{"id":"20d2150d-6058-40db-a5c3-0e1c03aa54b5","arxiv_id":"2506.17816","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"NbN superconducting microwave resonators show a temperature-independent quasiparticle density of about 50 per cubic micrometer at millikelvin temperatures, indicating non-equilibrium quasiparticles as a decoherence source.","lead":"The authors cooled niobium-nitride microwave resonators to near absolute zero and found a background of small energy particles, called quasiparticles, that persists even when thermal energy should be too weak to create them. The result matters because these particles are a known source of decoherence in superconducting quantum circuits made from this material.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 50 µm^-3 saturation at 120 mK is a residual after subtracting a TLS model carried over from ref. [22]; without the Q_TLS(T) parameters and propagated uncertainties, attribution to quasiparticles is not yet established.","rationale":"The reader's weakest_assumption captures the main load-bearing point: the excess loss at T < T_c/10 is defined as a residual after subtracting a TLS-loss model imported from the prior publication [22], and Eq. (7) then converts that residual into a quasiparticle density. My reading of the full manuscript confirms this is the critical step. The quantitative claim '50 µm^-3 at T = 120 mK' is exactly the residual divided by a conversion factor; it inherits all errors in Q_TLS and α and any unmodeled temperature-independent channel such as vortices, trapped flux, stray radiation, or surface two-level systems not captured by [22]. The manuscript presents no error bars in Fig. 4 or Fig. 6, and the TLS model parameters are not reproduced, so the uncertainty in the saturated density cannot be assessed from the text.\n\nThe paper does have real strengths: single-photon power calibration, standard Mattis-Bardeen conductivity calculation at higher temperatures, and the qualitative increase then decrease of Q_i(T) is consistent with TLS plus thermal quasiparticle crossover. The authors also explicitly qualify their conclusion by calling for tunneling spectroscopy and noting that intrinsic vs. external contributions are not yet distinguished. These limitations, plus the indirect extraction, justify a conditional rather than unconditional verdict.\n\nI considered whether a more serious internal inconsistency exists in Eq. (7) itself—the prefactor multiplying N0Δ(T)π/α differs from some published forms by a factor of π or a sqrt(2). If the prefactor were wrong, the 50 µm^-3 number would change but the existence of a non-thermal residual loss would not; so this is not the most load-bearing concern. Similarly, the Appendix photon-number calculation is plausible. No fraudulent or sloppy behavior is indicated; the issue is under-determined inference, not internal contradiction.","tokens_in":14461,"tokens_out":8328,"duration_ms":80336,"concrete_test":"Replot the Q_i(T) data of Fig. 4(a) and perform a global fit with 1/Q_total(T) = 1/Q_TLS(T) + 1/Q_MB(T) + 1/Q_extra, where Q_TLS uses the parameters from ref. [22] and Q_extra is a temperature-independent loss rate. Compare the fit with Q_extra fixed to zero vs. free (e.g., via F-test or AIC). If the data are fit equally well without Q_extra within the reported measurement scatter, the low-T residual cannot be uniquely attributed to quasiparticles and the 50 µm^-3 saturation is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—saturation of n_qp at about 50 µm^-3 at T = 120 mK (inset of Fig. 6(b))—is obtained entirely through Eq. (6): δ_qp,measured = 1/Q_i,measured − 1/Q_TLS, followed by Eq. (7). Both the TLS loss 1/Q_TLS(T) and the kinetic inductance fraction α are taken from the authors' prior study [22] and are not restated or refit here; Fig. 6(a) shows that Q_TLS is much larger than Q_qp,theory in the T < T_c/10 regime, so the residual at base temperature is the difference between two larger numbers. If the true Q_TLS at 120 mK is a factor of ~2 lower, the residual δ_qp,measured becomes consistent with zero and the 50 µm^-3 value disappears. Fig. 4(a) and Fig. 6 are shown without error bars, so the statistical significance of the residual cannot be assessed. The paper itself acknowledges this underdetermination: 'Future works are needed to distinguish between intrinsic saturation and external non-equilibrium contributions' and states that tunneling spectroscopy 'is critical' to validate the phenomenon. The low-temperature excess loss is likely real, but its specific attribution to quasiparticles—and the numerical density 50 µm^-3—is not established by the analysis presented here.