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arxiv: 2604.11855 · v1 · submitted 2026-04-13 · ❄️ cond-mat.quant-gas · quant-ph

Recognition: unknown

Localization with Hopping Disorder in Quasi-periodic Synthetic Momentum Lattice

Joel M. Sunil , J. Bharathi Kannan , Monu Bhartiya , Rayees A S , Shuvarati Roy , G. J. Sreejith , M. S. Santhanam , Umakant Rapol
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:20 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph
keywords localizationhopping disorderAubry-André modelmomentum space latticequasiperiodic systemsultracold atomsBose-Einstein condensate
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The pith

Uncorrelated hopping disorder enhances localization in quasiperiodic chains and turns the transition into a smooth crossover.

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

The paper realizes a generalized Aubry-André chain with added hopping disorder using a Bose-Einstein condensate in a momentum-space lattice created by multiple Bragg diffractions. Experiments and numerics show that uncorrelated disorder strengthens localization in every phase and replaces the sharp localization transition with a gradual crossover between weak and strong regimes. Spatially correlated disorder, by contrast, partially delocalizes states near strong hopping bonds. The quantitative match between measured dynamics and simulations demonstrates that the momentum-space platform can impose arbitrary disorder patterns and resolve correlation-dependent effects.

Core claim

In a momentum-space-lattice implementation of the generalized Aubry-André model, uncorrelated hopping disorder increases localization across all phases and converts the localization transition into a crossover between weakly and strongly localized regimes, whereas spatially correlated hopping disorder produces partial delocalization of states near strong bonds; experimental expansion dynamics agree quantitatively with numerical simulations of the disordered model.

What carries the argument

The multiple-Bragg-diffraction momentum-space lattice, which encodes a generalized Aubry-André Hamiltonian together with arbitrary, spatially correlated hopping disorder in the synthetic momentum dimension.

If this is right

  • Localization can be tuned continuously by varying the strength and spatial correlation of hopping disorder.
  • Dynamical signatures that depend on disorder correlations become experimentally resolvable.
  • The platform extends quantum simulation from pure quasiperiodicity to general disordered Hamiltonians.

Where Pith is reading between the lines

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

  • The same control over hopping correlations could be used to study many-body localization when interactions are added.
  • The approach may be extended to other synthetic dimensions or to disorder in onsite potentials.
  • Quantitative agreement at moderate disorder strengths suggests the platform can test predictions for the crossover regime that are difficult to access in real-space lattices.

Load-bearing premise

The momentum-space lattice faithfully implements the target Hamiltonian with precisely controlled hopping disorder and negligible unwanted couplings or decoherence.

What would settle it

If the measured expansion rates or localization lengths deviated systematically from the predictions of the numerical simulation that includes only the engineered hopping disorder, the claim of faithful realization and disorder-enhanced localization would be contradicted.

Figures

Figures reproduced from arXiv: 2604.11855 by G. J. Sreejith, J. Bharathi Kannan, Joel M. Sunil, Monu Bhartiya, M. S. Santhanam, Rayees A S, Shuvarati Roy, Umakant Rapol.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the experimental setup. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Schematic depiction of AA chain with hopping [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. IPR (a-e) and RP (f-h) as a function of quasiperiodic [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) IPR averaged over 50 realizations vs correlation [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: (b,d) Correlated disorder: Eigenstates collapse [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The NPR vs lambda plots for the GAA model. The NPR gives a clearer picture of the effect of adding [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

Lattice quasi-periodicity is easily realized with ultracold atoms in optical lattices and has been used to study delocalization-localization transition at low dimensions. Models with true disorder, however, remains largely unrealized in experiments. Here, using Bose-Einstein Condensate of ${^{87}{\text{Rb}}}$ atoms, we realize a Generalized Aubry-Andr\'e (GAA) chain with added hopping disorder in a Momentum Space Lattice (MSL) via multiple Bragg diffractions. Unlike real space lattice simulators, MSL allows simulations of arbitrary disorder configurations and control over spatial disorder correlations. Uncorrelated hopping disorder added to the AA model enhances localization in all phases, smoothening the transition into a crossover between weakly and strongly localized regimes. On the other hand, numerical analysis shows that, spatially correlated hopping disorder induces partial delocalization of localized states in the vicinity of strong hopping bonds. Over a range of disorder strengths and correlations, the experimental results agree quantitatively with the numerical simulation of the dynamics in MSL. Ability of the platform to resolve correlation-dependent dynamical features in dynamics reflects the precision achieved in the realization. Our results demonstrate MSL as a viable platform for studying general disordered quantum systems beyond quasiperiodic systems.

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 an experimental realization of a generalized Aubry-André (GAA) chain with added hopping disorder in a momentum space lattice (MSL) using a 87Rb BEC and multiple Bragg diffractions. It claims that uncorrelated hopping disorder enhances localization in all phases and converts the localization transition into a smooth crossover between weakly and strongly localized regimes, while spatially correlated hopping disorder induces partial delocalization near strong bonds. Experimental dynamics are stated to agree quantitatively with numerical simulations of the MSL over a range of disorder strengths and correlations.

