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REVIEW 5 major objections 4 minor 89 references

A strong microwave drive can fully erase the Josephson potential of a transmon qubit and then revive it inverted.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 02:21 UTC pith:HKJXKQ3F

load-bearing objection A likely real observation of Josephson-potential collapse and inversion in a carefully engineered circuit, but the central Floquet analysis is literally missing and the abstract overclaims; referee time is warranted only if the missing theory is supplied. the 5 major comments →

arxiv 2607.14344 v1 pith:HKJXKQ3F submitted 2026-07-15 quant-ph

Collapse and Inversion of the Josephson Potential in a Strongly Driven Superconducting Circuit

Sercan Deve , Marius Villiers , Marijn A. Morssink , Robin C. Dekker , Gary A. Steele This is my paper
classification quant-ph PACS 85.25.-j03.67.Lx
keywords Josephson potential collapseBessel function renormalizationflux-driven transmoninverted pendulum stabilizationmulti-excitation resonancescosine-cosine couplingdispersive readoutcircuit quantum electrodynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that a high-frequency flux drive does not merely shift the energy levels of a superconducting transmon; it renormalizes the Josephson potential itself. Because the effective Josephson energy picks up a factor of the zeroth Bessel function J0, the potential can be flattened completely at a critical drive amplitude (θ_ac ≈ 2.405) and then re-emerge with opposite sign. This collapse makes the qubit transition vanish, restores charge sensitivity, and beyond the collapse the eigenstates localize at phase π, a quantum analog of the inverted pendulum. The authors engineered a circuit with a cosine-cosine coupling that suppresses multi-photon resonances, allowing them to observe these regimes in spectroscopy and readout. If correct, the result defines a previously unknown power limit for strongly driven Josephson circuits and opens a path to protected qubits via dynamically engineered potentials.

Core claim

The central claim is that the time-averaged Josephson energy of a flux-driven transmon is E_J J_0(θ_ac), where J_0 is the zeroth-order Bessel function. For θ_ac ≈ 2.405 the effective potential flattens to zero, the qubit transition frequency vanishes, and the spectrum becomes gapless; for larger drives the potential revives with the opposite sign, shifting the phase-localization of the eigenstates by π. This inversion corresponds to the dynamical stabilization of the transmon at the unstable equilibrium φ = π. The paper supports this with two measurements: spectroscopy showing the qubit frequency dipping to zero and recovering, and a dispersive readout whose sign reverses exactly at the pred

What carries the argument

The workhorse is the renormalized transmon Hamiltonian H = 4E_C(N − N_g)² − E_J J_0(θ_ac) cos φ, in which the zeroth Bessel function J_0 multiplies the Josephson term. J_0 crosses zero at θ_ac ≈ 2.405 and then becomes negative, encoding both the collapse and the inversion. This form follows from the Jacobi–Anger expansion of the flux-modulated cosine and is valid when the drive frequency exceeds all transition frequencies; the rotating-wave conditions that justify it are spelled out as absence of multi-photon resonances. Equally important is the circuit implementation: a native cosine-cosine coupling between transmon and resonator that suppresses parity-allowed transitions, letting the drive

Load-bearing premise

The entire picture relies on the rotating-wave (time-averaging) approximation holding all the way through the collapse, and on the circuit being free of the multi-photon resonances that would invalidate that averaging at high drive strength.

What would settle it

Measure the qubit transition frequency as a function of drive amplitude in a symmetric-SQUID transmon with independently calibrated photon number. If the frequency does not dip to zero at the first zero of J_0, or if the dispersive readout shift fails to change sign at the same point, the collapse-and-inversion claim is falsified. Alternatively, a direct observation of a transition or a coherent population transfer at the collapse point would indicate that the rotating-wave approximation breaks down.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Strong drives can suppress the Josephson energy to zero, turning the transmon into a Cooper-pair box with restored charge sensitivity; this exposes the qubit to charge noise near the collapse point.
  • Driving through the collapse produces Landau–Zener transitions, as the instantaneous spectrum becomes gapless, which limits quantum-nondemolition readout and coherent control at high power.
  • The dispersive readout shift changes sign beyond the collapse, so readout contrast reverses; calibration of high-power readout must account for this dynamical renormalization.
  • The periodic renormalization can be used to engineer effective cos(2φ) terms, promising a fully dynamical route to a protected qubit without additional circuit elements.

