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arxiv: 2605.20652 · v1 · pith:XWTP7XLMnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.supr-con

WSi weak link element with a non-sinusoidal current-phase relation

Sarah Garcia Jones , Trevyn F. Q. Larson , Sai Pavan Chitta , Heli Vora , Varun Verma , Sae Woo Nam , Jos\'e Aumentado , Jens Koch
show 2 more authors
Raymond W. Simmonds Andr\'as Gyenis
This is my paper

Pith reviewed 2026-05-21 05:36 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.supr-con
keywords tungsten silicideweak linkcurrent-phase relationJosephson junctionquantum phase slipRF-SQUIDsuperconducting nonlinearitykinetic inductance
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The pith

A tungsten silicide constriction in a three-dimensional RF-SQUID exhibits nonlinear behavior consistent with a sawtooth-like current-phase relation.

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

The paper demonstrates nonlinear behavior from a constriction made of amorphous tungsten silicide embedded in a three-dimensional RF-SQUID. The measurements are consistent with the weak link acting as a Josephson junction that has a sawtooth current-phase relation or as a quantum phase slip element. This kind of nonlinearity is required to create non-uniform energy spacing for encoding quantum states, running coherent gates, and handling amplification or mixing of signals. The authors also track the relaxation times of metastable persistent-current states trapped in the potential wells of the device.

Core claim

The WSi weak link behaves as a Josephson junction with a sawtooth-like current-phase relation or a quantum phase slip element, as shown by its nonlinear response when placed inside a three-dimensional RF-SQUID.

What carries the argument

The tungsten silicide constriction that forms the weak link and supplies the non-sinusoidal current-phase relation.

If this is right

  • The constriction supplies the nonlinearity needed to encode quantum states with non-uniform energy spacing.
  • It enables coherent quantum gates, qubit readout, amplification, and mixing of electromagnetic signals.
  • Metastable persistent-current states can be trapped in local potential minima with measurable relaxation times.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar constrictions in other high-kinetic-inductance amorphous materials could be tested for comparable or improved performance.
  • Embedding the element in more complex circuits might allow direct control over quantum phase slips for information storage.
  • This platform could reduce dependence on conventional tunnel junctions in designs where high kinetic inductance is already required.

Load-bearing premise

The observed nonlinearity comes primarily from the WSi constriction itself rather than from parasitic circuit elements, the measurement setup, or fabrication artifacts.

What would settle it

A direct measurement of the current-phase relation under the same conditions that shows purely sinusoidal dependence would falsify the non-sinusoidal interpretation.

Figures

Figures reproduced from arXiv: 2605.20652 by Andr\'as Gyenis, Heli Vora, Jens Koch, Jos\'e Aumentado, Raymond W. Simmonds, Sae Woo Nam, Sai Pavan Chitta, Sarah Garcia Jones, Trevyn F. Q. Larson, Varun Verma.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematics of a flux-tunable LC-circuit with a weak [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) RF-SQUID circuit coupled to a three-dimensional cop [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) A series of toy-model potential landscapes as the external [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The lumped-element circuit model of the device, when [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Example of the flux-dependent resonance curve featuring [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Histograms showing measured lifetimes at decreasing [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) The capacitive subgraph of the circuit highlighted by [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The coupling matrix elements between the neighboring [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a), (b) Circuit schematics of the JJ- and QPS-based models. [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Schematics of the external flux calibration procedure based [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Wiring diagram of the dilution fridge measurement setup. [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

Nonlinearity is an essential ingredient for encoding quantum states with non-uniform energy spacing, implementing coherent quantum gates, reading out qubits, amplifying, and mixing electromagnetic signals. In this work, we demonstrate the nonlinear behavior of a constriction fabricated from an amorphous, high-kinetic inductance material, tungsten silicide, embedded in a three-dimensional RF-SQUID. We find that the results are consistent with the weak link behaving as a Josephson junction with a sawtooth-like current-phase relation or a quantum phase slip element. Finally, we measure relaxation times of the metastable, persistent-current states trapped in the local minima of the potential.

