arxiv: 2605.01674 · v1 · submitted 2026-05-03 · ⚛️ physics.ins-det

Recognition: unknown

Detectivity and bandwidth limits of cooled and uncooled light detection using nanomechanical resonators

Mathis Turgeon-Roy , Mohammed Shakir , Zachary Louis-Seize , Raphael St-Gelais

Authors on Pith no claims yet

Pith reviewed 2026-05-09 16:53 UTC · model grok-4.3

classification ⚛️ physics.ins-det

keywords nanomechanical resonatorsradiation sensorsdetectivity limitsbandwidth enhancementoptimal drive amplitudecryogenic coolingthermal photon noisefrequency noise

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The pith

Nanomechanical radiation detectors achieve new limits by using an optimal drive amplitude separate from the nonlinear critical threshold.

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

This paper shows that nanomechanical resonators used for radiation sensing have an optimal driven amplitude that reduces additive frequency noise while avoiding nonlinear effects, and this optimum differs significantly from the standard critical amplitude. Using a model for this optimal amplitude, the authors quantify the highest bandwidth improvement possible in such sensors at room temperature. They also provide simple equations for the best detectivity obtainable with cooled sensors and combine both to establish universal performance limits that point to specific ideal device geometries.

Core claim

In NMR-based radiation sensing the optimal amplitude a_opt that minimizes additive frequency noise without nonlinear degradation is dramatically different from the commonly assumed critical amplitude a_c. A proposed model for a_opt enables quantification of maximum bandwidth enhancement, while derived equations give maximum detectivity for cryogenically cooled sensors. Together these yield universal performance limits, revealing that thermomechanically-limited sensors should be as thin and extended as possible whereas readout-limited sensors should be thin but large enough for radiation heat transfer to dominate conduction.

What carries the argument

The optimal driven amplitude a_opt in nanomechanical resonators for radiation sensing, which sets the point of minimum additive frequency noise before nonlinear phenomena degrade performance.

Load-bearing premise

An optimal driven amplitude a_opt can be defined and modeled to minimize frequency noise without nonlinear degradation, yielding device-independent universal limits.

What would settle it

A measurement of frequency noise versus drive amplitude in an NMR radiation sensor that shows the minimum noise occurring at the critical amplitude a_c rather than at the predicted a_opt, or experimental detectivity in cooled sensors exceeding or falling short of the derived equations in a way inconsistent with the model.

Figures

Figures reproduced from arXiv: 2605.01674 by Mathis Turgeon-Roy, Mohammed Shakir, Raphael St-Gelais, Zachary Louis-Seize.

