Probing the Dynamics of Two-Level System Defect Ensembles via Broadband Cryogenic Transient Dielectric Spectroscopy

Jake Freeman; Juan S. Salcedo-Gallo; Mattias Fitzpatrick; Qianxu Wang; Roy Leibovitz; Salil Bedkihal; Sara Magdalena G\'omez; Simon A. Agnew; Sof\'ia \'Abrego; William J. Scheideler

REVIEW 3 major objections 5 minor 2 cited by

Probing the Dynamics of Two-Level System Defect Ensembles via Broadband Cryogenic Transient Dielectric Spectroscopy

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A broadband cryogenic waveguide technique, BCTDS, reads out the post-pulse transient emission of two-level system defect ensembles, encoding their eigenmode frequencies in V-shaped Fourier features and exposing memory effects.

desk verdict Genuinely new broadband TLS probe, but the unsubtracted empty-waveguide background at 10 mK keeps the central claim from being established. read the letter →

arxiv 2505.18263 v5 pith:YYDOMKJF submitted 2025-05-23 quant-ph cond-mat.mes-hallcond-mat.mtrl-sciphysics.ins-det

Qianxu Wang , Juan S. Salcedo-Gallo , Sara Magdalena Gómez , Roy Leibovitz , Jake Freeman , Sofía Ábrego , Simon A. Agnew , William J. Scheideler

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Salil Bedkihal Mattias Fitzpatrick

This is my paper · ORCID

classification quant-phcond-mat.mes-hallcond-mat.mtrl-sciphysics.ins-det

keywords two-levelsystemdefectstransientdielectricspectroscopybroadbandmicrowavewaveguidememoryeffectsnon-MarkoviandynamicsstandardtunnelingmodelFloquetdressedstatessuperconductingqubitdecoherence

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 introduces Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a technique for probing two-level system (TLS) defects that does not require fabricating qubits or resonators. A dielectric sample is mounted in a 3D waveguide at 10 mK, strongly pulsed with microwave radiation, and the homodyne response is recorded after the drive is turned off. The paper claims that the Fourier transform of this transient ring-down shows V-shaped features that reveal the eigenmode frequencies of the undriven TLS ensemble, and that the time trace exhibits collapse-and-revival oscillations that signal memory effects and non-Markovian dynamics. The authors support the interpretation with a driven standard tunneling model containing only a few interacting TLS defects, which reproduces the V-shapes and the sharpening of spectral features with pulse duration. If the claim holds, BCTDS offers a fast, modular, wafer-level probe of the defects that limit superconducting-qubit coherence, potentially enabling longitudinal studies of material processing steps. The paper also states that separating the sample signal from the waveguide's own oxide background is future work.

What carries the argument

The load-bearing object is the driven standard tunneling model: each TLS defect is a double-well system with energy detuning εj and tunneling amplitude Δj, coupled to the microwave field through its electric dipole and to other defects through dipole–dipole couplings Jij. During the pulse the periodic drive dresses the ensemble, producing Floquet quasi-energy sidebands; after the pulse, the emitted field is proportional to the collective polarization, and the Fourier components of the ring-down contain quasi-energy differences and sideband shifts that form the V-shaped structures. The model is solved with a Lindblad master equation that adds collective radiative decay mediated by the broadband waveguide, and the measured homodyne intensity is connected to the susceptibility through Kubo and input–output relations.

What would settle it

Re-run the measurement with the sample retracted in situ while keeping the waveguide, antennas, and readout chain identical: if the V-shaped features and revival oscillations appear unchanged, the signal cannot be assigned to the mounted sample. A complementary check is to fabricate a resonator or qubit on the same material and compare its resolved TLS frequencies to the V-shape vertices; agreement would support the assignment, and disagreement would falsify it.

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Extended reading notes

Core claim

The central discovery is that a strongly driven ensemble of TLS defects, observed through a broadband 3D waveguide, continues to emit coherently after the drive ends, and that this re-emission carries the frequency structure of the defect ensemble. In the measured Fourier spectra of the ring-down, V-shaped features appear whose arms converge toward the bare eigenfrequencies of the TLS ensemble as the pulse length increases; the paper interprets these as off-resonant emission from dominant defect modes made visible by the broadband environment. The time-domain signal shows repeated collapse and revival, the two-time correlation function g(2) decays non-exponentially with oscillations, and the extracted imaginary susceptibility χ''(ω) becomes non-monotonic and negative near the bright spectral features, which the paper reads as information backflow and physics beyond linear response. These observations are attributed to memory effects arising from TLS–TLS interactions and broadband excitation, and they are qualitatively reproduced by a driven standard tunneling model with a few interacting TLSs under collective dissipation.

