{"id":"b14b47fd-8e35-4655-9358-693496327f79","arxiv_id":"2501.03011","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A NIS junction and an MKID array measure substrate phonon burst speed in silicon, extracting vph = 12.9 ± 2.6 mm/µs and a 1.3% phonon-to-quasiparticle conversion efficiency from a power-dependent velocity model.","lead":"This paper measures how fast phonon bursts, the sound-like vibrations that disturb quantum chips, travel across a silicon substrate using superconductor detectors and an artificial burst source. The result is directly relevant to predicting how cosmic-ray hits spread errors in superconducting quantum computers.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported vph = 12.9 ± 2.6 mm/µs is an asymptotic extrapolation of a fixed-threshold model that already overshoots the known silicon sound velocity by 42%; a factor-of-2 algebra error in Eq. (6) further undercuts the quantitative fit.","rationale":"I read the paper as making two claims: a qualitative one—that the apparent MKID burst velocity increases with NIS power because of a detection threshold combined with flux decay—and a quantitative one—that Eq. (6) fits all data and yields the silicon longitudinal phonon velocity vph = 12.9 ± 2.6 mm/µs and η = 1.3%. The qualitative claim is well supported by Fig. 4 and by the independent calibration of N0_qp from Fig. 5. The quantitative claim is not. My main concern is not that the model is simple; it is that the specific way vph enters makes it an extrapolated intercept rather than a directly measured transit time. The reported value being 42% above the known sound velocity is a red flag, not a measured result, and the repeatable unexplained deviations show that the model is missing real physics. I also found an internal algebraic inconsistency: Eq. (6) has a factor of 2 relative to Eq. (5), which changes η by a factor of 2 and indicates the derivation has not been carefully checked. The reader's weakest_assumption pointed to the same family of issues (fixed threshold, no reflections, flat spectrum); my concrete concern is narrower—the intercept/extrapolation identification—so I mark partial agreement. The appropriate verdict remains CONDITIONAL: the qualitative picture should be accepted, but the quantitative vph/η claims need revision, additional analysis, or new data before they can be relied on.","tokens_in":8836,"tokens_out":9271,"duration_ms":90823,"concrete_test":"Re-fit the Fig. 4 td(x,V_NIS) data to Eq. (6) after correcting the prefactor to π/L, and repeat the fit using only the highest-power half of the V_NIS values (and, if possible, only the nearest MKIDs where the threshold term is smallest). If the intercept-derived vph moves by more than the quoted ±2.6 mm/µs, or if the fit with vph fixed at the known ~9.1 mm/µs value is not significantly worse (Δχ² ≲ 2 per dof), then the claimed velocity is an artifact of the extrapolation and the quantitative claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is that Eq. (6), td = x/vph + (2π/L)(N0_qp e R_N/η)(x/V_NIS), simultaneously fits all observed detection times and yields vph = 12.9 ± 2.6 mm/µs and η = 1.3%. The load-bearing step is the identification of the x/vph term as the intercept of a line in 1/V_NIS. Because the threshold term is proportional to x/V_NIS, vph is obtained by extrapolating td/x to 1/V_NIS → 0, i.e., to infinite NIS drive power. If the data at the highest powers are still threshold-limited, the extrapolated intercept is controlled by the assumed 1/V_NIS form rather than by a directly observed propagation time. The 42% excess over the accepted ~9.1 mm/µs longitudinal velocity in silicon is the observable symptom of this bias. The paper itself reports repeatable deviations from the fit and attributes them to hot spots or phonon reflections; those are exactly distance- and power-dependent effects that would also shift the intercept. In addition, Eq. (6) does not follow from Eq. (5): substituting W_ph from Eq. (5) into t_qp = N0_qp/(η W_ph) gives a prefactor π/L, not 2π/L, for the x/V_NIS term. The factor of two changes the derived η from 1.3% to about 0.65%, and shows that the algebra behind the quantitative fit has not been fully verified. The qualitative conclusion—apparent velocity increases with V_NIS—is supported, but the fitted vph and η are not yet established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a controlled