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Emergent Harmonics in Josephson Tunnel Junctions Due to Series Inductance

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper establishes that the second harmonic in the Josephson potential of Al/AlOx tunnel junctions is caused almost entirely by the inductance of the circuit traces, not by the junction barrier, bounding intrinsic Andreev harmonics to…

desk verdict A careful experimental paper that convincingly attributes the observed second harmonic in their Al/AlOx SQUIDs to series inductance, but the quantitative <0.1% bound on intrinsic Andreev harmonics rests on an untested assumption that the intrinsic ratio is area-independent. read the letter →

arxiv 2507.08171 v1 pith:VVMAIZDT submitted 2025-07-10 quant-ph cond-mat.supr-con

Junghyun Kim , Max Hays , Ilan T. Rosen , Junyoung An , Helin Zhang , Aranya Goswami , Kate Azar , Jeffrey M. Gertler
show 6 more authors
Bethany M. Niedzielski Mollie E. Schwartz Terry P. Orlando Jeffrey A. Grover Kyle Serniak William D. Oliver
This is my paper · ORCID
classification quant-phcond-mat.supr-con PACS 74.50.+r85.25.Dq
keywords JosephsontunneljunctionsecondharmonicseriesinductanceSQUIDspectroscopyAndreevboundstatessuperconductingqubitcurrent-phaserelationharmonics
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

Josephson tunnel junctions are usually modeled by a pure cosine potential, but measurements see a small second-harmonic term. This paper aims to determine where that term comes from: the intrinsic Andreev current–phase relation of the junction barrier, or the inductance of the metal traces that connect the junction to the rest of the circuit. Using flux-biased SQUIDs in which the fundamental harmonic is suppressed while the second harmonic survives, the authors find that the observed second harmonic scales linearly with the fundamental Josephson energy across junction sizes and across three chips. That scaling identifies the series inductance as the source, bounding the intrinsic Andreev second harmonic to below 0.1% of the fundamental in their Al/AlOx devices.

What carries the argument

The central object is the effective second-harmonic coefficient $E_{J2} \approx E_{J2,A} + E_{J2,L}$, with $E_{J2,L} \approx E_{J1}^2/(4E_L)$, and the resulting identity $E_{J2}/E_{J1} = \beta + (1/(4E_L))E_{J1}$. This ratio identity separates the two sources because the intrinsic contribution $\beta$ is assumed area-independent while the inductance contribution grows linearly with $E_{J1}$. The experimental lever is the near-half-flux SQUID: biasing a nearly symmetric SQUID at $\Phi_{\mathrm{ext}} \approx \Phi_0/2$ cancels the fundamental harmonics of the two arms and leaves the sum of second harmonics, making a small $\cos(2\varphi)$ term visible in the microwave transition spectrum, which is fit to a Hamiltonian with charging energy $4E_C \hat{n}^2$ plus first- and second-harmonic potentials.

What would settle it

Vary the trace inductance independently of junction area—for example, fabricate junctions of identical size with loop geometries whose simulated inductance differs by a factor of two—and check that $E_{J2}/E_{J1}$ at fixed $E_{J1}$ moves with the inductance while the intercept of the linear fit stays below 0.1%. If the intercept shifts with geometry, the constant-$\beta$ assumption is wrong; if the slope does not track the simulated inductance, the attribution to series inductance fails.

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Extended reading notes

Core claim

The paper's central claim is that in standard Al/AlOx tunnel junctions the second harmonic in the Josephson potential is an emergent, circuit-level effect: the series inductance of the wiring, not the junction barrier, generates the $\cos(2\varphi)$ term. Because the inductance-induced term grows as $E_{J2,L} \approx E_{J1}^2/(4E_L)$ while the intrinsic Andreev term grows only linearly with area, the ratio $E_{J2}/E_{J1}$ should be a linear function of $E_{J1}$ with slope $1/(4E_L)$ and intercept $\beta = E_{J2,A}/E_{J1}$. The measured ratio follows this line across five junction lengths on three chips; the intercept places the intrinsic Andreev second harmonic below 0.1% of $E_{J1}$, and the slope yields a series inductance of $10 \pm 1$ pH that agrees with the simulated loop inductance. Spectra near half flux that cannot be fit by a pure cosine potential are reproduced by including the second harmonic, supporting the model.