Load-bearing premise

The load-bearing premise is that the post-pulse transient signal is emitted by TLS defects in the mounted sample rather than by the waveguide's own oxide layers, antenna surfaces, or amplifier and detection artifacts, and the paper itself reports defect features in an empty waveguide at 10 mK and defers their removal as baseline to future work.

Editorial extensions

If this is right

Material screening becomes possible at the wafer stage: TLS-sensitive spectra can be recorded on bare sapphire, deposited oxide layers, and photoresist-covered samples without any resonator or qubit fabrication step.
Drive-pulse duration acts as a control knob: longer pulses sharpen the transient emission lines and prolong ring-downs, suggesting that coherent control and spectral resolution of TLS ensembles can be tuned pulse by pulse.
The observed memory effects imply that TLS ensembles can exhibit non-Markovian dynamics under broadband driving, which, if present in quantum processors, would matter for error-correction assumptions.
Thermocycling changes the transient spectral fingerprint of the same sample, consistent with TLS rearrangement, so BCTDS can track how thermal and processing history reshapes the defect environment.
A 2 nm oxide layer and a photoresist layer both increase the transient response relative to bare sapphire, indicating that thin-film morphology and interface quality dominate the defect population.

Reading between the lines

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

Editorial extension: the paper does not perform this check, but if the V-shape vertices are truly the bare TLS eigenfrequencies, then the dominant revival frequencies in the time-domain traces should coincide with those same vertices; fitting both spectra jointly would test the assignment more sharply.
Editorial extension: the empty-waveguide background the paper reports makes a decisive experiment available: retracting the sample in situ while leaving the waveguide untouched would directly measure how much of the V-shape survives without the sample, which the paper itself lists as future work.
Editorial extension: the paper attributes memory effects to TLS interactions plus broadband drive; a drive-amplitude sweep could distinguish that explanation from single-defect dynamics, since interaction-driven revivals should appear or intensify only above some coupling-related threshold.
Editorial extension: the authors note the technique should also detect non-spin defects such as dopants and vacancies; comparing a BCTDS spectrum on such a sample against an independently known defect resonance would test the generality of the method.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague, here's my take on 2505.18263. It's a genuinely new measurement modality, but the paper's central claim is not yet load-bearing: the 10 mK empty-waveguide background is not subtracted, so the V-shapes and memory effects can't yet be assigned to the mounted samples. The authors acknowledge this and propose an in-situ piezo retraction for future work, but that doesn't put the present data on solid ground.

What's actually new: the modular WR-229 waveguide with a sample clamp in the middle is a clean way to probe dielectric response over 3-6 GHz without qubit or resonator fabrication. The cooldown-dependent fingerprints in Appendix C and the pulse-length sharpening in Fig. 4 are real observations that the standard tunneling model plus Floquet dressing naturally explains. The few-spin simulations are qualitative, but they do reproduce the V-shaped arcs converging toward bare eigenfrequencies, which is a useful sanity check rather than a fit.

Where it's soft: the baseline issue is the big one. Fig. 3(c) shows strong transient features from the empty waveguide at 10 mK; Fig. 3(d)-(f) are unsubtracted superpositions. Until sample/background separation is demonstrated, the assignment of the observed dynamics to photoresist or AlOx on sapphire is defensible but unproven. Eq. 14 (chi'' from intensity correlations) is asserted by citation and applied outside linear response; the negative chi'' regions could be weak-signal artifacts near 3 GHz, as the authors partially concede. No error bars or public data either. None of these are fatal to the technique—they're the standard gap between a proof-of-concept and a validated method.

Who this is for: anyone working on TLS characterization, materials processing for superconducting qubits, or broadband dielectric probes. It deserves a serious referee; a competent reviewer should push hard on the baseline control, the derivation of Eq. 14, and a data release. My verdict would be major revision, not rejection.