measurement of high-energy phonon bursts in a silicon substrate using a normal metal-insulator-superconductor (NIS) junction as a repeatable phonon source and a linear array of microwave kinetic inductance detectors (MKIDs) as time-resolved phonon sensors. The authors observe that the apparent burst propagation velocity increases with NIS drive power, and they explain this through a model in which the measured detection time is the sum of a ballistic propagation time x/v_ph and an additional threshold-limited quasiparticle accumulation time t_qp = N0_qp/(eta W_ph). Fitting Eq. (6), t_d = x/v_ph + (2*pi/L)(N0_qp e R_N/eta)(x/V_NIS), to all data simultaneously yields v_ph = 12.9 +/- 2.6 mm/micro-s and a phonon-to-quasiparticle conversion efficiency eta = 1.3%. The paper concludes that the model can explain low apparent velocities and can be used to estimate burst-induced error propagation in superconducting circuits.","tokens_in":9196,"tokens_out":5511,"duration_ms":59500,"significance":"If the quantitative claims were established, this would be a valuable contribution to the current discussion of radiation-induced bursts in superconducting quantum circuits: it provides a repeatable, high-time-resolution injection-and-detection scheme, and it identifies a threshold effect that naturally explains power-dependent apparent velocities. A notable strength is that the minimum detectable quasiparticle number N0_qp is calibrated independently from temperature-dependent resonance-frequency shifts (Fig. 5 and Eq. (7)), rather than being treated as a purely free fit parameter. However, the central quantitative results are not yet established: the reported v_ph is 42% above the accepted longitudinal [100] sound velocity in silicon, the model relies on several explicitly acknowledged and untested simplifying assumptions, and Eq. (6) contains a factor-of-two algebra error that changes the extracted eta by a factor of two. The qualitative observation and the proposed mechanism are plausible and interesting, but the paper currently overstates the reliability of the fitted v_ph and eta.","major_comments":[{"comment":"Equation (6) does not follow from Eq. (5). Substituting W_ph(x) = (L/(2*pi*x))(2 V_NIS/(e R_N))(1 - 2*Delta/(e V_NIS)) into t_qp = N0_qp/(eta W_ph) and using 2*Delta << e V_NIS gives t_d = x/v_ph + (pi/L)(N0_qp e R_N/eta)(x/V_NIS), with a prefactor pi/L rather than the printed 2*pi/L. The factor of two changes the derived conversion efficiency from eta = 1.3% to approximately 0.65%, so the reported efficiency is not supported by the algebra as written.","section":"Eqs. (5)-(6)"},{"comment":"The extracted v_ph = 12.9 +/- 2.6 mm/micro-s is obtained by extrapolating t_d/x to 1/V_NIS -> 0, i.e., to infinite NIS drive power. If the threshold-limited quasiparticle term is still non-negligible at the highest measured powers, the intercept is controlled by the assumed 1/V_NIS scaling rather than by a directly observed propagation time. This concern is sharpened by the paper's own statement that the fit shows repeatable deviations possibly originating from hot spots or phonon reflections, effects that are distance- and power-dependent and would bias the intercept. Because the fitted value is 42% above the accepted longitudinal [100] sound velocity in silicon (about 9.1 mm/micro-s), I ask for a direct validation: a plot of t_d/x versus 1/V_NIS showing the extrapolation, a time-of-flight estimate at the highest available power, or a fit that allows power-dependent threshold dynamics. Without such a check, v_ph should be presented as a model-dependent extrapolation rather than as a measured propagation velocity.","section":"Fig. 4 and fitted v_ph"},{"comment":"The derivation of the quantitative fit rests on several assumptions that the manuscript itself acknowledges as rough: a flat phonon emission spectrum, complete conversion of absorbed NIS electrical power into phonons, no phonon attenuation or reflections, a point-like source, and a fixed minimum detectable quasiparticle number N0_qp independent of distance and power. These assumptions are not validated against independent data, and the quoted uncertainty of +/- 2.6 mm/micro-s reflects only statistical fit errors, not systematic errors from these modeling choices. The text should either propagate these systematics into the reported v_ph and eta or explicitly flag both quantities as effective model parameters