pith. sign in

arxiv: 2604.03494 · v1 · submitted 2026-04-03 · 🪐 quant-ph · cond-mat.mes-hall

Breakdown of Disorder-Suppressed Floquet Heating under Two-Frequency Driving

Cooper M. Selco , Christian Bengs , Chaitali Shah , Ashok Ajoy This is my paper

Pith reviewed 2026-05-13 18:09 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords Floquet heatingprethermalizationnuclear spinsdiamonddisordertwo-frequency drivingresonancequantum sensing
0
0 comments X

The pith

Two-frequency driving breaks disorder suppression of Floquet heating at specific multi-spin resonances

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

The paper shows that disorder normally delays heating in periodically driven quantum systems by creating long prethermal plateaus, yet this protection collapses when control introduces a second frequency and disorder fluctuates. In experiments on a natural-abundance 13C nuclear spin network in diamond, sharp peaks appear in the late-time heating rate exactly at the double- and triple-spin-flip conditions predicted by bimodal Floquet interference. These peaks are tracked as drive frequency varies, and a switching-noise model traces the absorption to stochastic electron-spin flips that temporarily bring rare nuclear clusters into multi-photon resonance. The result identifies a resonance-activated limit on how long disorder can stabilize nonequilibrium Floquet phases.

Core claim

In a natural-abundance 13C nuclear-spin network in diamond, sharp peaks appear in the late-time heating rate at the double- and triple-spin-flip resonance conditions predicted by bimodal Floquet interference, and these peaks evolve with drive frequency. A switching-noise model attributes the resonant absorption to stochastic electron-spin dynamics that intermittently tune rare nuclear clusters into multi-photon resonance.

What carries the argument

Bimodal Floquet interference, which identifies resonance conditions for double- and triple-spin flips when two driving frequencies are present.

Load-bearing premise

The switching-noise model correctly attributes the resonant absorption solely to stochastic electron-spin dynamics intermittently tuning rare nuclear clusters into multi-photon resonance, without other unmodeled effects dominating the observed peaks.

What would settle it

Heating rate measurements that show no sharp peaks at the predicted double- and triple-spin-flip frequencies when the drive frequency is scanned, or that fail to match the switching-noise model's predicted peak evolution.

Figures

Figures reproduced from arXiv: 2604.03494 by Ashok Ajoy, Chaitali Shah, Christian Bengs, Cooper M. Selco.

Figure 1
Figure 1. Figure 1: (a) Floquet driving sequence: initial θy pulse followed by train of detuned θx pulses (flip angle θ = ω1τp, detuning δω, inter-pulse spacing τs) with period T. During pulse (i) Hdrive = ω1Ix + δωIz; during delay (ii) Hdrive = δωIz. (b) Net rotation over one period defining ˆneff and ωeff . (c) Schematic of positionally disordered 13C dipolar network coupled to randomly distributed electron spins (red), ill… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Experimental prethermal magnetization [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Heating rate vs. detuning near double-spin-flip [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Periodic (Floquet) driving enables Hamiltonian engineering and nonequilibrium phases, but interacting systems eventually heat by absorbing energy from the drive. Disorder can greatly delay this process, yielding long-lived prethermal plateaus. Here we show that this protection can fail when pulse-train control introduces a second driving frequency and when the disorder fluctuates. Using a natural-abundance 13C nuclear-spin network in diamond, we observe sharp peaks in the late-time heating rate at the double- and triple-spin-flip resonance conditions predicted by bimodal Floquet interference, and track their evolution with drive frequency. A switching-noise model attributes the resonant absorption to stochastic electron-spin dynamics that intermittently tune rare nuclear clusters into multi-photon resonance. Our results reveal a resonance-activated limit for disorder-stabilized Floquet phases and suggest new routes to DC-field quantum sensing based on an abrupt breakdown of prethermalization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that disorder protection against Floquet heating breaks down under two-frequency driving when disorder fluctuates. In a natural-abundance 13C nuclear-spin network in diamond, sharp peaks appear in the late-time heating rate exactly at the double- and triple-spin-flip resonance conditions predicted by bimodal Floquet interference; these peaks evolve with drive frequency. A switching-noise model attributes the absorption to stochastic electron-spin dynamics that intermittently bring rare nuclear clusters into multi-photon resonance, revealing a resonance-activated limit to prethermalization and possible routes to DC-field sensing.

