The load-bearing premise is that every bit of loss left over after accounting for temperature-activated quasiparticles and the two-level-system model comes from non-equilibrium quasiparticles, and that the two-level-system model taken from an earlier tantalum device still describes this 40 nm film with no other loss channels contributing.

Editorial extensions

If this is right

  • If the reported density holds, α-Ta resonators should exhibit lower microwave dissipation than NbN at the same $T/T_c$, making them preferable for qubit readout resonators and kinetic-inductance detectors.
  • The persistent quasiparticle floor sets a limit on $Q_i$ at millikelvin temperatures, so further coherence gains will require quasiparticle trapping or mitigation rather than only surface preparation.
  • The normalized-temperature protocol gives a quantitative route for comparing quasiparticle densities across any superconducting material, not just Ta and NbN.
  • The extraction procedure of Eqs. (7)–(8) turns a standard resonator loss measurement into an on-chip quasiparticle sensor in the single-photon regime.
  • Because lower quasiparticle density directly reduces dissipation and charge noise, the comparison supports choosing α-Ta over NbN for coherence-limited circuit architectures.

Reading between the lines

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

  • A direct test at the same absolute temperature (rather than the same $T/T_c$) could show whether Ta's advantage persists at typical qubit operating points near 10–20 mK, where both densities are very low but the Ta benefit may change or vanish.
  • If non-equilibrium quasiparticles are indeed the residual loss source, adding quasiparticle traps or a gap-engineered layer to the Ta film should raise $Q_i$ toward the TLS-limited value; that is an implied design route not tested in the paper.
  • The method could be extended to other low-loss films such as aluminium or niobium and connected to qubit coherence measurements, since $Q_i$ suppression and qubit $T_1$ degradation share the same quasiparticle mechanism.
  • The normalized comparison suggests that a material's critical temperature alone is not the decisive figure of merit; the density of non-equilibrium quasiparticles at the fractional operating temperature matters, which reframes how new superconducting materials are screened.
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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. The manuscript reports fabrication and cryogenic microwave characterization of α-tantalum coplanar waveguide resonators on silicon with a niobium seed layer, including TEM, XRD, and EELS structural analysis. The authors measure the internal quality factor Qi as a function of temperature in the single-photon regime, compare it with a theoretical model combining two-level-system (TLS) loss and Mattis–Bardeen quasiparticle loss, and attribute the residual loss to persistent non-equilibrium quasiparticles at millikelvin temperatures. They extract a quasiparticle density from the residual loss and claim that α-Ta has a quasiparticle density roughly one-third that of NbN at equivalent normalized temperatures, based on a comparison with prior work.

Significance. If the residual-loss attribution is validated, the paper would provide a useful material-level study of quasiparticle loss in α-Ta resonators and a practical comparison platform for superconducting quantum circuits. The structural characterization is careful, the resonator quality factors are competitive, and the temperature- and power-dependent data set is valuable. The paper's main quantitative claims, however, depend on several unreported parameters and on a subtraction procedure that is not currently falsifiable. The material benchmarking claim against NbN is not traceable to the cited source. These issues are central to the abstract and conclusions, so the manuscript needs substantial revision before the claims can be accepted.