rather than material parameters.","section":"Eqs. (3)-(5) and model assumptions"}],"minor_comments":[{"comment":"The word 'cryogenicaly' in the concluding paragraph should be 'cryogenically'.","section":"Conclusion"},{"comment":"The caption refers to 'D06' while Table I and the text use 'D6'; please harmonize the detector naming throughout.","section":"Fig. 3 caption"},{"comment":"Please state explicitly the units and normalization of the phonon spectral density w_NIS_ph(epsilon) and clarify whether the angle theta in Eq. (3) is a planar angle in the substrate plane or a solid angle; the approximation theta approximately L/x then becomes easier to assess.","section":"Eqs. (3)-(4)"},{"comment":"The paper mentions repeatable deviations but does not show repeated runs or error bars in Fig. 4; adding per-point uncertainties or a representative repeat measurement would help the reader judge the statistical weight of the fit.","section":"Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"This is a borderline case. The experimental platform and the qualitative power dependence of the apparent velocity are interesting and likely publishable in a specialized venue, but the quantitative central claims are currently undercut by the factor-of-two error in Eq. (6), which changes eta by a factor of two, and by the unvalidated extrapolation that yields a v_ph 42% above the known silicon sound velocity. The issues are addressable within the manuscript's scope: correct the algebra, refit eta, and add a direct check or a clearly weakened claim for v_ph. I therefore support major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi [Colleague],\n\nQuick take on arXiv:2501.03011 (Moshel et al., MKID measurement of substrate phonon burst velocity). The paper is worth reading: the experiment is well-constructed, and the central qualitative observation—that the apparent burst velocity increases with NIS drive power—is convincingly demonstrated. The proposed mechanism (a fixed detection threshold combined with 1/x phonon flux decay) is simple and does explain the trend, and it may reinterpret the low apparent velocities seen in earlier work.\n\nThe quantitative fit, however, has a real problem. The stress-test note is correct: Eq. (6) does not follow from Eq. (5). Substituting the expression for W_ph into t_qp = N0_qp/(η W_ph) gives a prefactor π/L, not 2π/L, for the x/V_NIS term. That factor of two changes the derived efficiency η from 1.3% to about 0.65%, and suggests the algebra behind the headline result has not been carefully checked. This is a load-bearing error for the fitted vph and η, not a cosmetic one.\n\nThere is also the 42% discrepancy between the fitted vph = 12.9 ± 2.6 mm/µs and the accepted ~9.1 mm/µs longitudinal velocity in silicon. The paper acknowledges this and speculates about hot spots and reflections, but those are exactly the distance- and power-dependent effects that would also bias the intercept used to extract vph. The model also assumes a flat emission spectrum, full power-to-phonon conversion, and a fixed minimum detectable QP number N0_qp independent of distance and drive power. None of these are tested. The paper itself notes the repeatable deviations from the fit, which reinforces the concern.\n\nI don't think these problems invalidate the qualitative picture. The velocity-vs-power trend is robust, and the threshold model is a plausible, useful contribution. But the numerical values of vph and η should be treated as provisional until the algebra is corrected and the systematics (especially the NIS power calibration and the threshold dependence) are quantified.\n\nRecommendation: send to peer review. It deserves a serious referee. The authors need to fix Eq. (6), redo the fit, and address the velocity mismatch; with those revisions, the qualitative conclusion can stand. I'd bring it to the reading group; the phenomenon is relevant to any work on radiation-induced errors in quantum circuits.","headline":"Nice qualitative result and a plausible threshold model, but the quantitative fit has a factor-2 algebra error and a 42% velocity mismatch that undermine the extracted vph and η.","tokens_in":9688,"tokens_out":2522,"would_cite":true,"duration_ms":95569,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A linear array of MKIDs times phonon bursts in a silicon chip and extracts a longitudinal phonon velocity of 12.9 ± 2.6 