Significance. If the result holds, the work identifies a concrete mechanism that limits the lifetime of disorder-stabilized Floquet phases when a second drive frequency and fluctuating disorder are present. The direct experimental match between observed heating-rate peaks and bimodal-Floquet resonance conditions provides a falsifiable test of the theory. The suggested sensing application follows naturally from the abrupt breakdown. The experimental platform and the combination of theory with observation constitute the main strengths.

major comments (1)
  1. [Switching-noise model] Switching-noise model section: the attribution of resonant absorption solely to stochastic electron-spin dynamics intermittently tuning rare 13C clusters into multi-photon resonance is load-bearing for the central claim. The natural-abundance sample contains a dense electron-spin bath and the drive is a pulse train; without explicit controls (isotopic purification, pulse-shape variation, or independent measurement of the electron-spin switching rate), alternative resonance mechanisms cannot be excluded and the model's uniqueness remains unproven.
minor comments (2)
  1. [Methods] Methods and data analysis: full experimental methods, pulse sequences, raw data, error bars, and statistical significance tests for the reported heating-rate peaks are not provided, limiting reproducibility and assessment of the claimed sharpness.
  2. [Figures] Figure presentation: the plots tracking peak evolution with drive frequency would benefit from overlaid theoretical resonance lines and explicit indication of the fitted electron-spin switching rate used in the model.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed and constructive report. The concern about the uniqueness of the switching-noise model is well taken, and we address it directly below while proposing a targeted revision to strengthen the manuscript.

read point-by-point responses

  1. Referee: Switching-noise model section: the attribution of resonant absorption solely to stochastic electron-spin dynamics intermittently tuning rare 13C clusters into multi-photon resonance is load-bearing for the central claim. The natural-abundance sample contains a dense electron-spin bath and the drive is a pulse train; without explicit controls (isotopic purification, pulse-shape variation, or independent measurement of the electron-spin switching rate), alternative resonance mechanisms cannot be excluded and the model's uniqueness remains unproven.

    Authors: We agree that dedicated controls such as isotopic purification or direct switching-rate measurements would provide stronger exclusion of alternatives. Nevertheless, the observed heating-rate peaks occur at precisely the double- and triple-spin-flip resonance conditions predicted by bimodal Floquet interference and shift with drive frequency exactly as expected from the two-frequency model. These locations and their frequency evolution constitute a sharp, falsifiable signature that is not reproduced by generic pulse-train imperfections, static electron-nuclear couplings, or non-stochastic bath effects. The natural-abundance diamond sample necessarily includes the known stochastic electron-spin bath (NV centers and P1 centers), whose switching rates are independently characterized in the literature and enter our model only through their established statistics. We will add a dedicated paragraph in the discussion section that explicitly enumerates plausible alternative mechanisms, shows why each fails to match the resonance positions and frequency dependence, and notes the limitations of the current data set. This revision will make the evidential basis for the model more transparent without altering the central claims. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim rests on experimental observation of heating-rate peaks at resonance conditions derived from bimodal Floquet interference theory, with a switching-noise model used only for post-hoc attribution of the mechanism. No step reduces a prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames an input as an output. The experimental data provide an independent check against the theoretical resonance locations, keeping the derivation chain self-contained and non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of bimodal Floquet theory for predicting resonance locations and on the switching-noise model for explaining the mechanism; both introduce assumptions about the dominance of stochastic electron-spin dynamics.

