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arxiv: 2512.09600 · v2 · submitted 2025-12-10 · ⚛️ physics.ins-det · cond-mat.supr-con

Advanced microwave SQUID multiplexer model incorporating readout power effects and Josephson junction inhomogeneities

Martin Neidig , Mathias Wegner , Sebastian Kempf This is my paper

Pith reviewed 2026-05-16 23:34 UTC · model grok-4.3

classification ⚛️ physics.ins-det cond-mat.supr-con
keywords microwave SQUID multiplexerreadout power dependenceJosephson junction inhomogeneitycurrent-phase relationresonance characteristicsscreening parametertunnel barrier
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The pith

An advanced model for microwave SQUID multiplexers accounts for readout power dependence and non-sinusoidal current-phase relations from inhomogeneous tunnel barriers.

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

The paper presents a new model that describes how readout power changes the resonance behavior of microwave SQUID multiplexers. The model stays valid across the full practical range of screening parameters up to beta_L less than 1. It produces closer matches to measured data than earlier approaches, which opens the way to design choices that were previously out of reach. The same framework also handles non-sinusoidal current-phase relations that arise when the tunnel barriers in the Josephson junctions are uneven. These barrier effects look similar to screening effects but are distinct, so both must be treated separately for accurate results.

Core claim

Our model significantly improves agreement with experimental data compared to the existing models, thereby enabling optimization beyond the previously accessible parameter space. Moreover, our model supports non-sinusoidal current-phase relations of the rf-SQUID's Josephson junction, allowing, for the first time, for the modeling of devices based on Josephson tunnel junctions with inhomogeneous tunnel barriers. We show that the effects of such inhomogeneities are qualitatively similar to, yet distinct from, those of the screening parameter, making their inclusion essential for accurate characterization.

What carries the argument

The advanced readout-power-dependent model of resonance characteristics that incorporates non-sinusoidal current-phase relations for rf-SQUIDs.

Load-bearing premise

The model remains valid only for screening parameters below 1 and the chosen parametrization of non-sinusoidal current-phase relations accurately captures barrier inhomogeneities without creating unphysical artifacts at high readout power.

What would settle it

A set of resonance frequency and linewidth measurements versus readout power on devices whose tunnel-barrier inhomogeneity has been independently characterized would falsify the model if the new predictions show no clear improvement over standard models.

Figures

Figures reproduced from arXiv: 2512.09600 by Martin Neidig, Mathias Wegner, Sebastian Kempf.

Figure 1
Figure 1. Figure 1: Equivalent circuit diagram of a single µMUX channel. The channel comprises an rf-SQUID containing a Josephson junction with critical current Ic and a closed superconducting loop with inductance LS. The SQUID is inductively coupled to the input coil Lin and the inductor LT, which loads a superconducting quarter-wave microwave resonator. The resonator is coupled to a transmission line via a coupling capacito… view at source ↗
Figure 2
Figure 2. Figure 2: Measured dependence of the resonance frequency [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Flowchart outlining our numerical simulation framework. Re [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: rf-SQUID supercurrent and its time derivative, calculate [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the analytical µMUX model presented by Wegner et al. [8] and the present numerical model, assuming an rf-SQUID with hysteresis parameter βL = 0.9. Panel (a) displays the dependence of the resonance frequency fr on the applied magnetic flux in the limit of negligible power of the microwave probe tone (Φrf → 0). hfri = 5 GHz denotes the resonance frequency averaged over Φext. Panel (b) sho… view at source ↗
Figure 6
Figure 6. Figure 6: The figures show the effect of an inhomogeneous tunnel b [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Dependence of the measured resonance frequency [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

We present an advanced model for describing the readout power dependence of the resonance characteristics of a microwave SQUID multiplexer. Our model proves valid for SQUID screening parameters up to $\beta_\mathrm{L}<1$, hence covering the full range of practically relevant design parameters. We demonstrate that our model significantly improves agreement with experimental data compared to the existing models, thereby enabling optimization beyond the previously accessible parameter space. Moreover, our model supports non-sinusoidal current-phase relations of the rf-SQUID's Josephson junction, allowing, for the first time, for the modeling of devices based on Josephson tunnel junctions with inhomogeneous tunnel barriers. We show that the effects of such inhomogeneities are qualitatively similar to, yet distinct from, those of the screening parameter, making their inclusion essential for accurate characterization. Incorporating these effects yields great improved agreement with measurements, even at readout power conditions well beyond typical operating parameters.

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

2 major / 1 minor

Summary. The manuscript presents an advanced model for the readout power dependence of resonance characteristics in microwave SQUID multiplexers. It extends validity to screening parameters β_L < 1, incorporates non-sinusoidal current-phase relations to model Josephson junction inhomogeneities, claims significantly improved agreement with experimental data over existing models, and asserts that inhomogeneity effects are qualitatively similar yet distinct from screening-parameter effects.