mm/µs.","keywords":["kinetic inductance detectors","NIS junction","phonon propagation velocity","superconducting circuits","quasiparticle bursts","silicon substrate","burst detection threshold"],"falsifier":"Direct time-of-flight measurement of longitudinal phonons on the same chip at base temperature, with a calibrated detector threshold, would settle whether the high-power intercept is the true 12.9 mm/µs; if an independent acoustic measurement returns about 9.1 mm/µs, the model's assumptions are biased.","tokens_in":8596,"feed_emoji":"⚡","tokens_out":7409,"duration_ms":68211,"temperature":0.7,"pith_summary":"The paper sets out to measure how fast a localized high-energy phonon burst spreads across a silicon chip that hosts superconducting circuits, and to explain why the apparent speed depends on the burst strength. It injects controllable bursts with a normal metal–insulator–superconductor (NIS) junction and times their arrival at aluminum kinetic-inductance detectors (MKIDs) placed at increasing distances. The central finding is that the apparent velocity rises with NIS drive power, and that a two-term model—ballistic flight at $v_{\\mathrm{ph}}$ plus a threshold-limited quasiparticle accumulation time—fits all the data simultaneously. The fit gives the longitudinal phonon velocity in silicon, $v_{\\mathrm{ph}} = 12.9 \\pm 2.6$ mm/µs, and a phonon-to-quasiparticle conversion efficiency $\\eta = 1.3\\%$ in the aluminum detectors. If correct, this gives quantum-circuit engineers a direct way to predict how far and how fast radiation-induced errors will propagate across a chip.","feed_headline":"Phonon bursts cross silicon at 12.9 mm/µs, MKID fit shows","feed_subtitle":"A nine-detector silicon array shows burst speed rises with injection power; the model recovers the true velocity and conversion efficiency.","key_machinery":"The load-bearing object is the two-term detection-time formula (Eq. 6), which writes the measured time as $t_d = x/v_{\\mathrm{ph}} + t_{\\mathrm{qp}}$, where $t_{\\mathrm{qp}} = N_0^{\\mathrm{qp}}/(\\eta W_{\\mathrm{ph}})$ is the time for the MKID to accumulate the minimum detectable number of quasiparticles. The phonon flux $W_{\\mathrm{ph}}$ is modeled from a point source with a flat spectrum and full power conversion, giving $W_{\\mathrm{ph}} \\propto (L/x)(V_{\\mathrm{NIS}}/R_N)$, so $t_{\\mathrm{qp}} \\propto (x/V_{\\mathrm{NIS}})$. This makes the apparent velocity a parallel combination of the true phonon velocity and a power-dependent parasitic velocity, which is the mechanism that explains the observed slowdown at low power.","core_discovery":"The paper's claim is that the apparent propagation velocity of a phonon burst measured by MKIDs is not a material constant: it increases with the injected phonon flux, because each MKID only registers the burst once its quasiparticle population crosses a fixed detection threshold $N_0^{\\mathrm{qp}}$. Since the phonon flux reaching a detector falls as $1/x$ with distance, the threshold adds a delay proportional to $x/V_{\\mathrm{NIS}}$ on top of the ballistic time $x/v_{\\mathrm{ph}}$. Fitting $t_d = x/v_{\\mathrm{ph}} + (2\\pi/L)(N_0^{\\mathrm{qp}} e R_N / \\eta)(x/V_{\\mathrm{NIS}})$ simultaneously to all detectors and powers yields $v_{\\mathrm{ph}} = 12.9 \\pm 2.6$ mm/µs and $\\eta = 1.3\\%$.","pith_inferences":["If the threshold $N_0^{\\mathrm{qp}}$ can be tuned, for example by changing readout power, the model predicts that apparent-velocity versus power curves should shift in a specific way; testing this would separate threshold effects from genuine phonon physics.","The repeatable, non-statistical deviations from the fit could be used as a diagnostic: mapping them across the chip may reveal localized hotspots or edge reflections, effectively turning the MKID array into a phonon-imaging tool.","The same NIS-plus-MKID method could be applied to other substrate materials and to chips with qubits to measure burst velocities in the exact devices where radiation errors matter, rather than in a dedicated test structure."],"forward_implications":["At high burst energies the apparent velocity approaches the true phonon velocity, so large cosmic-ray-like events should appear to travel at about $12.9$ mm/µs, not at the lower speeds inferred from weak events.","The measured efficiency $\\eta = 1.3\\%$ quantifies how many substrate phonons become quasiparticles in an aluminum MKID, giving