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports temperature-dependent microwave spectroscopy of NbN coplanar-waveguide resonators operated near single-photon powers, together with a Mattis-Bardeen calculation of the complex conductivity. The central claim is that the measured internal quality factor at millikelvin temperatures implies a quasiparticle density that saturates near 50 µm^-3 at T = 120 mK, well below T_c/10, indicating a non-equilibrium quasiparticle population that limits Q_i. The paper presents Q_i and frequency-shift data for two resonator modes, calculates theoretical TLS and quasiparticle losses, and attributes the low-temperature deviation between Q_i,measured and Q_i,theory to non-equilibrium quasiparticles.","tokens_in":14752,"tokens_out":5462,"duration_ms":55530,"significance":"If the central claim is correct, the work would provide useful evidence for a millikelvin loss floor in NbN resonators, a material of growing interest for hybrid superconducting circuits. The calculation framework is largely standard: the Mattis-Bardeen thermal conductivity expression is parameter-light, and the resonator parameter extraction follows a published circuit model. The authors are also transparent about the limitations of their interpretation, explicitly noting that future work and tunneling spectroscopy are needed to distinguish intrinsic from external contributions. However, the quantitative result at the heart of the paper depends on a residual subtraction against a TLS model imported from a prior study, with no restated parameters and no visible uncertainty propagation, so the 50 µm^-3 saturation should currently be read as a plausible hypothesis rather than an established measurement.","major_comments":[{"comment":"The central result—n_qp,measured ≈ 50 µm^-3 at 120 mK—is defined as a residual, δ_qp,measured = 1/Q_i,measured − 1/Q_TLS, where Q_TLS(T) and α are taken from the authors' previous study [22] without restating their values, functional form, or fitting procedure. This is load-bearing: Fig. 6(a) indicates that Q_TLS and Q_i,measured are close near base temperature, so the inferred quasiparticle density is the difference of two comparable quantities, and a factor-of-order-two systematic error in the TLS model could make the residual consistent with zero. Please restate the TLS parameters, show the quality of the TLS fit for the specific resonators used here, and propagate uncertainties through Eq. (7).","section":"Section IV-C, Eqs. (6)-(7)"},{"comment":"No error bars or confidence intervals are shown for Q_i,measured(T), Δf/f_r, or the derived n_qp,measured, even though Fig. 2(a) demonstrates that such uncertainties exist for these measurements. Without an uncertainty estimate for the subtracted residual, the claimed saturation at 50 µm^-3 cannot be quantitatively assessed, and the word 'confirming' in the inset discussion is stronger than the displayed data support. Please include uncertainty propagation, for example from Monte Carlo resampling of the S21 fits, and show the resulting confidence band on n_qp,measured.","section":"Section IV-C, Figs. 4 and 6"},{"comment":"The manuscript itself states that 'future works are needed to distinguish between intrinsic saturation and external non-equilibrium contributions' and that tunneling spectroscopy 'is critical' to validate the phenomenon, yet the same section concludes that a non-equilibrium quasiparticle density 'confirms a source of decoherence in quantum circuits at millikelvin temperature.' These statements are in tension. The data may demonstrate a low-temperature excess loss, but the specific attribution of that loss to quasiparticles—rather than to stray radiation, vortices, or an incomplete TLS model—is not uniquely established by the analysis presented. Please either add a discriminating measurement or temper the conclusion to an observed excess loss with quasiparticles as one plausible and well-motivated explanation.","section":"Section IV-C, concluding paragraph"}],"minor_comments":[{"comment":"The denominator of the expression for δ_qp,theory appears to have a parenthesis mismatch; it should read ω(Im(Z_s/ω) + L_g) rather than ω(Im(Z_s/ω)) + L_g).","section":"Eq. (2)"},{"comment":"The notation is inconsistent: 'Q_qp,T heroy', 'Q_qp,theory', and 'δ_qp,T heory' all appear; please unify the notation, e.g., Q_qp,theory and δ_qp,theory, throughout the text and figures.","section":"Throughout"},{"comment":"The approximation conditions ℏω ≪ Δ0 and k_B T ≪ Δ0 should be stated quantitatively; at T = 3 K, k_B T/Δ0 ≈ 0.16 for T_c = 10.7 K, which is not deep in the low-temperature limit, so the validity range of the simplified Mattis-Bardeen expressions deserves a brief comment.","section":"Section IV-B, Eqs. (3)-(4)"},{"comment":"The inset uses a different horizontal range from the main panel and the caption does not state explicitly that it is a zoomed view; please add axis labels and state in the caption that the inset magnifies the T < T_c/10 region.","section":"Fig. 6(b) inset"},{"comment":"Because the TLS model from reference [22] is central to the extraction, please provide its explicit equations and best-fit parameters in the main text or in an appendix so that the residual calculation is reproducible without consulting the prior paper.