Load-bearing premise

The argument assumes that the intrinsic Andreev ratio $\beta = E_{J2,A}/E_{J1}$ is exactly constant across all junctions, so that a single intercept can be extrapolated; if the transparency distribution of the barrier changes with junction size, the intercept and slope would both be biased.

Editorial extensions

If this is right

  • The percent-level Josephson harmonics reported in some earlier tunnel-junction experiments are, in these devices, circuit-dressing artifacts rather than barrier properties; intrinsic Al/AlOx current–phase relations are much closer to sinusoidal.
  • Designs of flux-biased high-$E_J$ circuits—SNAILs, quartons, asymmetrically threaded SQUIDs, and Josephson diodes—must include the trace inductance to predict transition spectra and supercurrent asymmetries.
  • The supercurrent diode effect can arise in perfectly standard tunnel junctions from the embedding inductance alone, with estimated rectification efficiencies above 10% near half flux.
  • The extracted inductance from harmonic scaling ($10 \pm 1$ pH) serves as direct metrology of the circuit's series inductance accessible from qubit spectroscopy.

Reading between the lines

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

  • If the constant-$\beta$ assumption fails—say, transparency statistics drift with junction area—the reported 0.1% bound and the 10 pH slope would both move; the same SQUID protocol applied to a wider range of junction areas and independently varied trace geometries would test this directly.
  • The method could be exported to junctions with intentionally large intrinsic harmonics, such as high-transparency or semiconductor–superconductor junctions, where the intercept of the same ratio plot would no longer vanish, giving a clean separation of material physics from circuit dressing.
  • The simple $E_{J1}^2/(4E_L)$ scaling is derived under a small-phase-fluctuation approximation; the authors themselves caution that it breaks down for low-capacitance circuits, so in those regimes the linear-ratio analysis should be replaced by a full-circuit treatment before drawing conclusions about intrinsic harmonics.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper reports spectroscopic measurements of capacitively shunted SQUIDs with Al/AlOx tunnel junctions of varying length. The authors observe transition spectra near half-flux that require a cos(2φ) term in the potential, extract the ratio EJ2/EJ1 for each device, and show that this ratio grows linearly with EJ1 across three nominally identical chips. Interpreting the linear dependence through Eq. (7), they attribute the second harmonic almost entirely to the series inductance of the circuit traces and bound the intrinsic Andreev harmonic contribution to below 0.1% of EJ1; the fitted inductance of 10±1 pH agrees with InductEx simulations. The paper includes a full-circuit validation of the effective second-harmonic model and a dispersive-shift check against resonator spectroscopy.

Significance. If correct, these results are significant for the field: they would establish that the 'Josephson harmonics' reported in Al/AlOx tunnel junctions are, in the authors' devices, a circuit-dressing effect rather than a barrier-intrinsic property, with direct implications for qudit processors, coupler designs, and supercurrent-diode engineering. The manuscript's strengths are the reproducible multi-chip data set, the independent confirmation of the total series inductance by InductEx, and the explicit full-circuit comparison in the supplement. The main caveat is the untested assumption that the intrinsic ratio EJ2,A/EJ1 is area-independent, which is load-bearing for the 0.1% bound.