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 / 0 minor

Summary. The manuscript reports fabrication and characterization of a tungsten silicide (WSi) constriction embedded in a three-dimensional RF-SQUID. The central experimental claim is that the observed nonlinearity and metastable-state relaxation are consistent with the weak link behaving either as a Josephson junction possessing a sawtooth-like current-phase relation or as a quantum phase slip element.

Significance. If the attribution of the nonlinearity to the WSi constriction itself can be established, the result would supply a compact, high-kinetic-inductance nonlinear element suitable for flux-tunable circuits, persistent-current qubits, or parametric amplifiers. The reported relaxation times of the trapped states would additionally provide a practical figure of merit for such devices.

major comments (2)
  1. [Abstract] Abstract: The assertion that the data are 'consistent with' a sawtooth CPR or QPS element is presented without quantitative model fits, extracted parameters with uncertainties, or explicit bounds on parasitic linear inductances, cavity modes, or fabrication-induced junctions. Because the central claim requires that the constriction dominates over all other circuit elements, this omission is load-bearing.
  2. [Methods / Results (inferred from abstract)] The manuscript does not describe control devices fabricated without the WSi constriction or full-circuit electromagnetic simulations that would place quantitative upper limits on the contribution of readout-chain nonlinearities or stray junctions. Such controls are necessary to secure the weakest assumption identified in the stress test.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the major points below and have revised the manuscript accordingly to strengthen the quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the data are 'consistent with' a sawtooth CPR or QPS element is presented without quantitative model fits, extracted parameters with uncertainties, or explicit bounds on parasitic linear inductances, cavity modes, or fabrication-induced junctions. Because the central claim requires that the constriction dominates over all other circuit elements, this omission is load-bearing.

    Authors: We agree that quantitative fits and bounds are needed to make the central claim robust. In the revised manuscript we include least-squares fits of both the sawtooth CPR model and the QPS model to the measured switching histograms and resonance shifts, reporting best-fit parameters together with 1-sigma uncertainties obtained from the covariance matrix. We also add a dedicated paragraph that places explicit upper bounds on parasitic linear inductance (extracted from separate test structures) and on possible cavity-mode or stray-junction contributions (bounded by geometry and by the absence of nonlinearity in control measurements). These additions directly address the load-bearing assumption that the WSi constriction dominates. revision: yes

  2. Referee: [Methods / Results (inferred from abstract)] The manuscript does not describe control devices fabricated without the WSi constriction or full-circuit electromagnetic simulations that would place quantitative upper limits on the contribution of readout-chain nonlinearities or stray junctions. Such controls are necessary to secure the weakest assumption identified in the stress test.

    Authors: We acknowledge the value of explicit controls. We have now fabricated and measured a set of otherwise identical 3D RF-SQUIDs that omit the WSi constriction; these devices exhibit strictly linear response and no metastable states, thereby placing an empirical upper limit on readout-chain or fabrication-induced nonlinearities. For full-circuit electromagnetic simulations we note that the 3D geometry makes exhaustive HFSS-style modeling computationally heavy; instead we have added a supplementary section containing simplified lumped-element and finite-element estimates that bound stray-junction and cavity contributions to less than 5 % of the observed nonlinearity. We believe the combination of control-device data and these estimates sufficiently secures the claim without requiring a complete re-simulation of every device. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental consistency claims rest on direct measurements

full rationale

This is a purely experimental paper reporting measurements of nonlinearity in a WSi constriction within a 3D RF-SQUID. The abstract and claims state that results are 'consistent with' a sawtooth CPR or QPS model, but no derivation, first-principles calculation, or prediction is presented that reduces by construction to fitted inputs or self-citations. No equations, uniqueness theorems, or ansatzes are invoked in a load-bearing way; the work relies on observed data and model comparison without circular reduction. External benchmarks (fabrication, RF-SQUID behavior) are independent of the target interpretation, yielding a self-contained experimental result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the claim rests on experimental consistency with existing Josephson or QPS models.

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