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript is a useful characterization study and the authors are appropriately cautious in their closing statements, but the headline number (50 µm^-3 at 120 mK) is not yet supported as a quasiparticle density because it rests on an unstated TLS background subtraction and absent uncertainty propagation. This is fixable within the manuscript's scope by restating the TLS model, adding error bars, and softening the causal language, so major revision is appropriate rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Best to get straight to it: this is a useful NbN resonator dataset, but the headline number—50 quasiparticles per cubic micrometer at 120 mK—is a residual after subtracting a TLS model carried over from the authors' prior paper and never shown. I would not treat that number as established.\n\nWhat is genuinely new: a clean temperature sweep of Qi at single-photon powers for 100 nm NbN CPWs on Si, from 0.1 K to 3 K, for two resonators. The extraction of Qi and fr follows a published circuit model, and the Mattis-Bardeen complex conductivity calculation is standard and parameter-light. The authors are also honest at the end: they note that tunneling spectroscopy is critical and that intrinsic versus external non-equilibrium contributions are not distinguished. That candor counts.\n\nThe soft spots are concentrated in Eqs. (6)–(7) and Fig. 6. The measured n_qp is defined as 1/Q_i,measured minus 1/Q_TLS, with Q_TLS(T) and alpha taken from ref. [22] without restating parameters. Fig. 6(a) shows Q_TLS much larger than Q_qp,theory at low T, so the residual at base temperature is the difference of two larger numbers. If the true Q_TLS at 120 mK were a factor of about 2 lower, the residual would vanish. No error bars appear in Fig. 4 or Fig. 6, so the statistical significance of the residual cannot be assessed. That is not a minor caveat; it is the load-bearing step. The qualitative claim that Qi falls below the theoretical TLS-plus-thermal-quasiparticle prediction at millikelvin is likely robust, but the specific attribution to quasiparticles, and the 50 µm^-3 density, is not yet supported.\n\nOn the citation pattern: leaning on ref. [22] is not itself a problem, but here the TLS curve does real quantitative work and needs to be visible. Self-citation is not the issue; opacity is.\n\nWho this is for: people working on NbN or high-kinetic-inductance resonators and kinetic-inductance detectors will want the raw Qi(T) data. The analysis section is a useful case study in how residual-based loss attribution can overreach when background subtraction is not shown.\n\nMy recommendation: send it to peer review. A serious referee can ask for the Q_TLS parameters, error propagation, and a softened claim. The underlying measurement deserves publication; the current interpretation needs revision.","headline":"Useful NbN resonator data, but the 50 µm^-3 saturation number is a residual against an unseen TLS model and should not be taken at face value.","tokens_in":15340,"tokens_out":1907,"would_cite":false,"duration_ms":17759,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"NbN superconducting microwave resonators at single-photon powers contain a non-equilibrium quasiparticle population that saturates near 50 per cubic micrometer at 120 mK, limiting their internal quality factor.","keywords":["NbN superconducting resonators","quasiparticle density","non-equilibrium quasiparticles","Mattis-Bardeen conductivity","internal quality factor","single-photon regime","coplanar waveguide resonator","microwave loss"],"falsifier":"Measure the same NbN resonator at 120 mK with additional infrared shielding or with a directly biased tunnel junction on the same film; if $Q_i$ rises and the inferred density drops well below $50\\,\\mu\\mathrm{m}^{-3}$, or if the junction detects far fewer quasiparticles, the microwave-derived saturation is not an intrinsic quasiparticle density.","tokens_in":14247,"feed_emoji":"❄️","tokens_out":11419,"duration_ms":92945,"temperature":0.7,"pith_summary":"This paper tries to establish that NbN superconducting coplanar waveguide resonators, operated at single-photon power, contain a measurable population of non-equilibrium quasiparticles at millikelvin temperatures—well below $T_c/10$, where thermal quasiparticles should be negligible. The evidence is a temperature sweep of the internal quality factor: measured $Q_i$ is lower than the sum of two-level-system loss and Mattis-Bardeen thermal quasiparticle loss, and the residual