Referee Report

3 major / 5 minor

Summary. The paper introduces Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a 3D waveguide technique intended to probe ensembles of two-level-system (TLS) defects in dielectrics at millikelvin temperatures without fabricating qubits or resonators. The method applies strong microwave square pulses in the 3–5 GHz band and records the post-pulse homodyne transient response. The authors report coherent ring-down signals, V-shaped features in Fourier-transformed transients, collapse-and-revival patterns in two-time intensity correlations g(2), and estimates of χ'' that become negative, which they interpret as evidence of memory effects and non-Markovian dynamics of interacting TLS ensembles. Supporting numerics use driven interacting few-spin master-equation and Floquet calculations to reproduce qualitatively the pulse-length-dependent sharpening of spectral features. The abstract and introduction claim that BCTDS reveals eigenmode frequencies of undriven TLS ensembles and can serve as a modular wafer-level materials probe.

Significance. If the sample-specific assignment of the transient signals were established, BCTDS would fill a real gap: existing TLS probes based on qubits or resonators are narrowband, require full device fabrication, and couple to only a small mode volume. The paper contains several commendable elements: room-temperature control experiments, cooldown-to-cooldown reproducibility checks (Appendix C), an HFSS-based electric-field calibration (Appendix E), transmission/reflection comparisons (Appendix D), and qualitative Floquet/master-equation simulations that connect V-shaped spectral features and pulse-length sharpening to dressed-state physics. The central novelty—broadband, modular, transient dielectric spectroscopy of TLS ensembles—is potentially valuable for superconducting-circuit materials engineering. However, the current manuscript does not yet demonstrate that the observed transients originate from the mounted samples rather than from the waveguide's own TLS-hosting surface oxides and uncontrolled enclosure modes; the empty-waveguide background at 10 mK shows similar features.

major comments (3)

[III A and Fig. 3(c)–3(f)] The empty-waveguide control at 10 mK (Fig. 3(c)) already exhibits transient defect features, attributed by the authors to oxide layers on the waveguide and antenna surfaces and to uncontrolled modes in the fridge enclosure, and the text explicitly states that removing these baseline contributions is future work. Because Figs. 3(e), 3(f), 4, and 5 are unsubtracted superpositions of this background and any sample response, the V-shaped FFT features, the collapse-and-revival g(2), and the negative χ'' extracted from them cannot be uniquely assigned to TLS ensembles in the photoresist or AlOx films. The increased transient response for treated samples and the cooldown change in Appendix C are suggestive, but a thermal cycle also rearranges TLSs in the waveguide's own oxide layers, so these observations do not by themselves separate sample and background. Please provide interleaved empty-waveguide baselines and a subtraction or in-situ retraction protocol before claiming sample-specific TLS spectroscopy; without this, the central claim that BCTDS probes the material under test is not supported.
[II B, Eq. (14), and Fig. 5(d)] Equation (14) asserts χ''(ω) ∝ Im ∫ dt e^{iωt}⟨I(t)I(0)⟩, citing Ref. [47], but no derivation is given. Combining Eq. (13), A(t) ∝ ⟨P(t)⟩e^{iω0t}, with I(t) ∝ A²(t) makes the right-hand side of Eq. (14) a fourth-order dipole correlation, not the linear-response susceptibility defined in Eqs. (8)–(12). The cited reference concerns optomechanical sideband asymmetry via stochastic electrodynamics and does not establish this identity. The subsequent interpretation of negative χ'' as physics beyond linear response (Sec. III C, Fig. 5(d)) rests entirely on this unproven relation. Please either derive Eq. (14) from input-output theory with explicit assumptions, or replace χ'' with a directly defined spectral measure of the transient homodyne field and discuss the negativity in those terms.
[Appendix G] The few-spin simulations use hand-chosen parameters (drive amplitude, collective decay rate, dipole-dipole couplings, bare TLS frequencies) and are not fitted to the experimental data. The authors are appropriately cautious in calling the agreement qualitative, and the V-shaped mechanism follows from standard Floquet theory (Eqs. G13–G16), so this is not by itself an error. However, to make the comparison meaningful, the simulated observable should be matched to the experimental analysis pipeline: the experiment Fourier-transforms the logarithmic amplitude of the detected field, while the simulations show the collective population ⟨σ+σ−⟩. Please state explicitly how the simulated quantity maps to the measured I-Q transient and whether the V-shape persistence after the pulse is robust to the choice of collective versus independent decay, since the collective-decay assumption in Eq. (G18) is not derived from the waveguide geometry.