free parameters (1)
  • electron-spin switching rate
    Likely adjusted to match the observed resonance widths and heating rates in the switching-noise model.
axioms (1)
  • domain assumption Bimodal Floquet interference produces sharp resonances at double- and triple-spin-flip conditions when a second drive frequency is present.
    Invoked to predict the locations of the observed heating-rate peaks.
invented entities (1)
  • switching-noise model no independent evidence
    purpose: To explain resonant absorption via stochastic tuning of nuclear clusters by electron-spin flips.
    New modeling construct introduced to connect fluctuating disorder to the observed breakdown.

pith-pipeline@v0.9.0 · 5456 in / 1442 out tokens · 37368 ms · 2026-05-13T18:09:51.201686+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    D’Alessio and M

    L. D’Alessio and M. Rigol, Physical Review X4, 041048 (2014)

    work page 2014

  2. [2]

    T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Jour- nal of Physics B: Atomic, Molecular and Optical Physics 51, 112001 (2018)

    work page 2018

  3. [3]

    Oka and S

    T. Oka and S. Kitamura, Annual Review of Condensed Matter Physics10, 387 (2019)

    work page 2019

  4. [4]

    N. H. Lindner, G. Refael, and V. Galitski, Nature Physics 7, 490 (2011)

    work page 2011

  5. [5]

    M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Sza- meit, Nature496, 196 (2013)

    work page 2013

  6. [6]

    Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, Science342, 453 (2013)

    work page 2013

  7. [7]

    M. S. Rudner and N. H. Lindner, Nature Reviews Physics 2, 229 (2020)

    work page 2020

  8. [8]

    Weitenberg and J

    C. Weitenberg and J. Simonet, Nature Physics17, 1342 (2021)

    work page 2021

  9. [9]

    Randall, C

    J. Randall, C. E. Bradley, F. V. van der Gronden, A. Galicia, M. H. Abobeih, M. Markham, D. J. Twitchen, F. Machado, N. Y. Yao, and T. H. Taminiau, Science 374, 1474 (2021)

    work page 2021

  10. [10]

    S. Park, W. Lee, S. Jang, Y.-B. Choi, J. Park, W. Jung, K. Watanabe, T. Taniguchi, G. Y. Cho, and G.-H. Lee, Nature603, 421 (2022)

    work page 2022

  11. [11]

    S. Zhou, C. Bao, B. Fan, H. Zhou, Q. Gao, H. Zhong, T. Lin, H. Liu, P. Yu, P. Tang, S. Meng, W. Duan, and S. Zhou, Nature614, 75 (2023)

    work page 2023

  12. [12]

    P. Peng, C. Yin, X. Huang, C. Ramanathan, and P. Cap- pellaro, Nature Physics17, 444 (2021)

    work page 2021

  13. [13]

    L. S. Martin, H. Zhou, N. T. Leitao, N. Maskara, O. Makarova, H. Gao, Q.-Z. Zhu, M. Park, M. Tyler, H. Park,et al., Physical Review Letters130, 210403 (2023)

    work page 2023

  14. [14]

    Kuwahara, T

    T. Kuwahara, T. Mori, and K. Saito, Annals of Physics 367, 96 (2016)

    work page 2016

  15. [15]

    Moessner and S

    R. Moessner and S. L. Sondhi, Nature Physics13, 424 (2017)

    work page 2017

  16. [16]

    D. A. Abanin, W. De Roeck, W. W. Ho, and F. Huve- neers, Physical Review B95, 014112 (2017)

    work page 2017

  17. [17]

    W. W. Ho, T. Mori, D. A. Abanin, and E. G. Dalla Torre, Annals of Physics454, 169297 (2023)

    work page 2023

  18. [18]

    Scholz, J

    I. Scholz, J. D. van Beek, and M. Ernst, Solid State Nu- clear Magnetic Resonance37, 39 (2010)

    work page 2010

  19. [19]

    Bukov, L

    M. Bukov, L. D’Alessio, and A. Polkovnikov, Advances in Physics64, 139 (2015)

    work page 2015

  20. [20]

    Eckardt and E

    A. Eckardt and E. Anisimovas, New Journal of Physics 17, 093039 (2015)

    work page 2015

  21. [21]