Where Pith is reading between the lines

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

  • The collapse at the first zero of J_0 should be a universal feature of any symmetric-SQUID transmon under a high-frequency flux drive; a systematic study varying E_J/E_C would test whether the collapse amplitude is indeed independent of circuit parameters.
  • The observed residual drive-induced transitions (attributed to extrinsic two-level systems) suggest that the high-power dynamic range may be limited by defects in the dielectric rather than intrinsic multi-photon resonances; fabricating devices with different surface treatments could clarify this.
  • One could exploit the inverted regime to store quantum information in a metastable state localized at φ = π, but the uncontrolled offset charge near the collapse point would need to be actively stabilized; a pulsed offset-charge feedback scheme could test this.
  • The sign reversal of the dispersive shift might be used as an in-situ power calibration: the photon number at which the readout flips gives a direct measure of the zero-point phase fluctuations, without fitting the whole spectrum.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The manuscript reports measurements on a flux-tunable transmon with a native cosine-cosine coupling to a quarter-wave resonator. It claims that a strong resonator drive dynamically renormalizes the Josephson potential to E_J J_0(θ_ac) cos φ, so that at θ_ac ≈ 2.405 the potential collapses and, for larger drives, revives with opposite sign, stabilizing the transmon near φ = π — a quantum analog of the inverted pendulum. The evidence is two-fold: two-tone spectroscopy showing the qubit frequency dip to zero and then recover (Fig. 3), and a readout experiment showing a sign reversal of the dispersive shift near the same photon number (Fig. 4). The paper further claims that the circuit is free of intrinsic multi-excitation resonances due to the combination of a symmetric SQUID, cosine-cosine coupling, and large qubit–resonator detuning, supported by a Floquet spectrum shown in Fig. 2(b). The Supplementary Information contains derivations of the averaged Hamiltonian, the readout simulation, calibration procedures, and a characterization of drive-induced transitions. However, the central Floquet analysis is not actually present: SI Section III.D, which should contain the Floquet calculations, consists entirely of 'Coming soon...' placeholders.

Significance. If the claims are substantiated, this is a significant experimental advance: it would be the first demonstration of a fully collapsed and inverted Josephson potential in a superconducting circuit, with implications for high-power transmon readout, Floquet engineering of Josephson harmonics, and autonomous stabilization of π-state qubits. The spectroscopy data are striking and the Bessel-function renormalization is standard mathematics, not a fit. The engineering design — a two-mode circuit with a symmetry-protected cosine-cosine coupling — is well motivated and the authors provide a useful comparison of existing cosine-cosine coupling architectures. However, the manuscript currently omits the Floquet analysis that is explicitly used to support the inversion claim and to calculate the states entering the readout simulation (Eq. S34). The averaging conditions of the Supplementary Information are not numerically verified, and the offset-charge dependence is inferred rather than directly measured. These gaps are load-bearing and must be closed before the central claim can be accepted.