minor comments (5)

[III C, Eq. (15)] The normalized two-time correlation g(2)(τ') is defined with ⟨I(t)⟩² in the denominator, which is only appropriate for a stationary process; the transient signal is manifestly nonstationary. Please clarify whether the average is over t for each τ' and whether a product ⟨I(t)⟩⟨I(t+τ')⟩ would be more appropriate, or state the stationarity assumption explicitly.
[III C] There is a typo: 'non-Makovian' should be 'non-Markovian'.
[Appendix G] The sentence 'The assumption of collective decay is motivated by the broadband nature of the waveguide, which couples similarly to all TLSs' needs justification: a broadband waveguide generally provides independent emission channels whose phases depend on TLS positions and mode structure, and collective decay requires phase-matched coupling. Please either provide a quantitative argument or weaken the claim.
[Data availability] The data availability statement says data are available 'upon reasonable request'; for a new spectroscopy method with many nontrivial analysis steps, a public repository containing raw I-Q traces and analysis scripts would substantially strengthen reproducibility.
[Fig. 4 caption] The caption does not state which sample is used for the pulse-length study; from the text it appears to be the 2 nm AlOx sample, but this should be stated explicitly in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: BCTDS observations and Floquet-model interpretation are independent; the acknowledged empty-waveguide background is a confound, not a circular step.

full rationale

The paper's target observations—post-pulse coherent transients, V-shaped FFT features, g(2) oscillations, and negative χ''—are measured quantities, not outputs of a fitted model. The numerical simulations in Appendix G use hand-assigned parameters (e.g., 'randomly assigned bare frequencies and dipole-dipole couplings, drawn from uniform distributions ϵ ∈ [3.0, 5.0] GHz and J ∈ [−50.0, 50.0] MHz') and are explicitly qualitative ('The theoretical framework used here shows good qualitative agreement'), so no fitted input is relabeled as a prediction. The V-shape mechanism follows from standard Floquet theory (Eqs. G13–G16) with poles at ω = Eα − Eβ + lΩ; the bare eigenfrequencies are inputs to the illustrative simulation, not fit to the data. No self-citation is load-bearing: the Hamiltonian citing Lisenfeld et al. [19] and the tantalum-oxide claim citing Place et al. [51] (which includes the senior author) are independent external results, and neither is invoked to force BCTDS's interpretation. The most serious limitation is explicitly stated by the authors: 'In Fig. 3(c), we observe defect features in the absence of mounted samples, which we attribute to oxide layers present on the waveguide and antenna surfaces' and 'In future work, we intend to remove these baseline contributions by retracting the samples in situ.' That is a background-separation confound for the material-specific assignment of the transients, but it is not a circular derivation: the observed signals and the model remain logically independent of the inputs. Therefore no specific equation or fitted parameter reduces the predicted effect to an input by construction, and the circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central experimental observation does not rely on fitted parameters. The interpretation, however, relies on the standard tunneling model, Kubo susceptibility as a conceptual tool, input-output theory, a cited but not derived relation between intensity correlations and chi'', and a Lindblad model with hand-picked rates. The simulation parameters listed above are chosen, not measured. No new physical entities are postulated.

free parameters (4)

Drive amplitude A (simulation) = 100 MHz (N=2), 400 MHz (N=4)
Chosen by hand in Appendix G and Figs. 12-13 to produce visible sidebands; not measured or fitted to experimental data.
Collective decay rate Gamma (simulation) = 2.0 MHz (N=2), 1.0 MHz (N=4)
Chosen to give ring-down timescales; not extracted from experiment.
Dipole-dipole coupling J (simulation) = 50 MHz (N=2); random in [-50, 50] MHz (N=4)
Chosen to produce interference and revival features; no experimental constraint is given.
Bare TLS frequencies (simulation) = 3.5 and 4.5 GHz (N=2); uniform in [3.0, 5.0] GHz (N=4)
Chosen within the waveguide band; not determined from the data.

