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arxiv: 2505.06286 · v3 · submitted 2025-05-07 · ❄️ cond-mat.quant-gas · cond-mat.mes-hall· quant-ph

Observation of average topological phase in disordered Rydberg atom array

Zongpei Yue , Yu-Feng Mao , Xinhui Liang , Zhen-Xing Hua , Peiyun Ge , Yu-Xin Chao , Kai Li , Chen Jia
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Meng Khoon Tey Yong Xu Li You
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Pith reviewed 2026-05-22 17:18 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.mes-hallquant-ph
keywords average SPT phaseRydberg atom arraytopological phasestructural disorderdipolar interactionsedge modesquench dynamicshalf-filling
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The pith

Random structural disorder in a Rydberg atom array produces an observable average symmetry-protected topological phase.

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

The paper sets out to show that random offsets applied to the positions of optical tweezers create structural disorder in a half-filled Rydberg atom array, which in turn generates fluctuating long-range dipolar interactions and induces an average symmetry-protected topological phase. This phase is identified through atom-atom correlation functions that depend on dimer composition and through the persistence of edge magnetization during dynamics. A sympathetic reader would care because the result indicates that topological protection can appear in realistic, imperfect quantum systems through average symmetries rather than requiring flawless exact symmetries. The measurements compare disordered and regular lattices and track quench evolution from highly excited states.

Core claim

Here we report direct observations of disorder-induced many-body interacting average SPT phase in an atom array at half-filling, whereby random offsets to tweezer locations implement structural disorder, resulting in fluctuating long-range dipolar interactions. The induced topological phase is vindicated by the spatially resolved atom-atom correlation functions for different forms of dimer compositions. The ground state degeneracy in disordered configurations is detected and compared to the regular lattice without disorder. By probing the quench dynamics of a highly excited state, we observe markedly slower decay of edge spin magnetization in comparison to the bulk spin, consistent with the

What carries the argument

Structural disorder created by random offsets to tweezer locations, which produces fluctuating long-range dipolar interactions that stabilize the average symmetry-protected topological phase.

If this is right

  • Spatially resolved atom-atom correlations match the pattern expected for the average SPT phase under varying dimer compositions.
  • Disordered lattice configurations exhibit ground-state degeneracy that is absent in the regular lattice.
  • Quench dynamics from highly excited states produce slower decay of edge magnetization than bulk magnetization.
  • These signatures appear consistently in the presence of the structural disorder at half-filling.

Where Pith is reading between the lines

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

  • The same disorder-engineering method could be applied in other long-range interacting systems to search for average topological phases.
  • The results suggest that many existing quantum simulators with uncontrolled positional disorder may already realize average SPT phases.
  • Varying the amplitude of the random offsets would allow mapping of the disorder strength at which the average phase appears or disappears.

Load-bearing premise

The measured correlation functions for different dimer compositions and the slower edge versus bulk magnetization decay specifically demonstrate an average SPT phase rather than arising from unrelated disorder effects, finite-size artifacts, or experimental imperfections.

What would settle it

Repeating the quench-dynamics measurement and finding that edge spin magnetization decays at the same rate as bulk spin magnetization across disorder realizations would indicate the absence of protected edge modes.

Figures

Figures reproduced from arXiv: 2505.06286 by Chen Jia, Kai Li, Li You, Meng Khoon Tey, Peiyun Ge, Xinhui Liang, Yong Xu, Yu-Feng Mao, Yu-Xin Chao, Zhen-Xing Hua, Zongpei Yue.

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_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Topological phases have been extensively studied over the past two decades, primarily in quantum pure states, where they are protected by exact symmetries. Recently, numerous studies have theoretically demonstrated the existence of average symmetry-protected topological (SPT) phases in mixed quantum states, which naturally arise in real systems due to decoherence or disorder. Despite extensive experimental observations of exact SPT phases in various systems, ranging from solid-state materials to synthetic matters, average SPT phases are yet to be observed until this work. Here we report direct observations of disorder-induced many-body interacting average SPT phase in an atom array at half-filling, whereby random offsets to tweezer locations forming a lattice implement structural disorder, resulting in fluctuating long-range dipolar interactions between tweezer confined single atoms. The induced topological phase is vindicated by the spatially resolved atom-atom correlation functions for different forms of dimer compositions. The ground state degeneracy in disordered configurations is detected and compared to the regular lattice without disorder. By probing the quench dynamics of a highly excited state, we observe markedly slower decay of edge spin magnetization in comparison to the bulk spin, consistent with the presence of topologically protected edge modes in disordered lattices.

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 manuscript reports the experimental observation of a disorder-induced many-body interacting average symmetry-protected topological (SPT) phase in a Rydberg atom array at half-filling. Structural disorder is implemented via random offsets to tweezer locations, producing fluctuating long-range dipolar interactions. The central evidence consists of spatially resolved atom-atom correlation functions across different dimer compositions, a comparison of ground-state degeneracy between disordered and regular lattices, and quench dynamics in which edge spin magnetization decays more slowly than in the bulk.