major comments (3)
  1. [Supplement S2.A, Eq. (S11); Section IV, Eq. (7), Fig. 4] The identification of the ODR intercept with the intrinsic Andreev ratio β = EJ2,A/EJ1 requires β to be strictly constant across the five junction lengths. Supplement S2.A obtains this constancy only by assuming a common transparency distribution ρ(T) for all devices; the paper asserts this from co-fabrication but provides no test. A systematic area-dependent change in ρ(T) — for example, from edge transparency, oxidation nonuniformity, or defect-density variation with junction length — would be absorbed into the fitted intercept and slope, so the extrapolated intercept would not bound β at the measured EJ1 values. Because the headline claim is a quantitative upper bound on intrinsic harmonics, the authors should either supply a robustness test in which β is allowed to vary (e.g., β ∝ E_J1^γ) and show that the bound survives, or explicitly restate the claim as conditional on area-independent β.
  2. [Section IV, Fig. 4] The paper does not report the ODR intercept, its confidence interval, the covariance of intercept and slope, or any goodness-of-fit statistic. With 14 data points and one excluded device, the reader cannot verify the stated '<0.1%' bound or the '10 ± 1 pH' inductance from the information given. The authors should report the full fit results, including the intercept and its uncertainty, the reduced chi-square (or equivalent), and a sensitivity analysis showing how the intercept changes when each individual point or chip is removed.
  3. [Supplement S2.B, Fig. S4] The full-circuit check of the second-harmonic approximation is shown only for the 6 µm and 2 µm devices, while the fitted intermediate lengths (3–5 µm) are not covered by this validation. Since the validity of EJ2,L ≈ E_J1^2/(4EL) is directly load-bearing for Eq. (7), the authors should extend the comparison to all measured device lengths or provide a quantitative bound on the maximum eigenvalue error over the full range of fit parameters used in the main-text analysis.
minor comments (5)
  1. [Section IV] The sentence 'due to the the varying JJ length' contains a duplicated 'the' and should be corrected.
  2. [Fig. 3 and Section III] The text and figure use garbled Unicode symbols such as 'ωr,|0ð' and 'ïi|ˆn|0ð'; these should be rendered with proper mathematical notation.
  3. [Table I] The table should state how EC/h is defined for each device (including which capacitances are included) and report the uncertainties of the fitted parameters.
  4. [Supplement S2.A] The phrase 'Assuming a large number of channels N k 1' appears to contain a typesetting error; N ≫ 1 is presumably intended.
  5. [Section IV, Fig. 4] The caption of Fig. 4 should list the fitted slope and intercept values in addition to showing the fit line, so that the linear scaling claim is directly reproducible from the figure.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular step found: EJ2/EJ1 is a free fit parameter, the linear scaling of Eq. (7) is a falsifiable test, and the InductEx comparison provides independent support; the <0.1% bound rests on a stated but untested β-constancy assumption that is a correctness risk, not circularity.

full rationale

The derivation is self-contained with no circular step: the per-device ratio α = E_J2/E_J1 is a free fit parameter in Supplement S3.A (Eq. S45), and the linear scaling predicted by Eq. (7) is tested against those fitted values in Fig. 4 rather than imposed by the fit, so the linearity is a falsifiable outcome; the ODR slope is independently checked against the geometry-based InductEx simulation (L_fit = 10 ± 1 pH vs L_sim = 10.2–10.7 pH), and the additive form E_J2 ≈ E_J2,A + E_J2,L of Eq. (2) is derived within the paper in Supplement S2.C, with the harmonic approximation validated against a full-circuit diagonalization in S2.B (Fig. S4). No load-bearing self-citation exists: the only co-author reference is Ref. [27] (Orlando et al., flux-qubit background), which is descriptive, and no uniqueness theorem or ansatz is imported from the authors' prior work. Two flagged limitations do not rise to circularity: (i) the <0.1% intrinsic bound assumes a strictly constant Andreev ratio β across junction lengths (Supplement S2.A, Eq. S11, justified only by common fabrication and not tested), so an area-dependent β would bias the intercept and invalidate the bound; this is a stated modeling assumption that affects the strength of the headline claim but does not reduce Eq. (7) to its input, because β is not defined as the fitted intercept and the linearity of Fig. 4 is an independent, observable outcome; and (ii) the main text asserts the <0.1% bound 'from the intercept' without quoting the intercept value or its uncertainty, which hampers verification but is a reporting gap, not a constructional equivalence. Score 2 reflects only the presence of a minor, non-load-bearing self-citation; the central empirical claim is otherwise independently supported.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The analysis introduces no new physical entities. The free parameters are the circuit model parameters fitted to spectroscopy data plus the global linear fit parameters. The key assumptions are the constancy of the intrinsic ratio beta and the validity of the second-harmonic approximation; both are reasonable but not independently verified.