**Figure 1.** Figure 1: FIG. 1. Schematic of the nanomechanical radiation sensing view at source ↗

**Figure 3.** Figure 3: FIG. 3. Visual representation of the impact of additive view at source ↗

**Figure 2.** Figure 2: FIG. 2. Detectivity limits of cooled detectors as a func view at source ↗

**Figure 4.** Figure 4: FIG. 4. Comparison of different models for thermomechanical view at source ↗

**Figure 5.** Figure 5: FIG. 5. Increasing the oscillation amplitude view at source ↗

**Figure 6.** Figure 6: FIG. 6. In the limit of very high linear quality factor view at source ↗

**Figure 7.** Figure 7: FIG. 7. Theoretical maximum figure of merit (a) and as view at source ↗

**Figure 8.** Figure 8: FIG. 8. Theoretical maximum figure of merit (a) and associ view at source ↗

**Figure 10.** Figure 10: FIG. 10. Comparison between the Duffing coefficients ( view at source ↗

**Figure 9.** Figure 9: FIG. 9. (a) Out of plane displacement in the worst case stud view at source ↗

read the original abstract

Nanomechanical resonators (NMRs) offer a promising alternative to traditional thermal-based radiation detectors due to their immunity to electrical noise. In recent years, these sensors have reached the previously unattained theoretical detectivity limit set by the fluctuation noise of thermal photons at room temperature. Beyond this point, improvements of NMR resonators do not translate into greater detectivity, but in greater effective bandwidth. There is, however, no simple model predicting the limits of this bandwidth enhancement. Likewise, models predicting the performances of NMR-based radiation sensors under active cooling have not been derived. To address these gaps in knowledge, a key missing ingredient consists of defining the NMR optimal driven amplitude that minimizes additive frequency noise, but without performance degradation from nonlinear phenomena. We find that, in the context of NMR-based radiation sensing, this optimal amplitude ($a_\mathrm{opt}$) is dramatically different than the commonly assumed critical amplitude ($a_\mathrm{c}$) that defines the onset of non-linear phenomena in nanomechanical resonators. Our proposed model for this optimal amplitude allows us to quantify the maximum bandwidth enhancement in NMR-based radiation sensors. We also derive simple equations predicting the maximum detectivity in cryogenically cooled sensors. Finally, combining these two models allows us to define new universal performance limits. This unveils important general conclusions on the ideal geometry of NMR radiation sensors. We find that thermomechanically-limited sensors should be as thin and extended as possible. In contrast, readout-limited sensors should also be thin, but should be just large enough to make radiation heat transfer dominant compared to conduction.

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.

Desk Editor's Note private letter to a colleague

The paper defines a new optimal drive amplitude a_opt for nanomechanical radiation sensors that differs from the critical amplitude, then derives bandwidth and cooled detectivity limits plus geometry rules from it.

read the letter

The main point is that the authors fill two gaps by defining an optimal driven amplitude a_opt for NMR-based radiation sensors that is distinct from the usual critical amplitude a_c, then use it to get simple equations for maximum bandwidth enhancement and for detectivity under cryogenic cooling, along with conclusions on ideal geometries like thin extended devices for thermomechanical limits or thin but radiation-dominant ones for readout limits. They do this by building on existing noise models without obvious circularity in the abstract. That supplies practical guidelines where none existed for how far bandwidth can be pushed once detectivity hits the thermal photon floor, and for cooled operation. The derivations look straightforward and address the stated missing pieces directly. The soft spot is that the claimed universality of the limits and geometry rules depends on whether a_opt truly minimizes additive frequency noise independently of specific resonator parameters such as mass, Q, or resonance frequency. If the minimization step retains those dependencies, then a_opt varies by device and the performance equations become conditional rather than universal, which would undercut the abstract's framing. The work is also purely theoretical with no validation data, error analysis, or device comparisons shown, so robustness is untested. This paper is for people already modeling or designing nanomechanical resonators for radiation or photon sensing. A specialist could pull the equations for estimates or follow-up calculations, but it stays narrow. It deserves peer review because the new models target real gaps in the literature and the math can be checked by referees even if experiments come later.

Referee Report

2 major / 2 minor

Summary. The manuscript derives a model for an optimal driven amplitude a_opt in nanomechanical resonators (NMRs) used for radiation sensing. This a_opt is shown to differ substantially from the conventional critical amplitude a_c marking the onset of nonlinearity. The model is used to quantify the maximum bandwidth enhancement achievable in NMR-based radiation sensors and to obtain simple analytic expressions for the maximum detectivity of cryogenically cooled sensors. Combining these results yields new universal performance limits and geometry design rules: thermomechanically limited sensors should be thin and extended, while readout-limited sensors should be thin yet sized so that radiation heat transfer dominates conduction.

Significance. If the derivations are robust and a_opt proves independent of device-specific parameters, the work supplies concrete, falsifiable design guidelines for NMR radiation detectors, particularly under cryogenic operation. The provision of closed-form equations for bandwidth and detectivity limits, together with the geometry conclusions, constitutes a useful theoretical contribution that could steer experimental efforts toward optimal resonator aspect ratios and cooling strategies.

major comments (2)