loss converts to a quasiparticle density that saturates near $50\\,\\mu\\mathrm{m}^{-3}$ at 120 mK. If correct, this means millikelvin NbN quantum circuits have a decoherence floor set by non-equilibrium quasiparticles, and mitigation strategies such as quasiparticle traps, infrared shielding, or gap engineering would be needed to raise coherence times.","feed_headline":"At 120 mK, NbN resonators hold 50 quasiparticles per cubic micron","feed_subtitle":"The excess loss cannot be explained by thermal quasiparticles, so it sets a decoherence floor for NbN circuits.","key_machinery":"The load-bearing object is the Mattis-Bardeen complex conductivity $\\sigma(T)=\\sigma_1(T)-j\\sigma_2(T)$ of the NbN film, evaluated in the superconducting dirty limit where the mean free path is much shorter than the coherence and penetration lengths. The real part $\\sigma_1$ is the resistive channel that lowers $Q_i$; the imaginary part $\\sigma_2$ is the inductive channel that shifts the resonance frequency. The paper computes $\\sigma_1/\\sigma_N$ and $\\sigma_2/\\sigma_N$ from the standard Mattis-Bardeen formulas, feeds them into the surface-impedance expression to obtain the theoretical thermal quasiparticle loss $\\delta_{qp,\\mathrm{theory}}$, and defines the measured quasiparticle loss as $\\delta_{qp,\\mathrm{measured}} = 1/Q_{i,\\mathrm{measured}} - 1/Q_{\\mathrm{TLS}}$, with $Q_{\\mathrm{TLS}}$ and the kinetic inductance fraction $\\alpha$ taken from the prior study of the same resonators. Equation (7) then carries the argument from residual loss to quasiparticle density using the normal-state density of states $N_0$, the gap $\\Delta(T)$, and $\\alpha$.","core_discovery":"The paper's central claim is that the low-temperature internal quality factor of NbN coplanar waveguide resonators is limited by a non-equilibrium quasiparticle population. After subtracting the two-level-system loss $1/Q_{\\mathrm{TLS}}$ from the measured $1/Q_i$, the remaining loss is attributed to quasiparticles; converting that residual loss through the Mattis-Bardeen relation yields a quasiparticle density that stops decreasing around $T \\simeq 120\\,$mK and saturates near $50\\,\\mu\\mathrm{m}^{-3}$. Since thermal equilibrium theory predicts a negligible quasiparticle density in this temperature range, the paper concludes that the saturation is a non-equilibrium population acting as a decoherence source in NbN quantum circuits at millikelvin temperatures.","pith_inferences":["One implication the authors leave implicit: if the saturation is dominated by stray radiation rather than intrinsic material properties, then the same device with better infrared shielding should show a higher $Q_i$ and a lower inferred quasiparticle density, which is a testable separation between environmental and intrinsic contributions.","The resonance frequency shift observed between 1.6 K and 1.8 K is attributed to quasiparticle inductance, so a quantitative joint fit of $\\Delta f/f_r$ and $Q_i$ would provide an independent cross-check of the inferred density.","The density conversion assumes a uniform quasiparticle distribution and a constant kinetic inductance fraction $\\alpha$; if quasiparticles are concentrated near resonator edges, the reported $50\\,\\mu\\mathrm{m}^{-3}$ is an effective average rather than a local density.","A direct test would be to fabricate a small tunnel junction on the same NbN film and measure its subgap current at 120 mK; the inferred quasiparticle density should match the microwave-derived saturation if the attribution is correct."],"forward_implications":["At temperatures below about 1 K, the internal quality factor of these NbN resonators is capped by quasiparticle loss rather than by two-level-system loss alone, so reducing TLS defects will not by itself raise $Q_i$ at base temperature.","The saturation density near $50\\,\\mu\\mathrm{m}^{-3}$ at 120 mK means millikelvin NbN circuits have a decoherence floor tied to non-equilibrium quasiparticles, not to thermal excitation.","Mitigation strategies that reduce non-equilibrium quasiparticle populations—shielding stray infrared light, adding quasiparticle traps, or gap engineering—should translate directly into higher $Q_i$ and longer coherence times in NbN devices.","Mattis-Bardeen equilibrium theory is insufficient for NbN below $T_c/10$; a model including quasiparticle trapping, diffusion, and recombination is needed to describe the measured loss."],"supporting_citations":[{"why":"Supplies the TLS loss curve $Q_{\\mathrm{TLS}}(T)$ and the kinetic inductance fraction $\\alpha$ used to convert residual loss to quasiparticle density.","marker":"[22]"},{"why":"Provides the Mattis-Bardeen complex-conductivity theory used for the thermal quasiparticle loss calculations.","marker":"[39]"},{"why":"Supplies the surface-impedance expression and