major comments (4)
  1. [§2.2, Eqs. (5) and (7)–(9)] The central extraction of nqp,measured is not reproducible as reported. The kinetic inductance fraction α appears in Eq. (5) and is carried through Eq. (8), but no value or measurement of α is given anywhere in the manuscript. Likewise, the TLS parameters 1/Q0_TLS, nc, and β that determine QTLS,derived in Eq. (7) are said to be 'obtained [9]' but no values or uncertainties are reported for the 40 nm device. Since nqp,measured scales as 1/α and depends directly on the subtracted TLS loss, the claimed absolute quasiparticle density and the factor-of-three comparison with NbN cannot be checked without these inputs.
  2. [§2.2, Eqs. (6)–(8)] The residual-loss attribution silently sets δ_other to zero. Equation (6) defines total loss as δTLS + δqp + δ_other, but Eq. (7) equates δqp,measured directly to 1/Qi,measured − 1/QTLS,derived. No bound is placed on magnetic, radiation, interface, or TLS-model-mismatch losses, and no uncertainty is reported for Qi. The paper itself notes (Fig. 4(e)) that for T ≲ 0.5 K the system is coupling limited and Qi is only weakly constrained by the resonance lineshape; in that regime the inferred residual loss is particularly sensitive to fitting systematics. Without uncertainty propagation or an explicit upper bound on δ_other, the conclusion that the residual is a persistent quasiparticle population is not yet falsifiable.
  3. [Fig. 6(c,d) and Eqs. (8)–(12)] The claimed agreement between experiment and Mattis–Bardeen theory is partly circular. The 'measured' nqp values are generated by inverting Eq. (8), which is an algebraic rearrangement of the same loss formula (Eq. 5) used to produce the theoretical curves, and the conductivity components come from Eqs. (1)–(2) with the same nqp–T relation. Therefore the red circles and blue lines in Figs. 6(c,d) are not independent measurements of the same relation; they test internal consistency of the inversion rather than validating the electrodynamic model. An independent validation would require comparing the measured complex conductivity or Qi to a model with independently determined nqp.
  4. [Abstract and §2.2 (final paragraph)] The quantitative benchmark against NbN is not traceable. The text states that Ta has nqp = 0.3×10^3 µm^-3 at T/Tc = 200 and that NbN has 1×10^3 µm^-3, citing [24]; however, [24] is an analytical theory paper (Fischer and Catelani) and does not report a measured NbN quasiparticle density. The value T/Tc = 200 is also physically impossible, suggesting a typographical error, and no uncertainty or temperature is given for either number. This comparison should either be removed or replaced with a direct, referenced experimental comparison.
minor comments (5)
  1. [Introduction and §2] The stated measurement temperature range is inconsistent: the Introduction says 0.77–1 K, while the experimental section and Fig. 4 use 77 mK to 1 K; please clarify whether 0.77 K is a typo or the actual base temperature used for the analysis.
  2. [§2.1, page 7] The phrase 'beak a significant number' should read 'break a significant number.'
  3. [Eq. (4)] Equation (4) writes '1.76×K_B×Tc'; this should use the conventional notation 1.76 k_B T_c for consistency with the rest of the text.
  4. [§2.2] The sentence 'the values of 1/Q0_TLS, nc, and β are obtained [9]' should state explicitly that the values are taken from the prior work and should list them in a table or appendix, since they are central to the subtraction.
  5. [Figure 6 and §2.2] The caption and text do not report the units of nqp on the axes of Fig. 6 or the calibration used to define ⟨nph⟩ ∼ 1; please add this information so that the quantitative claims can be interpreted.

Circularity Check

2 steps flagged · score 6.0 of 10

The σ–n_qp 'agreement' is enforced by inverting the same Mattis–Bardeen loss formula, and the residual n_qp extraction rests on an unreported self-cited TLS subtraction; the excess-loss observation itself is not circular.

  1. self definitional [Sec. 2.2, Eqs. (5)-(8) and Fig. 6(c,d)]
    "We can rewrite the Eq.7 to obtain nqp,theory: nqp,measured(T)≈δqp,measured(T)N0∆(T)π/α sqrt(hfr/2∆(T)) (8) ... Excellent agreement over the measured range is observed when the experimental results (red circles) are compared with the Mattis-Bardeen theoretical predictions (blue lines)."

    Equation (8) is the algebraic inverse of the loss formula Eq. (5), so n_qp,measured is just a constant rescaling of the residual loss in Eq. (7). Plotting this same rescaled quantity against red σ1/σn and σ2/σn data while generating the blue curves from the same Mattis–Bardeen relations forces the reported 'excellent agreement' in Fig. 6(c,d); it is a consistency check of the conversion, not an independent confirmation of the inferred quasiparticle density. The qualitative excess-loss observation survives, but the quantitative n_qp values and the σ–n_qp concordance reduce by construction to the input loss residual.