    D. A. Abanin, W. De Roeck, and F. Huveneers, Physical Review Letters115, 256803 (2015)

    work page 2015

  22. [22]

    K. L. Ivanov, K. R. Mote, M. Ernst, A. Equbal, and P. K. Madhu, Progress in Nuclear Magnetic Resonance Spectroscopy126–127, 17 (2021)

    work page 2021

  23. [23]

    Serbyn, Z

    M. Serbyn, Z. Papi´ c, and D. A. Abanin, Physical Review 6 Letters111, 127201 (2013)

    work page 2013

  24. [24]

    N. Y. Yao, C. R. Laumann, S. Gopalakrishnan, M. Knap, M. M¨ uller, E. A. Demler, and M. D. Lukin, Physical Re- view Letters113, 243002 (2014)

    work page 2014

  25. [25]

    Smith, A

    J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Nature Physics12, 907 (2016)

    work page 2016

  26. [26]

    Y. Hou, A. Pizzi, H. Jin, J. Knolle, R. Moessner, and H. Zhao, arXiv preprint arXiv:2511.12877 (2025)

    work page arXiv 2025

  27. [27]

    H. Guo, R. Mukherjee, and D. Chowdhury, Physical Re- view Letters134, 226501 (2025)

    work page 2025

  28. [28]

    Ponte, Z

    P. Ponte, Z. Papi´ c, F. Huveneers, and D. A. Abanin, Physical Review Letters114, 140401 (2015)

    work page 2015

  29. [29]

    Zhang, V

    L. Zhang, V. Khemani, and D. A. Huse, Phys. Rev. B 94, 224202 (2016)

    work page 2016

  30. [30]

    M. Joos, D. Bluvstein, Y. Lyu, D. Weld, and A. Bleszyn- ski Jayich, npj Quantum Information8, 47 (2022)

    work page 2022

  31. [31]

    E. J. Davis, B. Ye, F. Machado, S. A. Meynell, W. Wu, T. Mittiga, W. Schenken, M. Joos, B. Kobrin, Y. Lyu, Z. Wang, D. Bluvstein, S. Choi, C. Zu, A. C. Bleszyn- ski Jayich, and N. Y. Yao, Nat. Phys.19, 836 (2023)

    work page 2023

  32. [32]

    Psaroudaki, E

    C. Psaroudaki, E. Peraticos, and C. Panagopoulos, Appl. Phys. Lett.123, 260501 (2023)

    work page 2023

  33. [33]

    C. M. Selco, C. Bengs, C. Shah, Z. Zhang, and A. Ajoy, arXiv preprint arXiv:2511.07785 (2025)

    work page arXiv 2025

  34. [34]

    Abragam,The principles of nuclear magnetism, 32 (Oxford university press, 1961)

    A. Abragam,The principles of nuclear magnetism, 32 (Oxford university press, 1961)

    work page 1961

  35. [35]

    A. Ajoy, B. Safvati, R. Nazaryan, J. Oon, B. Han, P. Raghavan, R. Nirodi, A. Aguilar, K. Liu, X. Cai,et al., Nature communications10, 5160 (2019)

    work page 2019

  36. [36]

    Dr´ eau, J.-R

    A. Dr´ eau, J.-R. Maze, M. Lesik, J.-F. Roch, and V. Jacques, Physical Review B—Condensed Matter and Materials Physics85, 134107 (2012)

    work page 2012

  37. [37]

    A. Ajoy, K. Liu, R. Nazaryan, X. Lv, P. R. Zangara, B. Safvati, G. Wang, D. Arnold, G. Li, A. Lin, P. Ragha- van, E. Druga, S. Dhomkar, D. Pagliero, J. A. Reimer, D. Suter, C. A. Meriles, and A. Pines, Science Advances 4, eaar5492 (2018)

    work page 2018

  38. [38]

    Pillai, M

    A. Pillai, M. Elanchezhian, T. Virtanen, S. Conti, and A. Ajoy, The Journal of Chemical Physics159(2023)

    work page 2023

  39. [39]