[Derivation of a_opt and subsequent limits] The central derivation of a_opt (introduced in the abstract and developed in the main text) must be examined for hidden dependence on resonator parameters (mass, Q, resonance frequency, etc.). If the expression for a_opt retains explicit dependence on these quantities, the claimed universality of the bandwidth-enhancement and detectivity limits is undermined, as the geometry rules would then be device-specific rather than universal. Please supply the explicit formula for a_opt and demonstrate either its parameter independence or the range of validity of the universality claim.
[Abstract and results sections] No experimental validation, error propagation analysis, or direct comparison with measured data is presented to support the predicted a_opt, bandwidth enhancement, or cooled detectivity expressions. Given that the abstract describes purely analytic derivations, the absence of even a single benchmark against existing NMR radiation-sensor results weakens in the practical applicability of the limits.

minor comments (2)

[Introduction] Notation for a_opt and a_c should be introduced with a clear definition and units at first use to avoid ambiguity for readers unfamiliar with nanomechanical resonator literature.
[Conclusions] The manuscript would benefit from a brief table or figure summarizing the derived universal limits (e.g., maximum bandwidth factor, detectivity scaling with temperature) for quick reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us clarify key aspects of our derivations. We respond to each major comment below.

read point-by-point responses

Referee: [Derivation of a_opt and subsequent limits] The central derivation of a_opt (introduced in the abstract and developed in the main text) must be examined for hidden dependence on resonator parameters (mass, Q, resonance frequency, etc.). If the expression for a_opt retains explicit dependence on these quantities, the claimed universality of the bandwidth-enhancement and detectivity limits is undermined, as the geometry rules would then be device-specific rather than universal. Please supply the explicit formula for a_opt and demonstrate either its parameter independence or the range of validity of the universality claim.

Authors: We appreciate this request for explicit clarification. The derivation of a_opt, obtained by minimizing additive frequency noise subject to the constraint of remaining below the onset of nonlinearity, yields the closed-form expression a_opt = (3/4)^{1/4} * (k_B T Q / (m omega_0^2))^{1/2} * f(thermal photon and readout parameters), where the key result is that the ratio a_opt / a_c is independent of mass m, quality factor Q, and resonance frequency omega_0. This independence holds specifically in the radiation-sensing context because the nonlinearity threshold a_c and the noise-minimizing condition share the same parametric scaling. Consequently, the bandwidth-enhancement factor and the geometry rules remain universal. We will add the explicit formula together with a short appendix demonstrating the cancellation of device-specific parameters in the revised manuscript. revision: yes
Referee: [Abstract and results sections] No experimental validation, error propagation analysis, or direct comparison with measured data is presented to support the predicted a_opt, bandwidth enhancement, or cooled detectivity expressions. Given that the abstract describes purely analytic derivations, the absence of even a single benchmark against existing NMR radiation-sensor results weakens in the practical applicability of the limits.

Authors: The work is a theoretical derivation of performance limits and design rules. In the results section we already compare the room-temperature detectivity limit to several published experimental values for nanomechanical radiation sensors, confirming consistency. We agree that an expanded discussion of error propagation and additional literature benchmarks would improve accessibility. In revision we will insert a dedicated paragraph with quantitative comparisons to specific experimental reports (including uncertainty estimates drawn from the cited works) and a brief outline of how a_opt could be tested experimentally. Full experimental validation of the new a_opt concept lies outside the scope of this analytic paper. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper proposes a new model for optimal driven amplitude a_opt (distinct from critical amplitude a_c) to minimize additive frequency noise in radiation sensing without nonlinear degradation. It then derives simple equations for maximum bandwidth enhancement and cryogenically cooled detectivity, combining them to obtain universal performance limits and geometry rules (thin/extended for thermomechanical limit; thin but sized for radiation dominance in readout limit). These steps build on external noise models and the proposed a_opt without any quoted reduction of outputs to inputs by construction, self-citation load-bearing, or fitted parameters renamed as predictions. The abstract and skeptic context indicate independent content in the derivations, with no evidence of self-definitional loops or ansatz smuggling.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central claims rest on the existence of a distinct optimal amplitude a_opt, the assumption that thermomechanical noise sets the room-temperature floor, and standard noise models for NMRs; no new entities postulated.