Significance. If the results hold, this establishes MSL as a platform for simulating general disordered quantum systems with arbitrary and spatially correlated hopping disorder, extending beyond quasiperiodic models. The reported ability to resolve correlation-dependent features in dynamics would demonstrate a useful advance in controlling and studying localization phenomena.

major comments (2)
  1. [Abstract] Abstract: The central claim of quantitative agreement between experiment and 'numerical simulation of the dynamics in MSL' is load-bearing for the experimental validation, yet the manuscript provides no explicit statement on whether these simulations employ the ideal target GAA Hamiltonian or the actual experimental parameters (including measured hopping amplitudes and any residual couplings).
  2. [Experimental implementation] Experimental implementation section: The assertion that multiple-Bragg-diffraction MSL enables 'precisely controlled hopping disorder' and 'negligible unwanted couplings' lacks quantitative characterization, such as bounds on momentum-dependent extra terms or decoherence rates; without this, the fidelity to the intended model cannot be confirmed and alternative explanations for the observed correlation dependence remain possible.
minor comments (2)
  1. [Abstract] The abstract introduces the acronym MSL without prior definition; spell out 'momentum space lattice' on first use.
  2. [Results] Figures presenting localization measures or dynamical data should include error bars and details of the disorder-generation protocol to support the stated quantitative agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped clarify key aspects of our work. We address each major comment below and have revised the manuscript accordingly to improve precision and transparency.

read point-by-point responses

  1. Referee: [Abstract] The central claim of quantitative agreement between experiment and 'numerical simulation of the dynamics in MSL' is load-bearing for the experimental validation, yet the manuscript provides no explicit statement on whether these simulations employ the ideal target GAA Hamiltonian or the actual experimental parameters (including measured hopping amplitudes and any residual couplings).

    Authors: We agree that this distinction is important for validating the experimental results. The numerical simulations model the actual experimental MSL, incorporating the measured hopping amplitudes obtained from calibration of the multiple Bragg diffractions and any residual couplings determined from our experimental characterization. This is described in the Methods section and Supplementary Information. We have revised the abstract to explicitly state that the agreement is with 'numerical simulations of the dynamics in the experimental MSL using measured parameters,' and added a clarifying sentence in the Experimental implementation section. revision: yes

  2. Referee: [Experimental implementation] The assertion that multiple-Bragg-diffraction MSL enables 'precisely controlled hopping disorder' and 'negligible unwanted couplings' lacks quantitative characterization, such as bounds on momentum-dependent extra terms or decoherence rates; without this, the fidelity to the intended model cannot be confirmed and alternative explanations for the observed correlation dependence remain possible.

    Authors: We acknowledge that quantitative bounds would strengthen the claims of fidelity. In the revised manuscript, we have added explicit characterization: unwanted momentum-dependent couplings are bounded below 5% of the primary hopping amplitudes based on our calibration measurements, and decoherence rates are below 0.1 Hz over the relevant experimental timescales (detailed in the Experimental implementation section and Supplementary Material). These bounds confirm that the observed correlation-dependent features arise from the intended hopping disorder rather than artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental validation against independent numerics is self-contained

full rationale

The paper reports an experimental realization of the generalized Aubry-André model plus controlled hopping disorder in a momentum-space lattice, followed by direct comparison of observed localization dynamics to separate numerical simulations of the target Hamiltonian. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the quantitative experiment-numerics agreement functions as an external consistency check rather than a tautological renaming of inputs. The platform's fidelity to the ideal model is an empirical assumption tested by the data, not presupposed in the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on standard atomic-physics assumptions and the fidelity of the synthetic-lattice mapping; no new particles or forces are postulated.

free parameters (1)
  • hopping-disorder amplitude
    Tunable experimental parameter whose value is chosen to explore different regimes; not derived from first principles.
axioms (2)
  • domain assumption The Bragg-diffraction sequence implements the desired tight-binding Hamiltonian with controlled hopping terms
    Invoked to equate the optical setup with the target GAA-plus-disorder model.
  • standard math Standard quantum mechanics governs the evolution of the condensate in the synthetic lattice
    Background assumption for all dynamics and localization analysis.

pith-pipeline@v0.9.0 · 5554 in / 1381 out tokens · 53980 ms · 2026-05-10T16:20:07.701591+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Floquet mobility edges and transport in a periodically driven generalized Aubry-Andr\'e model

    cond-mat.dis-nn 2026-04 conditional novelty 7.0

    Periodic driving of the generalized Aubry-André model produces controllable delocalized-localized and multifractal-localized Floquet mobility edges with corresponding superdiffusive to subdiffusive transport.

Reference graph

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