dirty-limit equations for quasiparticle loss in superconducting resonators.","marker":"[48]"},{"why":"Origin of the Mattis-Bardeen approximations in Eqs. (3)-(4) used to compute $\\sigma_1$ and $\\sigma_2$.","marker":"[49]"},{"why":"Provides the relation linking measured residual loss to quasiparticle density used in Eq. (7).","marker":"[53]"},{"why":"Supplies the normal-state density of states $N_0$ at the Fermi level used in the density conversion.","marker":"[54]"},{"why":"Establishes the baseline expectation that thermal quasiparticle density is negligible below $T_c/10$, which the saturation result contradicts.","marker":"[55]"},{"why":"Gives an analytical non-equilibrium quasiparticle distribution model the paper cites as motivation for deviations from Mattis-Bardeen theory in high-kinetic-inductance films.","marker":"[52]"}],"fun_headline_variants":["Non-equilibrium quasiparticles set NbN resonator decoherence floor","NbN resonators hit a quasiparticle floor at 120 mK","50 quasiparticles per µm³ limit NbN resonators","Non-thermal quasiparticles cap NbN resonator quality","Quasiparticle saturation at 120 mK sets NbN decoherence floor"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that all microwave loss not explained by the material's two-level-system defects and by thermally excited quasiparticles is caused by quasiparticles; if stray radiation, vortices, or another loss channel contributes at millikelvin temperatures, the reported saturation density is an artifact rather than a quasiparticle population.","fun_headline_variants_meta":{"raw":{"variants":["Non-equilibrium quasiparticles set NbN resonator decoherence floor","NbN resonators hit a quasiparticle floor at 120 mK","50 quasiparticles per µm³ limit NbN resonators","Non-thermal quasiparticles cap NbN resonator quality","Quasiparticle saturation at 120 mK sets NbN decoherence floor"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000573,"raw_usage":{"total_tokens":2632,"prompt_tokens":796,"completion_tokens":1836,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":412,"completion_tokens_details":{"reasoning_tokens":1741}},"tokens_in":412,"tokens_out":1836,"duration_ms":11802,"temperature":1.0,"reasoning_tokens":1741,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:00:57.402373+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the same NbN resonator at 120 mK with additional infrared shielding or with a directly biased tunnel junction on the same film; if $Q_i$ rises and the inferred density drops well below $50\\,\\mu\\mathrm{m}^{-3}$, or if the junction detects far fewer quasiparticles, the microwave-derived saturation is not an intrinsic quasiparticle density.","supporting_citations":[{"cited_title":"Characterizing nio- bium nitride-based superconducting coplanar waveguide resonators for microwave hybrid circuit quantum electro- dynamics,","cited_arxiv_id":null,"evidence_quote":"Supplies the TLS loss curve $Q_{\\mathrm{TLS}}(T)$ and the kinetic inductance fraction $\\alpha$ used to convert residual loss to quasiparticle density."},{"cited_title":"Theory of the anomalous skin effect in normal and superconducting metals,","cited_arxiv_id":null,"evidence_quote":"Provides the Mattis-Bardeen complex-conductivity theory used for the thermal quasiparticle loss calculations."},{"cited_title":"Measuring and Trapping Quasiparticles in Superconducting Coplanar Waveguide Resonators,","cited_arxiv_id":null,"evidence_quote":"Supplies the surface-impedance expression and dirty-limit equations for quasiparticle loss in superconducting resonators."},{"cited_title":"Gao,The physics of superconducting microwave res- onators","cited_arxiv_id":null,"evidence_quote":"Origin of the Mattis-Bardeen approximations in Eqs. (3)-(4) used to compute $\\sigma_1$ and $\\sigma_2$."},{"cited_title":"Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits,","cited_arxiv_id":null,"evidence_quote":"Provides the relation linking measured residual loss to quasiparticle density used in Eq. (7)."},{"cited_title":"Superconducting properties and hall effect of epitaxial nbn thin films,","cited_arxiv_id":null,"evidence_quote":"Supplies the normal-state density of states $N_0$ at the Fermi level used in the density conversion."},{"cited_title":"Quasiparticle number fluctu- ations in superconductors,","cited_arxiv_id":null,"evidence_quote":"Establishes the baseline expectation that thermal quasiparticle density is negligible below $T_c/10$, which the saturation result contradicts."},{"cited_title":"Nonequilibrium quasiparticle distribution in superconducting resonators: An analytical approach,","cited_arxiv_id":null,"evidence_quote":"Gives an analytical non-equilibrium quasiparticle distribution model the paper cites as motivation for deviations from Mattis-Bardeen theory in high-kinetic-inductance films."}],"review_version":1}