major comments (5)
  1. [SI III.D (Floquet Analysis), D1–D4] This section, which is supposed to contain the Floquet analysis of the device, consists entirely of 'Coming soon...' placeholders. The omitted material is load-bearing: Fig. 2(b) of the main text presents a computed Floquet spectrum showing the absence of multi-excitation resonances, Eq. (2) is derived using Floquet-dressed states, and SI IV.B states that the expectation values ⟨i(n)|cos φ|i(n)⟩ used in Eq. (S34) 'are obtained from a Floquet branch analysis.' Without the actual Floquet calculations, neither the claim of resilience to multi-excitation resonances nor the quantitative agreement in Fig. 4(c) can be checked. This is not a presentation issue; the central inversion claim currently rests on missing numerics.
  2. [SI Eqs. (S4)–(S5); Fig. 3] The rotating-wave/averaging conditions (S4)–(S5) are stated but never numerically evaluated for the device parameters. At the collapse point θ_ac ≈ 2.405, J_2 ≈ 0.43 and E_J/h ≈ 5.2 GHz, so the leading Floquet–Magnus correction scale (E_J J_2 ⟨cos φ⟩)^2/(2ω_d)/h is roughly 0.3 GHz, comparable to the 4E_C/h ≈ 0.41 GHz scale that defines the collapsed spectrum. These corrections could shift the apparent collapse point, prevent exact gap closure, or modify the sign-reversal condition. The spectroscopy fit in Fig. 3 is suggestive but cannot rule out such corrections because it uses the averaged Hamiltonian Eq. (1) by construction. The authors should provide a numerical check of the averaging conditions and ideally a Floquet calculation of the spectrum near collapse to support the extrapolation of the averaged model into the gapless regime.
  3. [Main text, 'single fit parameter'; SI V.B] The main text states that the spectroscopy fit 'contains a single fit parameter used for converting the resonator input power to photon number.' However, SI V.B introduces a second-degree polynomial ν₁(P_in) (Eq. S35) and a cubic spline ν₂(P_in) (Eq. S36) to correct for component nonlinearity and resonator frequency shift, before the single parameter P₀ in Eq. (S38) converts rescaled power to photon number. These are additional fitted degrees of freedom. While they are presented as calibration steps, the phrase 'single fit parameter' is misleading. The manuscript should either justify these calibrations as independently measured (e.g., from separate resonator spectroscopy) or qualify the claim to state that the physics model has one free parameter after auxiliary power calibration.
  4. [Fig. 3, Fig. 4(b); offset-charge inference] The vanishing of the spectroscopy signal near 12.5×10³ photons is attributed to restoration of charge sensitivity and charge noise, but the offset charge is not measured or controlled in the experiment. The fits in Fig. 3 bracket the data with N_g = 0 and 0.5, and the readout simulation in Fig. 4(c) averages over N_g ∈ [0, 0.5]. The qualitative agreement is reasonable, but the offset-charge distribution remains an inferred quantity. This is a legitimate interpretation, but it should be clearly labeled as such, and the authors should discuss whether a direct measurement of charge dispersion (e.g., through Ramsey or echo measurements at fixed drive power) is feasible to support the claim.
  5. [Fig. 4(a)–(c); Eq. (2) and Eq. (S34)] The readout sign reversal is presented as 'unequivocal evidence' of the inverted potential. However, the theoretical curves in Fig. 4(c) are generated with the same averaged/Floquet model that is being tested, and the only free parameter in the comparison is a y-axis scaling. The offset-charge averaging and the use of ⟨i(n)|cos φ|i(n)⟩ from the model mean that the readout measurement is a consistency check of the model, not an independent derivation of the inversion. Furthermore, the sign difference between data and theory is dismissed as a 'trivial mirroring during demodulation.' This does not invalidate the result, but it weakens the word 'unequivocal' and should be reworded. A more independent test of inversion, if available, would strengthen the claim.
minor comments (4)
  1. [Main text, Fig. 2 caption] Typo: 'Brioullin zone' should be 'Brillouin zone.' Also, 'aπphase shift' should be 'a π phase shift.'
  2. [Abstract] The abstract states the circuit is 'free of any detrimental unwanted transitions,' but Section VI and Fig. 4(b) clearly show drive-induced transitions, which the authors attribute to extrinsic TLSs and environmental modes. The phrase 'any detrimental' is too strong and contradicts the body of the paper.
  3. [SI IV.B, after Eq. (S34)] The sign convention for −Re(α) is explained only parenthetically. A short sentence stating that the demodulation sign is fixed by the experimental reference frame would make the comparison in Fig. S6 less confusing.
  4. [SI Table I] The table lists p_I, I_zpf, and I_S for the three resonator geometries but does not report the resulting coupling dilution factor p = p_I p_L. Since p is central to the effective drive amplitude, reporting p_L and p would help the reader connect the simulation to the device parameters in the main text.

Circularity Check

0 steps flagged

No significant circularity; central Bessel renormalization is derived via Jacobi-Anger, and the readout agreement is a consistency check using the same calibrated photon number. The missing Floquet section is a verification gap, not a circular step.

full rationale

The central derivation starts from the flux-driven transmon Hamiltonian and obtains the renormalized Hamiltonian Eq. (1) through the Jacobi-Anger expansion (SI Eqs. S1-S3); this is standard mathematics, not a fitted ansatz. The only physical fit parameter, P0, converts input power to photon number (SI Eq. S38), and the spectroscopy fit tests the nontrivial J0(θac) lineshape against data. The readout simulation (SI Eq. S34) then uses this same P0-calibrated photon-number axis and dressed states to compute ⟨cosφ⟩, so the agreement in Fig. 4 is a cross-check of the same model rather than an independent prediction. This is not circular by construction: the sign reversal of the readout quadrature is a separate observable that could in principle disagree, and only a y-axis scaling is freely adjusted. The more serious concern is that the Floquet analysis promised in SI III.D is entirely placeholder ('Coming soon...'), while SI IV.B states that the dressed states are 'obtained from a Floquet branch analysis.' This missing material is a major completeness and verifiability gap, but it is not an equation reducing to its own input or a fitted parameter renamed as a prediction. Self-citations to the group's prior longitudinal-coupling work are not load-bearing for the collapse/inversion claim. Overall, no specific circular step can be exhibited; the derivation chain is self-contained at the level of the averaged Hamiltonian, with the absent Floquet verification being a correctness risk rather than circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central claim rests on standard Bessel math plus several domain assumptions about the validity of averaging, the semiclassical treatment, and the effective two-mode circuit. The most fragile premise is the asserted absence of intrinsic multi-excitation resonances, whose derivation (Floquet analysis) is missing from the submission. One explicit fit parameter (P₀) plus two auxiliary rescaling fits set the power-to-photon conversion, and the readout simulation adds a free y-scale.