free parameters (7)
  • EC/h (per device) = 0.096 to 0.161 GHz
    Charging energy fit to two-tone transition spectra; listed in Table I.
  • EJ1^(L)/h (per device) = 84 to 231 GHz
    Fundamental Josephson energy of the left arm, fit per device.
  • dEJ (per device) = 0.27% to 1.02%
    Junction asymmetry between arms, fit per device.
  • alpha = EJ2/EJ1 (per device) = approximately 0 to 0.4%
    Ratio of second to first harmonic, fit per device via the Hamiltonian in Eq. S44.
  • gc/2pi (per device) = 30.8 to 52 MHz
    Qubit-resonator coupling extracted from single-tone resonator spectroscopy (Table I).
  • ODR intercept beta = bounded <0.1% (exact CI not stated)
    Intercept of EJ2/EJ1 versus EJ1 linear fit, representing intrinsic Andreev ratio.
  • ODR slope 1/(4EL), leading to L_fit = L_fit = 10 +/- 1 pH
    Slope of EJ2/EJ1 versus EJ1 line; converted to series inductance.
assumptions (4)
  • domain assumption The Josephson potential of a tunnel junction is 2pi-periodic and can be written as -sum_n EJn cos(n phi).
    Standard result for SIS junctions under time-reversal symmetry; used in Eq. (1).
  • domain assumption The intrinsic Andreev ratio beta = EJ2,A/EJ1 is constant across all devices.
    Requires identical transparency distribution rho(T) across junction sizes; Supplement S2.A Eq. S11. Not experimentally verified.
  • domain assumption The series-inductance second harmonic is EJ2,L approximately EJ1^2/(4EL), valid when phase fluctuations of the inductor are small.
    Derived via current conservation in Supplement S2.B; the paper verifies it against full-circuit simulations for its parameter regime but notes it fails for typical transmon parameters.
  • standard math Each SQUID arm is modeled as a junction in series with a linear inductor, and the external circuit responds to the total phase.
    Circuit model in Fig. 2a and Eq. (3).

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Cite this review

Pith. "Pith review of Emergent Harmonics in Josephson Tunnel Junctions Due to Series Inductance." pith.science (2026). https://pith.science/paper/VVMAIZDT

@misc{pith2026250708171,
  author       = {Pith},
  title        = {Pith review of: Emergent Harmonics in Josephson Tunnel Junctions Due to Series Inductance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VVMAIZDT}},
  note         = {Machine review of arXiv:2507.08171}
}
abstract

Josephson tunnel junctions are essential elements of superconducting quantum circuits. The operability of these circuits presumes a $2\pi$-periodic sinusoidal potential of a tunnel junction, but higher-order corrections to this Josephson potential, often referred to as "harmonics," cause deviations from the expected circuit behavior. Two potential sources for these harmonics are the intrinsic current-phase relationship of the Josephson junction and the inductance of the metallic traces connecting the junction to other circuit elements. Here, we introduce a method to distinguish the origin of the observed harmonics using nearly-symmetric superconducting quantum interference devices (SQUIDs). Spectroscopic measurements of level transitions in multiple devices reveal features that cannot be explained by a standard cosine potential, but are accurately reproduced when accounting for a second-harmonic contribution to the model. The observed scaling of the second harmonic with Josephson-junction size indicates that it is due almost entirely to the trace inductance. These results inform the design of next-generation superconducting circuits for quantum information processing and the investigation of the supercurrent diode effect.

Figures

Figures reproduced from arXiv: 2507.08171 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
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Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Higher Josephson harmonics in a tunable double-junction transmon qubit

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Reference graph

Works this paper leans on

45 extracted references · 38 canonical work pages · cited by 1 Pith paper

  1. [1]

    Blais, R.-S

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

    2004

  2. [2]

    Likharev and V

    K. Likharev and V. Semenov, IEEE Transactions on Ap- plied Superconductivity 1, 3 (1991)

    work page 1991

  3. [3]

    Barone and G

    A. Barone and G. Paterno, Physics and applications of the Josephson effect (Wiley, 1982)

    work page 1982

  4. [4]

    anomalous

    Note that the 4 µm device of Chip C (orange square) is excluded because fabrication imperfec- tions resulted in a large JJ asymmetry of approximately 10%, masking signatures of the second harmonic. We observe the predicted linear dependence of the ratio EJ2/E J1 on EJ1 and extract the y-intercept and slope us- ing an Orthogonal Distance Regression (ODR). ...

    work page

  5. [5]

    accurately captures the device properties. IV. Determining the source of harmonics Equipped with the extracted EJ1, E J2 from the spec- tra fits, we can estimate the relative contributions of the intrinsic Andreev process and the series inductance to the second harmonic. Due to the linear and quadratic scaling of EJ2,A and EJ2,L with junction area, respect...

    work page

  6. [6]

    Misaki and N

    K. Misaki and N. Nagaosa, Phys. Rev. B 103, 245302 (2021)

    work page 2021

  7. [7]

    Peacock, P

    A. Peacock, P. Verhoeve, N. Rando, A. van Dordrecht, B. G. Taylor, C. Erd, M. A. C. Perryman, R. Venn, J. Howlett, D. J. Goldie, J. Lumley, and M. Wallis, Na- ture 381, 135 (1996)

    1996

  8. [8]

    Barzanjeh, S

    S. Barzanjeh, S. Pirandola, D. Vitali, and J. M. Fink, Science Advances 6, eabb0451 (2020)

    work page 2020

Show all 45 references
  1. [9]