Significance. If the central claims hold, the work would enable more accurate modeling and optimization of SQUID multiplexers at higher readout powers and for devices with inhomogeneous tunnel barriers. This is relevant for superconducting detector arrays in applications such as particle detection and quantum sensing, where precise characterization of non-ideal Josephson junctions can improve overall system performance.

major comments (2)
  1. Abstract: the claim of 'significantly improved agreement with experimental data' and 'greatly improved agreement with measurements' is stated without any quantitative metrics (e.g., fit residuals, χ² values, or direct comparison tables), preventing assessment of whether the improvement is load-bearing or merely incremental.
  2. Non-sinusoidal CPR section: the parametrization of non-sinusoidal current-phase relations for inhomogeneous barriers lacks an explicit derivation from first principles or a limits check against full circuit dynamics at high readout power, leaving open the possibility that observed distinctions from β_L effects are artifacts of added degrees of freedom rather than physical separation.
minor comments (1)
  1. Ensure all symbols (including β_L and the CPR parameters) are defined at first use and that any figures comparing model to data include error bars and quantitative goodness-of-fit indicators.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and recommendation for major revision. We address each major comment below with proposed changes to strengthen the manuscript's clarity and rigor.

read point-by-point responses

  1. Referee: Abstract: the claim of 'significantly improved agreement with experimental data' and 'greatly improved agreement with measurements' is stated without any quantitative metrics (e.g., fit residuals, χ² values, or direct comparison tables), preventing assessment of whether the improvement is load-bearing or merely incremental.

    Authors: We agree that quantitative metrics would better substantiate the claims of improvement. In the revised manuscript, we will add specific metrics such as χ² reduction factors and RMS fit residuals comparing the new model against prior ones, either incorporated into the abstract (subject to length constraints) or explicitly referenced from a new summary table in Section 3. This will enable direct evaluation of the improvement's significance. revision: yes

  2. Referee: Non-sinusoidal CPR section: the parametrization of non-sinusoidal current-phase relations for inhomogeneous barriers lacks an explicit derivation from first principles or a limits check against full circuit dynamics at high readout power, leaving open the possibility that observed distinctions from β_L effects are artifacts of added degrees of freedom rather than physical separation.

    Authors: The parametrization follows standard phenomenological extensions for inhomogeneous Josephson barriers (higher-harmonic CPR terms), consistent with prior literature on tunnel junction non-idealities. To address the concern directly, we will include an explicit step-by-step derivation in the revised main text or supplementary material, along with additional numerical checks of the model against full circuit simulations at elevated readout powers. These additions will confirm that the distinctions from β_L effects arise from distinct physical mechanisms rather than parameter freedom. revision: partial

Circularity Check

0 steps flagged

No significant circularity; model extends standard SQUID theory with independent parametrizations

full rationale

The paper presents an advanced model extending established rf-SQUID equations to include readout power dependence and non-sinusoidal current-phase relations for tunnel-barrier inhomogeneities. The central claims rest on improved experimental agreement and qualitative distinction from screening-parameter effects, without any quoted reduction of predictions to fitted inputs by construction, self-citation chains, or ansatzes smuggled from prior author work. The derivation remains self-contained against external benchmarks and data validation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Model rests on standard rf-SQUID circuit equations plus two extensions: power-dependent terms and a parametrization of non-sinusoidal CPR. No free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption Model validity for screening parameter β_L <1
    Stated as covering the full range of practically relevant design parameters.

pith-pipeline@v0.9.0 · 5459 in / 1118 out tokens · 30185 ms · 2026-05-16T23:34:22.151698+00:00 · methodology

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

  1. [1]

    Irwin K and Hilton G 2005 Transition-Edge Sensors (Berlin, Heidelberg: Springer Berlin Heidelberg) pp 63–150 ISBN 978-3-540-31478-3 URL https://doi.org/10.1007/10933596_3

    work page doi:10.1007/10933596_3 2005

  2. [2]

    Ullom J N and Bennett D A 2015 Superconductor Science and Technology 28 084003 URL https://dx.doi.org/10.1088/0953-2048/28/8/084003

    work page doi:10.1088/0953-2048/28/8/084003 2015

  3. [3]

    Fleischmann A, Enss C and Seidel G 2005 Metallic Magnetic Calorimeters (Springer Berlin Heidelberg) pp 151–216 URL https://doi.org/10.1007/10933596_4

    work page doi:10.1007/10933596_4 2005

  4. [4]