assumptions (6)

domain assumption Standard tunneling model represents each defect as a two-level double-well system (Eq. 1).
Central model for TLS defects in disordered solids, cited to Anderson-Halperin-Varma and Phillips; used throughout the interpretation.
domain assumption Kubo linear response susceptibility, Eqs. 8-9, relates polarization to field.
Authors explicitly state this is only a conceptual tool and that the experiment is likely far from the linear regime, yet it is used to motivate chi'' extraction.
domain assumption Input-output relation A(t) proportional to <P(t)> exp(i omega0 t), Eq. 13.
Connects the measured homodyne amplitude to the dipole response; needed for the spectral interpretation.
ad hoc to paper Eq. 14 relates chi'' to the intensity autocorrelation <I(t)I(0)> via a citation to Novotny et al.
The relation is asserted for a strongly driven, nonlinear regime without derivation, and negative chi'' is then interpreted as evidence of memory effects.
domain assumption Lindblad master equation with collective radiative decay, Eqs. G17-G18.
Used to model the driven ensemble; collective decay is motivated by the broadband waveguide but is not independently verified.
standard math Floquet formalism for time-periodic drives, Eqs. G1-G7.
Standard mathematical framework used to interpret dressed states and sidebands during the pulse.

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Cite this review

Pith. "Pith review of Probing the Dynamics of Two-Level System Defect Ensembles via Broadband Cryogenic Transient Dielectric Spectroscopy." pith.science (2026). https://pith.science/paper/YYDOMKJF

@misc{pith2026250518263,
  author       = {Pith},
  title        = {Pith review of: Probing the Dynamics of Two-Level System Defect Ensembles via Broadband Cryogenic Transient Dielectric Spectroscopy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YYDOMKJF}},
  note         = {Machine review of arXiv:2505.18263}
}

read the original abstract

Two-level system (TLS) defects in dielectrics are a major source of decoherence in superconducting circuits, yet their microscopic origin and distribution remain poorly understood. Existing circuit-QED probes access limited frequency ranges and mode volumes, restricting studies of isolated materials and interfaces. Here, we present Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a technique for probing TLS-hosting materials over a broad frequency range at cryogenic temperatures. Under strong finite-duration microwave excitation, the transient homodyne I-Q response exhibits coherent phase dynamics after the drive is turned off. Fourier analysis of the transient phase reveals characteristic V-shaped structures that move between cooldowns, consistent with thermocycling-induced changes in the local TLS defect environment that shift defect resonance frequencies. The transient response of BCTDS further enables estimation of susceptibility and two-time correlation functions of the TLS defect ensemble. The observed phase dynamics are qualitatively captured by a driven standard tunneling model containing only a few representative TLS defects. Despite its simplicity relative to the full experimental ensemble, the model reproduces the essential Floquet-dressed dynamics during the drive and generates post-pulse V-shaped structures and interference fringes consistent with the experimental data. The observed BCTDS response may reflect a crossover from localized TLS defect dynamics to a delocalized regime under strong driving, before being quenched into a transient regime that reflects the TLS defect resonance frequencies. Overall, BCTDS represents a potentially useful broadband, time-resolved wafer-level approach for probing TLS defects relevant to quantum technologies.

Figures

Figures reproduced from arXiv: 2505.18263 by the authors.

**Figure 2.** FIG. 2. Broadband waveguide design. (a) Photograph of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Dielectric spectroscopy of different samples. We send a 30 ns pulse (marked by black dashed lines) and readout over [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: FIG. 4. Dielectric response of 2 nm aluminum oxide sample [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Transient dielectric response of Shipley 1813 photoresist on sapphire. We use the same data as Fig. 3(f). (aii) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 7.** Figure 7: FIG. 7. Designs for SMA to WR-229 3D rectangular waveg [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8. Cryogenic dielectric spectroscopy measurements of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: FIG. 9. Dielectric response of Shipley 1813 photoresist on sap [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: FIG. 10. Electric field amplitude calibration at the sample [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

**Figure 11.** Figure 11: FIG. 11. Measurement setup for transient dielectric spec [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

**Figure 12.** Figure 12: FIG. 12. Numerical simulation of collective excitation dy [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]

**Figure 13.** Figure 13: FIG. 13. Numerical simulation of a driven, interacting four-spin system ( [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]

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