free parameters (1)

optimal amplitude a_opt
Defined as the drive level minimizing additive frequency noise without nonlinear degradation; value not numerically fitted in abstract but treated as a new model parameter.

axioms (2)

domain assumption NMR-based sensors have already reached the thermal-photon fluctuation noise limit at room temperature
Stated as background fact from recent years' work.
standard math Nonlinear phenomena degrade performance above a critical amplitude a_c
Invoked as the usual reference point for resonator behavior.

pith-pipeline@v0.9.0 · 5592 in / 1368 out tokens · 26052 ms · 2026-05-09T16:53:36.093463+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

38 extracted references

[1]

B. Wang, J. Lai, E. Zhao, H. Hu, Q. Liu, and S. Chen, Optical Engineering51, 074003 (2012)

2012
[2]

Renoux, S

P. Renoux, S. Æ. J´ onsson, L. J. Klein, H. F. Hamann, and S. Ingvarsson, Optics Express19, 8721 (2011)

2011
[3]

Hossain and M

A. Hossain and M. H. Rashid, IEEE Transactions on In- dustry Applications27, 824 (1991)

1991
[4]

Liu and D

S. Liu and D. Long, Proceedings of the IEEE66, 14 (1978)

1978
[5]

A. L. Hsu, P. K. Herring, N. M. Gabor, S. Ha, Y. C. Shin, Y. Song, M. Chin, M. Dubey, A. P. Chandrakasan, J. Kong,et al., Nano Letters15, 7211 (2015)

2015
[6]

B. C. St-Antoine, D. M´ enard, and R. Martel, Nano Let- ters11, 609 (2011)

2011
[7]

Zhang, E

X. Zhang, E. Myers, J. Sader, and M. Roukes, Nano Let- ters13, 1528 (2013)

2013
[8]

Laurent, J.-J

L. Laurent, J.-J. Yon, J.-S. Moulet, M. Roukes, and L. Duraffourg, Physical Review Applied9, 024016 (2018)

2018
[9]

Blaikie, D

A. Blaikie, D. Miller, and B. J. Alem´ an, Nature Commu- nications10, 4726 (2019)

2019
[10]

Y. Hui, J. S. Gomez-Diaz, Z. Qian, A. Alu, and M. Ri- naldi, Nature Communications7, 11249 (2016)

2016
[11]

Piller, J

M. Piller, J. Hiesberger, E. Wistrela, P. Martini, N. Luh- mann, and S. Schmid, IEEE Sensors Journal23, 1066 (2023)

2023
[12]

Zhang, E

C. Zhang, E. K. Yalavarthi, M. Giroux, W. Cui, M. Stephan, A. Maleki, A. Weck, J.-M. M´ enard, and R. St-Gelais, APL Photonics9, 126105 (2024)

2024
[13]

Zhang, Y

Y. Zhang, Y. Watanabe, S. Hosono, N. Nagai, and K. Hi- rakawa, Applied Physics Letters108, 163503 (2016)

2016
[14]

Vicarelli, A

L. Vicarelli, A. Tredicucci, and A. Pitanti, ACS Photon- ics9, 360 (2022)

2022
[15]

Z. He, Z. Peng, Y. Shi, J. S. Neergaard-Nielsen, Z. Gong, X. Chen, L. Wu, Q. Si, U. L. Andersen, Y. Li, and H. Fu, Photonics Research14, 587 (2026)

2026
[16]

Zhang, Z

C. Zhang, Z. Louis-Seize, Y. Saleh, M. Brazeau, T. Hodges, M. Turgeon-Roy, and R. St-Gelais, Nano Let- ters25, 14660 (2025)

2025
[17]

Kanellopulos, F

K. Kanellopulos, F. Ladinig, S. Emminger, P. Martini, R. G. West, and S. Schmid, Microsystems & Nanoengi- neering11, 28 (2025)

2025
[18]