  2. self citation load bearing [Sec. 2.2, Eqs. (6)-(9)]
    "δqp,measured(T) = 1/Qi,measured − 1/QTLS,derived (7). ... By plotting Qi versus the photon number and fitting using [Eq. 9], the values of 1/Q0 TLS, nc, and β are obtained [9], which facilitates the derivation of δTLS. Then, by substituting Eqs. (7) and (8), δqp,measured(T) and nqp,measured(T) are obtained ..."

    The central residual is obtained by subtracting a TLS term whose parameters are taken from the authors' previous paper [9]; no values, error bars, or re-fits for the present 40 nm device are given. The δ_other term in Eq. (6) is silently discarded in Eq. (7), so any residual after the self-cited TLS subtraction—including TLS-model mismatch or unmodeled magnetic/radiation loss—is automatically defined as non-equilibrium quasiparticle loss. The 'persistent quasiparticle' inference is therefore load-bearing on an unverified self-citation rather than on an independent measurement or prediction in this paper.

full rationale

Step 1 is the main circularity: Eq. 8 is the algebraic inverse of Eq. 5, so 'n_qp,measured' is a fixed rescaling of the measured loss residual. The blue σ–n_qp curves in Fig. 6(c,d) are generated from the same Mattis–Bardeen relations, and the red circles use Eq. 8 for the horizontal coordinate, so the reported 'excellent agreement' is largely enforced by construction. The underlying observation that Qi,measured lies below Qi,theory at low temperature is not circular and may indicate real excess loss; however, the quantitative n_qp values and the material comparison inherit the model. Step 2 identifies that the residual is defined after subtracting a TLS term whose parameters come from the authors' prior work [9] and whose uncertainty is not propagated, with δ_other silently dropped from Eq. 6 to Eq. 7; any error in that self-cited TLS model is automatically relabeled as non-equilibrium quasiparticles. Separately, the NbN benchmark in the text (n_qp = 1×10^3 µm^-3 for NbN, cited to [24], and 'T/Tc = 200') is not traceable to data: [24] is an analytical theory paper and the stated normalized temperature is nonphysical; this is a correctness or traceability issue rather than a circularity. On balance, the central qualitative claim has independent content, but the quantitative quasiparticle-density results and the validation plots are partially self-referential, giving a score of 6.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central inference of non-equilibrium quasiparticles depends on three free parameters (alpha, TLS parameters, Tc) and four modeling assumptions. The paper does not provide error bars or parameter values, so the quantitative n_qp and the Ta/NbN comparison carry unquantified systematic uncertainty.

free parameters (3)
  • kinetic inductance fraction alpha = not stated
    Used in Eqs. 5, 8, and 12 to convert measured loss to quasiparticle density. The paper never gives its value or how it was calculated, and the derived n_qp scales inversely with alpha.
  • TLS fitting parameters (1/Q0_TLS, n_c, beta) = not reported in this paper
    Taken from prior work [9] according to the text. These parameters determine the TLS loss subtracted in Eq. 7, so they directly set the residual attributed to quasiparticles.
  • Critical temperature Tc for 40 nm Ta = 4.06 K
    Stated without a measurement shown. Affects the normalized temperature T/Tc and the energy gap Delta_0 through Eq. 4.
assumptions (4)
  • domain assumption Mattis-Bardeen theory describes the complex conductivity of the thin Ta film in the local limit.
    The paper uses Eqs. 1-2 without discussing the validity conditions for the film microstructure, grain size, or disorder.
  • ad hoc to paper The TLS loss model of Eq. 9 with parameters from [9] applies to the current 40 nm device.
    The paper uses TLS parameters from a different device (ref [9]) and does not re-fit or validate them on the present sample.
  • domain assumption All residual loss after subtracting TLS and thermal quasiparticle loss is due to non-equilibrium quasiparticles.
    Eq. 6 includes a term delta_other, but the paper sets it to zero and assigns the entire residual to quasiparticles.
  • domain assumption The kinetic inductance fraction alpha is constant over the measured temperature range.
    Alpha is used to convert loss to n_qp and to compute delta_i,theory, but its temperature dependence is not considered.

