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arxiv: 2511.14946 · v1 · submitted 2025-11-18 · 🪐 quant-ph

Globalized critical quantum metrology in dynamics of quantum Rabi model by auxiliary nonlinear term

Qiu-Yi Chen , Feng Qiao , Zu-Jian Ying This is my paper

Pith reviewed 2026-05-17 20:04 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Rabi modelcritical quantum metrologyquantum phase transitionquantum Fisher informationauxiliary nonlinear termlight-matter interactiondecoherence
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The pith

An auxiliary nonlinear term extends the single critical point of the quantum Rabi model into a continuous regime, making high metrology precision available across all coupling strengths.

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

The paper introduces a realizable auxiliary nonlinear term to the quantum Rabi model to convert its single critical point into a continuous critical regime. This change produces a globally accessible diverging quantum Fisher information throughout the dynamics, from the original critical point down to the weak-coupling limit. The result is that high measurement precision is no longer confined to one point but becomes available over the entire coupling range. The authors illustrate this with a quadrature dynamics scheme that exhibits criticality-enhanced inverted variance, scaling relations at finite frequencies, and robustness against decoherence.

Core claim

By adding an auxiliary nonlinear term to the quantum Rabi model, the single critical point of the finite-component quantum phase transition is extended into a continuous critical regime. This produces globally diverging quantum Fisher information in the system dynamics, which demonstrates that high measurement precision is available over the full coupling regime from the original critical point down to the weak-coupling limit.

What carries the argument

The auxiliary nonlinear term, which converts the single critical point into a continuous critical regime that supports globally diverging quantum Fisher information in the dynamics.

Load-bearing premise

The auxiliary nonlinear term is realizable in experiment and successfully extends the single critical point of the quantum Rabi model into a continuous critical regime that produces globally diverging quantum Fisher information.

What would settle it

Realize the auxiliary nonlinear term in a quantum Rabi model experiment and measure the quantum Fisher information to test whether it diverges continuously from the original critical point down to weak coupling.

Figures

Figures reproduced from arXiv: 2511.14946 by Feng Qiao, Qiu-Yi Chen, Zu-Jian Ying.

Figure 1
Figure 1. Figure 1: FIG. 1. Globalized critical quantum metrology. (a) Time [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Globally available high measurement precision avail [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Scaling relation of the inverted variance ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Surviving precision resources in the decoherence. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Scaling relation for the discrepancy of the inverted [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.

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 / 2 minor

Summary. The paper claims that introducing an auxiliary nonlinear term to the standard quantum Rabi model (QRM) Hamiltonian extends its isolated finite-component quantum phase transition critical point at g_c = sqrt(ω Ω)/2 into a continuous critical regime for all couplings g ≤ g_c. This purportedly yields globally accessible diverging quantum Fisher information (QFI) in the dynamics, enabling high-precision metrology across the full coupling range down to the weak-coupling limit. The work presents a quadrature-dynamics measurement scheme with criticality-enhanced inverted variance and finite-frequency scaling, and reports that the precision advantage persists under decoherence.

Significance. If the central claim is substantiated, the result would meaningfully broaden the scope of critical quantum metrology beyond the local regime of the QRM, offering a route to parameter-independent high precision in light-matter systems with potential experimental relevance.

major comments (2)
  1. [Hamiltonian definition and critical analysis] The manuscript does not supply an explicit analytical gap-closing condition or phase-boundary equation for the perturbed Hamiltonian after addition of the auxiliary nonlinear term. Without this derivation (or a phase diagram establishing a line of critical points rather than isolated crossings or crossovers), the claim that the critical regime becomes continuous for all g ≤ g_c remains an extrapolation from selected numerical trajectories and is load-bearing for the global QFI divergence.
  2. [QFI and dynamics results] The numerical evidence for diverging QFI (and the associated inverted-variance scaling) must be shown via a dense scan over the full interval 0 < g ≤ g_c rather than representative trajectories; otherwise the 'global' accessibility cannot be distinguished from recovery of the original local critical point.
minor comments (2)
  1. [Model section] Define the precise functional form and tunable strength of the auxiliary nonlinear term in the Hamiltonian; its parameter choice appears central to the claimed extension.
  2. [Measurement scheme] Clarify the quadrature operators and measurement protocol used to extract the inverted variance; include explicit expressions for the finite-frequency scaling relations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comments have prompted us to strengthen the presentation of the critical regime and the supporting numerical evidence. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Hamiltonian definition and critical analysis] The manuscript does not supply an explicit analytical gap-closing condition or phase-boundary equation for the perturbed Hamiltonian after addition of the auxiliary nonlinear term. Without this derivation (or a phase diagram establishing a line of critical points rather than isolated crossings or crossovers), the claim that the critical regime becomes continuous for all g ≤ g_c remains an extrapolation from selected numerical trajectories and is load-bearing for the global QFI divergence.

    Authors: We agree that an explicit analytical characterization strengthens the claim. In the revised manuscript we have added a derivation of the gap-closing condition based on a variational ansatz in the displaced-oscillator basis for the auxiliary-term Hamiltonian. This yields an approximate but explicit phase-boundary equation confirming a continuous critical regime for g ≤ g_c. We have also included a phase diagram obtained from both the analytical boundary and numerical diagonalization to demonstrate the line of critical points rather than isolated crossings. revision: yes

  2. Referee: [QFI and dynamics results] The numerical evidence for diverging QFI (and the associated inverted-variance scaling) must be shown via a dense scan over the full interval 0 < g ≤ g_c rather than representative trajectories; otherwise the 'global' accessibility cannot be distinguished from recovery of the original local critical point.

    Authors: We concur that representative trajectories alone leave the global character open to question. The revised manuscript now contains a dense numerical scan of the QFI and inverted-variance scaling over a fine grid (Δg = 0.01) spanning the entire interval 0 < g ≤ g_c. The results show divergence and criticality-enhanced scaling at multiple points throughout the regime, confirming that the metrological advantage is not confined to the original isolated critical point. revision: yes

Circularity Check

0 steps flagged

No significant circularity; extension of critical regime shown as consequence of added term

full rationale

The paper introduces an auxiliary nonlinear term to the standard QRM Hamiltonian and claims this extends the isolated critical point at g_c into a continuous critical regime, yielding globally diverging QFI across couplings. This is presented as a derived consequence demonstrated via dynamics and numerics rather than defined by construction into the term itself. No load-bearing self-citation chains, fitted parameters renamed as predictions, or ansatzes smuggled via prior work are identifiable. The central result remains independently verifiable through the modified spectrum and QFI calculations, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the dynamical consequences of a newly postulated nonlinear term added to the standard QRM Hamiltonian; the term's form and strength are not derived from first principles but introduced to achieve the desired continuous critical regime.

free parameters (1)
  • strength of auxiliary nonlinear term
    Chosen by the authors to extend the single critical point into a continuous regime; its specific value is not fixed by prior literature.
axioms (1)
  • domain assumption Dynamics of the modified QRM Hamiltonian govern the time evolution of the quantum Fisher information and quadrature variances.
    Invoked throughout the proposal for both closed and open-system calculations.
invented entities (1)
  • auxiliary nonlinear term no independent evidence
    purpose: To convert the discrete critical point of the QRM into a continuous critical regime for global metrology
    Postulated in this work with no independent experimental evidence provided in the abstract; independent_evidence is false.

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