Significance. If the signatures are shown to be diagnostic of average SPT order rather than generic disorder effects, the result would constitute the first experimental realization of an average SPT phase in an interacting many-body system. This would directly connect theoretical predictions for topological order in mixed states and disordered environments to a controllable quantum simulator platform, with implications for understanding decoherence-protected topology and for engineering robust edge modes in realistic settings.

major comments (2)
  1. [Abstract and correlation measurements] Abstract and results on correlation functions: the claim that spatially resolved atom-atom correlations for varying dimer compositions directly vindicate an average SPT phase lacks an explicit ensemble-averaged topological invariant (such as a disorder-averaged string order parameter) or a quantitative comparison to a symmetry-broken control; without this, the distinction from generic disorder-induced correlations or localization remains unresolved.
  2. [Quench dynamics] Quench dynamics section: the observation of markedly slower edge versus bulk spin magnetization decay is presented as consistent with topologically protected edge modes, yet the manuscript does not report a control that breaks average symmetry while preserving disorder strength; this leaves open whether the slower decay arises from average SPT protection or from finite-size boundary pinning and imperfect initialization.
minor comments (2)
  1. [Methods] The description of statistical analysis, error bars, and data exclusion criteria is insufficiently detailed to allow independent assessment of the robustness of the reported correlations and decay rates.
  2. [Figures] Figure captions and legends should explicitly indicate which panels show ensemble averages over disorder realizations versus single realizations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have incorporated revisions to strengthen the evidence for the average SPT phase.

read point-by-point responses

  1. Referee: [Abstract and correlation measurements] Abstract and results on correlation functions: the claim that spatially resolved atom-atom correlations for varying dimer compositions directly vindicate an average SPT phase lacks an explicit ensemble-averaged topological invariant (such as a disorder-averaged string order parameter) or a quantitative comparison to a symmetry-broken control; without this, the distinction from generic disorder-induced correlations or localization remains unresolved.

    Authors: We thank the referee for this suggestion. The spatially resolved correlations across dimer compositions were intended to capture the robustness under structural disorder, but we agree that an explicit ensemble-averaged topological invariant strengthens the claim. In the revised manuscript we have added the disorder-averaged string order parameter, which remains finite across the ensemble of disordered configurations and vanishes in the trivial phase, providing a direct quantitative distinction from generic disorder or localization effects. For the symmetry-broken control, the regular lattice already serves as a reference without disorder; we have further added a theoretical comparison to a symmetry-broken disordered model in the supplement to address this point explicitly. revision: yes

  2. Referee: [Quench dynamics] Quench dynamics section: the observation of markedly slower edge versus bulk spin magnetization decay is presented as consistent with topologically protected edge modes, yet the manuscript does not report a control that breaks average symmetry while preserving disorder strength; this leaves open whether the slower decay arises from average SPT protection or from finite-size boundary pinning and imperfect initialization.

    Authors: We acknowledge that a direct experimental control breaking average symmetry at fixed disorder strength would be ideal. Such a control is experimentally demanding in the current Rydberg platform, as it would require additional symmetry-breaking fields that risk altering the interaction disorder. Instead, we have revised the quench-dynamics section and supplementary material to include finite-size scaling of the edge decay, improved initialization fidelity checks, and comparisons to non-topological disordered regimes. These additions show that the slower edge decay persists beyond finite-size effects and is absent when average symmetry is explicitly broken in the model, supporting the topological interpretation. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental observation grounded in direct measurements

full rationale

The paper reports an experimental observation of a disorder-induced average SPT phase in a Rydberg atom array, supported by measured atom-atom correlation functions across dimer compositions, comparisons of ground-state degeneracy with and without disorder, and quench dynamics showing slower edge versus bulk magnetization decay. No theoretical derivation chain exists that reduces predictions or invariants to fitted parameters, self-definitions, or self-citation load-bearing steps; the claims rest on empirical data from the physical setup rather than any closed-loop mathematical construction. This is a standard honest experimental finding with independent content from the measurements themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum mechanics and Rydberg interaction models with no new free parameters or invented entities introduced in the abstract; the interpretation of data as evidence for average SPT is the key step.

axioms (1)
  • standard math Standard assumptions of quantum mechanics, Rydberg atom physics, and optical tweezer control.
    The experiment builds on established techniques for trapping and interacting Rydberg atoms.

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Forward citations

Cited by 3 Pith papers

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

  1. Bridging Krylov Complexity and Universal Analog Quantum Simulator

    quant-ph 2026-05 unverdicted novelty 6.0

    Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.

  2. Many-Body Amplified Nonclassical Photon Emission in Cavity-Coupled Atomic Arrays

    quant-ph 2026-04 unverdicted novelty 6.0

    Cavity-mediated many-body interactions in atomic arrays with programmable phase φ enable switching between high-purity single-photon emission (φ=0) and bright photon-pair bundles (φ=π).

  3. Recent progress on disorder-induced topological phases

    cond-mat.dis-nn 2026-01 unverdicted novelty 2.0

    A review summarizing theoretical and experimental progress on disorder-induced topological phases including TAIs, quasiperiodic extensions, non-Hermitian systems, and many-body realizations.

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