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Pith. "Pith review of On-chip microwave sensing of quasiparticles in tantalum superconducting circuits on silicon for scalable quantum technologies." pith.science (2026). https://pith.science/paper/U5A2PB7K

@misc{pith2026250907669,
  author       = {Pith},
  title        = {Pith review of: On-chip microwave sensing of quasiparticles in tantalum superconducting circuits on silicon for scalable quantum technologies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U5A2PB7K}},
  note         = {Machine review of arXiv:2509.07669}
}
read the original abstract

The performance and scalability of superconducting quantum circuits are fundamentally constrained by non-equilibrium quasiparticles, which induce microwave losses that limit resonator quality factors and qubit coherence times. Understanding and mitigating these excitations is therefore central to advancing scalable quantum technologies. Here, we demonstrate on-chip microwave sensing of quasiparticles in high-Q {\alpha}-tantalum coplanar waveguide resonators on silicon, operated in the single-photon regime. Temperature-dependent measurements reveal persistent non-equilibrium quasiparticles at millikelvin temperatures, producing a measurable suppression of the internal quality factor (Qi) relative to theoretical expectations. By benchmarking across materials, we find that the quasiparticle density in {\alpha}-Ta is approximately one-third that of NbN at equivalent normalised temperatures (T/Tc), directly correlating with reduced microwave loss. Our methodology establishes a scalable platform for probing quasiparticle dynamics and points towards new routes for engineering superconducting circuits with improved coherence, with impact on qubit readout resonators, kinetic-inductance detectors, and emerging quantum processors and sensors.

Figures

Figures reproduced from arXiv: 2509.07669 by the authors.

Figure 1
Figure 1. (a) Cross-sectional dark-field STEM image of a bare Ta film with an Nb seed layer on a Si substrate. (b) Zoomed-in view of STEM image of the area selected in (a), which shows the thickness of the Nb layer. (c) TEM image of the sample. (d) Zoomed-in view of TEM image of the area selected in (c) showing the thickness of Ta oxide. (e) XRD diffraction pattern of 40 nm α−Ta film on Si substrate with an Nb seed layer. The… view at source ↗
Figure 2
Figure 2. STEM–EELS analysis of a 40 nm Ta device. (a) O K-edge, (b) Ta M-edge, and (c) Nb M-edge spectra collected from the indicated regions (insets). (d) Corresponding elemental (atomic) concentration profile (O, Ta, Nb) extracted along the scan direction, confirming the spatial distribution of the oxide, Ta, and Nb layers. The red cross indicates the beam position during scanning. In order to confirm the film’s crystallin… view at source ↗
Figure 3
Figure 3. (a) Top view SEM image of superconducting Ta chip with three CPW resonators coupled to a transmission line. (b) Zoomed-in view of SEM image of the Ta circuit with W=4 µm and S=2 µm. (c) The surface current density magnitude |Js| (A/m) for three typical resonators at their resonance frequencies. The device follows the design and fabrication methods reported in [9]. The device consists of three quarter-wavelength reso… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: 3-D view of measured amplitude (a), and phase (b) of the resonator at fr=3.65 GHz at different temperatures from T = 77 mk to T = 1 K. (c) Internal quality factor (Qi) of three (different thicknesses) Ta CPW resonators on Si as a function of power at T=77 mK. (d) Inter…
Figure 5
Figure 5. Figure 5: (a) The calculated real part of the complex conductivity, σ1, as a function of temperature. (b) The calculated imaginary part of the complex conductivity, σ2, as a function of temperature for the Ta superconducting CPW resonator. Both plots are calculated from all the …
Figure 6
Figure 6. Figure 6: (a) Qi,measured and Qi,theory versus temperature at single photon regime (⟨nph⟩ ∼ 1) with the theoretical model of TLS and quasiparticle loss. Both plots are calculated and measured at fr = 3.65 GHz. (b) Theoretical and measured quasiparticle density of Ta CPW resonato…
Figure 7
Figure 7. Figure 7: Schematic of the cryogenic setup for sub-Kelvin microwave spectroscopy of the chip. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.