    Beatrez, O

    W. Beatrez, O. Janes, A. Akkiraju, A. Pillai, A. Oddo, P. Reshetikhin, E. Druga, M. McAllister, M. Elo, B. Gilbert, D. Suter, and A. Ajoy, Physical Review Let- ters127, 170603 (2021)

    work page 2021

  40. [40]

    Sahin, H

    O. Sahin, H. Al Asadi, P. M. Schindler, A. Pillai, E. Sanchez, M. Markham, M. Elo, M. McAllister, E. Druga, C. Fleckenstein,et al., Physical Review Re- search7, 043272 (2025)

    work page 2025

  41. [41]

    M. M. Maricq, Physical Review B31, 127 (1985)

    work page 1985

  42. [42]

    J. S. Waugh, Applied Magnetic Resonance27, 165 (2004)

    work page 2004

  43. [43]

    Schuster and N

    T. Schuster and N. Y. Yao, Physical Review Letters131, 160402 (2023)

    work page 2023

  44. [44]

    Jarmola, V

    A. Jarmola, V. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Physical review letters108, 197601 (2012)

    work page 2012

  45. [45]

    ´Ethier-Majcher, D

    G. ´Ethier-Majcher, D. Gangloff, R. Stockill, E. Clarke, M. Hugues, C. Le Gall, and M. Atat¨ ure, Physical review letters119, 130503 (2017)

    work page 2017

  46. [46]

    Takahashi, R

    S. Takahashi, R. Hanson, J. van Tol, M. S. Sherwin, and D. D. Awschalom, Physical Review Letters101, 047601 (2008)

    work page 2008

  47. [47]

    Belthangady, N

    C. Belthangady, N. Bar-Gill, L. M. Pham, K. Arai, D. Le Sage, P. Cappellaro, and R. L. Walsworth, Physical review letters110, 157601 (2013)

    work page 2013

  48. [48]

    L. J. I. Moon, P. M. Schindler, Y. Sun, E. Druga, J. Knolle, R. Moessner, H. Zhao, M. Bukov, and A. Ajoy, Nature Physics , 1 (2025)

    work page 2025

  49. [49]

    Jiang, Y

    M. Jiang, Y. Qin, X. Wang, Y. Wang, H. Su, X. Peng, and D. Budker, Physical Review Letters128, 233201 (2022)

    work page 2022

  50. [50]

    Bluhm, S

    H. Bluhm, S. Foletti, I. Neder, M. Rudner, D. Ma- halu, V. Umansky, and A. Yacoby, Nature Physics7, 109 (2011)

    work page 2011

  51. [51]

    J. M. Nichol, S. P. Harvey, M. D. Shulman, A. Pal, V. Umansky, E. I. Rashba, B. I. Halperin, and A. Ya- coby, Nature communications6, 7682 (2015)

    work page 2015

  52. [52]

    A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, Nature Physics9, 570 (2013)

    work page 2013

  53. [53]

    M¨ uller, J

    C. M¨ uller, J. Lisenfeld, A. Shnirman, and S. Poletto, Phys. Rev. B92, 035442 (2015)

    work page 2015

  54. [54]

    Breakdown of Disorder-Suppressed Floquet Heating under Two-Frequency Driving

    T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndtsson, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Westerhout, Y. Zhang,et al., Nature 638, 79 (2025). 7 Supplementary Information for “Breakdown of Disorder-Suppressed Floquet Heating under Two-Frequency Driving” CONTENTS References 5 S1. Guide to the Supplementary Information 7 S2. Extract...

    work page 2025

  55. [55]

    +δ. Eqs. S48 and S50 then indicate that the first-order dipo- lar contribution vanishes,L (0,0) 2 = 0. In this scenario, each nucleus relaxes independently at a rate proportional to its individual distance from the electron, causing the total polarization to persist for at least as long as the longest nuclear relaxation time. This leads to an appar- ent r...

    work page