    A. A. Golubov, M. Y. Kupriyanov, and E. Il’ichev, Rev. Mod. Phys. 76, 411 (2004)

    2004

  2. [10]

    Willsch, D

    D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Krause, Y. Ando, R. Lescanne, Z. Leghtas, N. T. Bronn, P. Deb, O. Lanes, Z. K. Minev, B. Dennig, S. Geisert, S. G¨ unzler, S. Ihssen, P. Paluch, T. Reisinger, R. Hanna, J. H. Bae, P. Sch¨ uffelgen, D. Gr¨ utzmacher, L....

    2024

  3. [11]

    Putterman, K

    H. Putterman, K. Noh, R. N. Patel, G. A. Peairs, G. S. MacCabe, M. Lee, S. Aghaeimeibodi, C. T. Hann, I. Jar- rige, G. Marcaud, Y. He, H. Moradinejad, J. C. Owens, T. Scaffidi, P. Arrangoiz-Arriola, J. Iverson, H. Levine, F. G. S. L. Brand˜ ao, M. H. Matheny, and O. Painter, Phy...

    2025

  4. [12]

    Vanselow, B

    A. Vanselow, B. Beauseigneur, L. Lattier, M. Villiers, A. Denis, P. Morfin, Z. Leghtas, and P. Campagne- Ibarcq, Dissipating quartets of excitations in a supercon- ducting circuit (2025), arXiv:2501.05960 [quant-ph]

    2025

  5. [13]

    T. A. Fulton, L. N. Dunkleberger, and R. C. Dynes, Phys. Rev. B 6, 855 (1972) . 7

    1972

  6. [14]

    Y. V. Fominov and D. S. Mikhailov, Phys. Rev. B 106, 134514 (2022)

    2022

  7. [15]

    R. S. Souto, M. Leijnse, and C. Schrade, Phys. Rev. Lett. 129, 267702 (2022)

    2022

  8. [16]

    A. M. Bozkurt, J. Brookman, V. Fatemi, and A. R. Akhmerov, SciPost Phys. 15, 204 (2023)

    2023

  9. [17]

    Greco, Q

    A. Greco, Q. Pichard, and F. Giazotto, Applied Physics Letters 123, 092601 (2023)

    2023

  10. [18]

    Nadeem, M

    M. Nadeem, M. S. Fuhrer, and X. Wang, Nature Reviews Physics 5, 558 (2023)

    2023

  11. [19]

    Z. Wang, R. W. Parker, E. Champion, and M. S. Blok, Systematic study of high EJ/ EC transmon qudits up to d = 12 (2024), arXiv:2407.17407 [quant-ph]

    2024 arXiv

  12. [20]

    F´ echant, M

    M. F´ echant, M. F. Dumas, D. B´ enˆ atre, N. Gosling, P. Lenhard, M. Spiecker, W. Wernsdorfer, B. D’Anjou, A. Blais, and I. M. Pop, Offset charge dependence of measurement-induced transitions in transmons (2025), arXiv:2505.00674 [quant-ph]

    2025

  13. [21]

    See Supplemental Material

  14. [22]

    Kafri, C

    D. Kafri, C. Quintana, Y. Chen, A. Shabani, J. M. Mar- tinis, and H. Neven, Phys. Rev. A 95, 052333 (2017)

    2017

  15. [23]

    Rymarz and D

    M. Rymarz and D. P. DiVincenzo, Phys. Rev. X 13, 021017 (2023)

    2023

  16. [24]

    I. L. Egusquiza and A. Parra-Rodriguez, Phys. Rev. X 15, 028001 (2025)

    2025

  17. [25]

    D. P. DiVincenzo and M. Rymarz, Phys. Rev. X 15, 028002 (2025)

    2025

  18. [26]

    T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuem- meth, P. Krogstrup, K. D. Petersson, and C. M. Marcus, Phys. Rev. Lett. 125, 056801 (2020)

    2020

  19. [27]

    W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. De- voret, npj Quantum Information 6, 8 (2020)

    2020

  20. [28]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 76, 042319 (2007)

    2007

  21. [29]

    T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo, Phys. Rev. B 60, 15398 (1999)

    1999

  22. [30]

    V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Science 326, 113 (2009)

    2009

  23. [31]

    A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Ma- jer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Nature 449, 328–331 (2007)

    2007

  24. [32]