    Low Temp

    Kempf S, Fleischmann A, Gastaldo L and Enss C 2018 J. Low Temp. Phys. 193 365–379 URL https://doi.org/10.1007/s10909-018-1891-6

    work page doi:10.1007/s10909-018-1891-6 2018

  5. [5]

    Irwin K D and Lehnert K W 2004 Applied Physics Letters 85 2107–2109 URL https://doi.org/10.1063/1.1791733

    work page doi:10.1063/1.1791733 2004

  6. [6]

    Mates J A B, Hilton G C, Irwin K D, Vale L R and Lehnert K W 2008 Applied Physics Letters 92 URL https://doi.org/10.1063/1.2803852

    work page doi:10.1063/1.2803852 2008

  7. [7]

    7 015007 URL https://doi.org/10.1063/1.4973872

    Kempf S, Wegner M, Fleischmann A, Gastaldo L, Herrmann F, Paps t M, Richter D and Enss C 2017 AIP Adv. 7 015007 URL https://doi.org/10.1063/1.4973872

    work page doi:10.1063/1.4973872 2017

  8. [8]

    Wegner M, Enss C and Kempf S 2022 Superconductor Science and Technology 35 075011 URL https://dx.doi.org/10.1088/1361-6668/ac6d15

    work page doi:10.1088/1361-6668/ac6d15 2022

  9. [9]

    Schuster C, Wegner M and Kempf S 2023 Journal of Applied Physics 133 044503 ISSN 0021-8979 URL https://doi.org/10.1063/5.0135124

    work page doi:10.1063/5.0135124 2023

  10. [10]

    Garc ´ ıa Redondo M E, M¨ uller N A, Salum J M, Ferreyro L P, Bonilla-N eira J D, Geria J M, Bonaparte J J, Muscheid T, Gartmann R, Almela A, Hampel M R, Fuste r A E, Ardila-Perez L E, Wegner M, Platino M, Sander O, Kempf S and Weber M 2024 Journal of Applied Physics 136 114401 ISSN 0021-8979 URL https://doi.org/10.1063/5.0222656

    work page doi:10.1063/5.0222656 2024

  11. [11]

    thesis University of Colorado

    Mates J A B 2011 The microwave SQUID multiplexer Ph.D. thesis University of Colorado

    work page 2011

  12. [12]

    Kempf S, Wegner M, Deeg L, Fleischmann A, Gastaldo L, Herrman n F, Richter D and Enss C 2017 Superconductor Science and Technology 30 065002 URL https://dx.doi.org/10.1088/1361-6668/aa6d17

    work page doi:10.1088/1361-6668/aa6d17 2017

  13. [13]

    Mates J A B, Irwin K D, Vale L R, Hilton G C, Gao J and Lehnert K W 201 2 Journal of Low Temperature Physics 167 707–712 URL https://doi.org/10.1007/s10909-012-0518-6

    work page doi:10.1007/s10909-012-0518-6

  14. [14]

    34 805–890 URL https://doi.org/10.1017/S0962492924000096

    Saad Y 2025 Acta Numer. 34 805–890 URL https://doi.org/10.1017/S0962492924000096

    work page doi:10.1017/s0962492924000096 2025

  15. [15]

    Adam F, Enss C and Kempf S 2024 Superconductor Science and Technology 37 085013 URL https://dx.doi.org/10.1088/1361-6668/ad59cf

    work page doi:10.1088/1361-6668/ad59cf 2024

  16. [16]

    Willsch D, Rieger D, Winkel P, Willsch M, Dickel C, Krause J, Ando Y, L escanne R, Leghtas Z, Bronn N T, Deb P, Lanes O, Minev Z K, Dennig B, Geisert S, G¨ unzler S, Ihssen S, Paluch P, Reisinger T, Hanna R, Bae J H, Sch¨ uffelgen P, Gr¨ utzmacher D, Buim aga-Iarinca L, Morari C, Wernsdorfer W, DiVincenzo D P, Michielsen K, Catelani G and Pop I M 20 24 Nat...

    work page doi:10.1038/s41567-024-02400-8

  17. [17]

    Jung H, Kim Y, Jung K, Im H, Pashkin Y A, Astafiev O, Nakamura Y, Lee H, Miyamoto Y and Tsai J S 2009 Phys. Rev. B 80(12) 125413 URL https://link.aps.org/doi/10.1103/PhysRevB.80.125413

    work page doi:10.1103/physrevb.80.125413 2009

  18. [18]

    Rippard W H, Perrella A C, Albert F J and Buhrman R A 2002 Phys. Rev. Lett. 88(4) 046805 URL https://link.aps.org/doi/10.1103/PhysRevLett.88.046805

    work page doi:10.1103/physrevlett.88.046805 2002

  19. [19]

    Ashcroft N W and Mermin N D 1976 Solid State Physics (Saunders College Publishing)

    work page 1976