free parameters (5)
  • P₀ (single-photon power) = 41.2 nW/photon
    The only explicit fit parameter in Eq. (S38), converting rescaled input power to photon number. It sets the x-axis of Figs. 3 and 4 and thus the location of the collapse point.
  • ν₁(P_in) polynomial coefficients = second-degree polynomial fit
    Corrects for nonlinear power transfer through room-temperature microwave components; affects photon-number calibration (SI V.B).
  • ν₂(P_in) spline coefficients = cubic spline interpolation
    Corrects for the nonmonotonic frequency shift of the resonator with input power; affects photon-number calibration (SI V.B).
  • Y-axis scaling in readout simulation = not quantified
    The only free parameter used to match the simulated intracavity field to the measured I-quadrature data (Fig. 4c caption).
  • Offset charge N_g = sampled in [0, 0.5]
    Uncontrolled in the experiment; the fit uses N_g=0 and 0.5, and the simulation averages over the range. It influences the spectrum near the collapse point.
axioms (6)
  • standard math Jacobi-Anger expansion for cos(θac cos ωt)
    Used to decompose the driven Hamiltonian into dc and ac parts (SI Eq. S2-S3). Standard identity; not a free choice.
  • domain assumption RWA/averaging conditions (SI Eqs. S4-S5) hold up to and beyond the collapse point
    Load-bearing: justifies replacing the driven Hamiltonian by the time-averaged Eq. (1). The conditions involve higher Bessel functions J_n (n>0) and are asserted to be satisfied due to the absence of multi-excitation resonances; the supporting Floquet analysis is missing (SI III.D).
  • domain assumption Semiclassical (stiff-drive) approximation for the resonator, with transmon dressed states |i(n)> computed via Floquet analysis
    Used in the readout simulation (SI IV.B, Eqs. S30-S34). The Floquet states are said to come from a branch analysis, but the relevant SI section is 'Coming soon...'.
  • domain assumption Effective lumped-element circuit with two modes; differential SQUID mode frozen
    The device is distributed; the authors write an effective circuit after HFSS simulation (SI III.B). The separation of timescales and neglect of the differential mode is a modeling choice.
  • domain assumption Absence of intrinsic multi-excitation resonances in the device
    Central enabling premise for reaching θac≈2.405. Supported only by a Floquet spectrum (Fig. 2b) 'computed numerically' with details in the missing SI Section III.D.
  • domain assumption Observed drive-induced transitions are attributed to extrinsic TLSs and spurious modes, not intrinsic resonances
    Argued in SI Section VI based on frequency-ratio arguments and cooldown-to-cooldown variability, but the dataset does not allow definitive identification.

pith-pipeline@v1.3.0-alltime-deepseek · 30477 in / 15998 out tokens · 152452 ms · 2026-08-02T02:21:19.462053+00:00 · methodology

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read the original abstract

Superconducting circuits embedding Josephson junctions leverage microwave drives for control and measurement of quantum states. Although increasing the drive power is desirable for improving the efficiency of these operations, it eventually triggers unwanted transitions to uncontrolled states. While careful choice of circuit symmetries and parameters can mitigate these effects, the presence of spurious circuit modes spoils the resilience to high power. In this work, we engineer a transmon-resonator system free of any detrimental unwanted transitions. This resilience enables us to access drive powers at which we uncover a remarkable physical phenomenon: the collapse and inversion of the Josephson potential. Through spectroscopy and readout experiments, we confirm that the driven potential goes to zero and inverts as the power increases. The inversion corresponds to the dynamical stabilization of the transmon at its unstable equilibrium point, directly analogous to an inverted pendulum. This result reveals a new limitation of strongly driven superconducting circuits beyond drive-induced transitions. In addition, the dynamical renormalization of the Josephson potential opens up novel avenues for the control of superconducting circuits, and the autonomous stabilization of noise-resilient quantum states.

Figures

Figures reproduced from arXiv: 2607.14344 by Gary A. Steele, Marijn A. Morssink, Marius Villiers, Robin C. Dekker, Sercan Deve.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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