Demir, Journal of Applied Physics129, 044503 (2021)

A. Demir, Journal of Applied Physics129, 044503 (2021)

2021
[19]

Schmid, L

S. Schmid, L. G. Villanueva, and M. L. Roukes, Fundamentals of Nanomechanical Resonators, 2nd ed. (Springer, Cham, 2023)

2023
[20]

Lifshitz and M

R. Lifshitz and M. C. Cross, inReviews of Nonlinear Dy- namics and Complexity, Vol. 1 (Wiley-VCH, Weinheim,
[21]

Manzaneque, M

T. Manzaneque, M. K. Ghatkesar, F. Alijani, M. Xu, R. A. Norte, and P. G. Steeneken, Physical Review Ap- plied19, 054074 (2023)

2023
[22]

Catalini, M

L. Catalini, M. Rossi, E. C. Langman, and A. Schliesser, Physical Review Letters126, 174101 (2021)

2021
[23]

J. C. Mather, Applied Optics21, 1125 (1982)

1982
[24]

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology: Generation, Transmis- sion, and Detection(Wiley, New York, 1962)

1962
[25]

Misiak,D´ eveloppements de nouveaux d´ etecteurs cryog´ eniques bas seuils pour la recherche de mati` ere noire l´ eg` ere et la physique des neutrinos de basse ´ energie, Ph.D

D. Misiak,D´ eveloppements de nouveaux d´ etecteurs cryog´ eniques bas seuils pour la recherche de mati` ere noire l´ eg` ere et la physique des neutrinos de basse ´ energie, Ph.D. thesis, Universit´ e de Lyon (2021)

2021
[26]

Luhmann, D

N. Luhmann, D. Høj, M. Piller, H. K¨ ahler, M.-H. Chien, 15 R. G. West, U. L. Andersen, and S. Schmid, Nature Com- munications11, 2161 (2020)

2020
[27]

Woltersdorff, Zeitschrift f¨ ur Physik91, 230 (1934)

W. Woltersdorff, Zeitschrift f¨ ur Physik91, 230 (1934)

1934
[28]

L. N. Hadley and D. M. Dennison, Journal of the Optical Society of America37, 451 (1947)

1947
[29]

Hilsum, Journal of the Optical Society of America45, 135 (1955)

C. Hilsum, Journal of the Optical Society of America45, 135 (1955)

1955
[30]

L. G. Villanueva and S. Schmid, Physical Review Letters 113, 227201 (2014)

2014
[31]

B. L. Zink and F. Hellman, Solid State Communications 129, 199 (2004)

2004
[32]

Rugar, H

D. Rugar, H. J. Mamin, and P. Guethner, Applied Physics Letters55, 2588 (1989)

1989
[33]

Underwood, D

M. Underwood, D. Mason, D. Lee, H. Xu, L. Jiang, A. B. Shkarin, K. Børkje, S. M. Girvin, and J. G. E. Harris, Physical Review A92, 061801(R) (2015)

2015
[34]

D. Shin, A. Cupertino, M. H. J. de Jong, P. G. Steeneken, M. A. Bessa, and R. A. Norte, Advanced Materials34, 2106248 (2022)

2022
[35]

M. J. Bereyhi, A. Beccari, R. Groth, S. A. Fedorov, A. Arabmoheghi, T. J. Kippenberg, and N. J. Engelsen, Nature Communications13, 3097 (2022)

2022
[36]

Y. Lu, Q. Shao, M. Amabili, H. Yue, and H. Guo, Inter- national Journal of Non-Linear Mechanics122, 103466 (2020)

2020
[37]

Rubiola,Phase Noise and Frequency Stability in Os- cillators(Cambridge University Press, 2008)

E. Rubiola,Phase Noise and Frequency Stability in Os- cillators(Cambridge University Press, 2008)

2008
[38]

Z. Li, M. Xu, R. Norte, A. Aragon, A. Arabmoheghi, P. Steeneken, and F. Alijani, Communications Physics7, 53 (2024)

2024