a number that microscopic models of the phonon–quasiparticle coupling must reproduce.","The same model can convert a measured detection time and distance into an estimate of the burst energy, since the $x/V_{\\mathrm{NIS}}$ term ties arrival times to source strength.","For a known error threshold in a qubit or readout element, the model predicts the time a burst at distance $x$ takes to cause an error, which sets the spatial range of a single radiation event on a chip."],"supporting_citations":[{"why":"reports a low apparent propagation velocity for phonon bursts that the present model is invoked to explain","marker":"[10]"},{"why":"established the use of an NIS junction to inject phonon bursts into a superconducting circuit","marker":"[18]"},{"why":"supplies the operating principle of microwave kinetic inductance detectors","marker":"[19]"},{"why":"provides the resonator physics linking quasiparticle density to frequency shift","marker":"[23]"},{"why":"justifies efficient phonon transfer from the thin superconductor film into the substrate","marker":"[26]"},{"why":"gives the few-micron quasiparticle diffusion length that justifies treating the source as point-like","marker":"[27]"},{"why":"provides the literature longitudinal sound velocity in silicon that the fitted value is compared with","marker":"[29]"},{"why":"supplies the quasiparticle-density formula used to calibrate the MKID frequency shifts","marker":"[31]"},{"why":"supports the linear relation between quasiparticle density and frequency shift used in the calibration","marker":"[34]"}],"fun_headline_variants":["MKIDs clock phonon bursts: true speed 12.9 mm/µs","Phonon burst speed not constant: MKID model extracts 12.9 mm/µs","Silicon phonon bursts measured: power-dependent, MKIDs correct it","MKID array pins phonon velocity at 12.9 mm/µs","Apparent phonon speed varies, MKID fit gives true 12.9 mm/µs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model assumes a point-like ballistic source with a flat phonon spectrum and a detector threshold that does not depend on distance or power; if phonon reflections, local hot spots, or a power-dependent threshold contribute, the fitted velocity is biased.","fun_headline_variants_meta":{"raw":{"variants":["MKIDs clock phonon bursts: true speed 12.9 mm/µs","Phonon burst speed not constant: MKID model extracts 12.9 mm/µs","Silicon phonon bursts measured: power-dependent, MKIDs correct it","MKID array pins phonon velocity at 12.9 mm/µs","Apparent phonon speed varies, MKID fit gives true 12.9 mm/µs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000424,"raw_usage":{"total_tokens":2141,"prompt_tokens":876,"completion_tokens":1265,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":492,"completion_tokens_details":{"reasoning_tokens":1152}},"tokens_in":492,"tokens_out":1265,"duration_ms":10364,"temperature":1.0,"reasoning_tokens":1152,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:58:55.389544+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Direct time-of-flight measurement of longitudinal phonons on the same chip at base temperature, with a calibrated detector threshold, would settle whether the high-power intercept is the true 12.9 mm/µs; if an independent acoustic measurement returns about 9.1 mm/µs, the model's assumptions are biased.","supporting_citations":[{"cited_title":"Patel, I","cited_arxiv_id":null,"evidence_quote":"established the use of an NIS junction to inject phonon bursts into a superconducting circuit"},{"cited_title":"Gao, The physics of superconducting microwave resonators (California Institute of Technology, 2008)","cited_arxiv_id":null,"evidence_quote":"provides the resonator physics linking quasiparticle density to frequency shift"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"justifies efficient phonon transfer from the thin superconductor film into the substrate"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"gives the few-micron quasiparticle diffusion length that justifies treating the source as point-like"},{"cited_title":"McSkimin, Journal of applied physics 24, 988 (1953)","cited_arxiv_id":null,"evidence_quote":"provides the literature longitudinal sound velocity in silicon that the fitted value is compared with"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supports the linear relation between quasiparticle density and frequency shift used in the calibration"}],"review_version":1}