    Fourie and W

    C. Fourie and W. Perold, IEEE Transactions on Applied Superconductivity 15, 300 (2005)

    2005

  25. [33]

    Haenel and O

    R. Haenel and O. Can, Superconducting diode from flux biased Josephson junction arrays (2022), arXiv:2212.02657 [cond-mat.supr-con]

    2022 arXiv

  26. [34]

    Y. Ye, J. B. Kline, S. Chen, A. Yen, and K. P. O’Brien, Science Advances 10, eado9094 (2024)

    2024

  27. [35]

    Emergent Harmonics in Josephson Tunnel Junctions Due to Series Inductance

    B. J. Chapman, S. J. de Graaf, S. H. Xue, Y. Zhang, J. Teoh, J. C. Curtis, T. Tsunoda, A. Eickbusch, A. P. Read, A. Koottandavida, S. O. Mundhada, L. Frunzio, M. Devoret, S. Girvin, and R. Schoelkopf, PRX Quantum 4, 020355 (2023) . Supplemental Material for “Emergent Harmonics...

    2023

  28. [36]

    (S24) S6 Csh L CJ (R), EJ (R)CJ (L), EJ (L) L Φext φ1 ϕ1 ϕ2 φ2 FIG

    − E(L) J cos (ϕ 1) − E(R) J cos (ϕ 2) Lfull = T − U. (S24) S6 Csh L CJ (R), EJ (R)CJ (L), EJ (L) L Φext φ1 ϕ1 ϕ2 φ2 FIG. S3. A full-circuit model of the capacitively shunted SQUI D including two series inductors. 0.498 0.500 0.502 Φext/Φ0 0 1 2 3 4 5Frequency (GHz) 0.46 0.47 0...

  29. [37]

    For the first model, we optimize L, CJ , S8 and the resonator coupling strength J as global fit parameters across the three cooldown datasets

    the same model as 1) but including the second Andreev harmonic EJ2,A . For the first model, we optimize L, CJ , S8 and the resonator coupling strength J as global fit parameters across the three cooldown datasets. For the second model, we fix J = 85 MHz and optimize the shunt cap...

  30. [38]

    Willsch, D

    D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Krau se, Y. Ando, R. Lescanne, Z. Leghtas, N. T. Bronn, P. Deb, O. Lanes, Z. K. Minev, B. Dennig, S. Geisert, S. G¨ unzler, S . Ihssen, P. Paluch, T. Reisinger, R. Hanna, J. H. Bae, P. Sch¨ uffelgen, D. Gr¨ utzmacher, ...

    2024

  31. [39]

    W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. Devoret, Superc onducting circuit protected by two-Cooper-pair tunneling, npj Quantum Information 6, 8 (2020)

    2020

  32. [40]

    Putterman, K

    H. Putterman, K. Noh, R. N. Patel, G. A. Peairs, G. S. MacCabe , M. Lee, S. Aghaeimeibodi, C. T. Hann, I. Jarrige, G. Marcaud, Y. He, H. Moradinejad, J. C. Owens, T. Scaffidi, P. Arrang oiz-Arriola, J. Iverson, H. Levine, F. G. S. L. Brand˜ ao, M. H. Matheny, and O. Painter, Pre...

    2025

  33. [41]

    Kafri, C

    D. Kafri, C. Quintana, Y. Chen, A. Shabani, J. M. Martinis, and H. Neven, Tunable inductive coupling of superconducting qubits in the strongly nonlinear regime, Phys. Rev. A 95, 052333 (2017)

    2017

  34. [42]

    Greco, Q

    A. Greco, Q. Pichard, and F. Giazotto, Josephson diode effec t in monolithic dc-squids based on 3d dayem nanobridges, Applied Physics Letters 123, 092601 (2023)

    2023

  35. [43]

    Y. V. Fominov and D. S. Mikhailov, Asymmetric higher-harmon ic squid as a Josephson diode, Phys. Rev. B 106, 134514 (2022)

    2022

  36. [44]

    R. S. Souto, M. Leijnse, and C. Schrade, Josephson diode effe ct in supercurrent interferometers, Phys. Rev. Lett. 129, 267702 (2022) . S14

    2022

  37. [45]

    A. M. Bozkurt, J. Brookman, V. Fatemi, and A. R. Akhmerov, Doub le-fourier engineering of Josephson energy-phase relationships applied to diodes, SciPost Phys. 15, 204 (2023)

    2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.