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arxiv: 2508.09338 · v1 · submitted 2025-08-12 · 🪐 quant-ph · cond-mat.mes-hall

Oscillating bound states in waveguide-QED system with two giant atoms

F. J. L\"u , W. Z. Jia This is my paper

Pith reviewed 2026-05-18 22:49 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords bound states in the continuumgiant atomswaveguide QEDdark statesoscillating bound stateslight-matter interactionsquantum information processing
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The pith

Two giant atoms coupled to a waveguide support both static and oscillating bound states in the continuum.

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

This paper examines bound states in the continuum for two identical two-level giant atoms coupled to a one-dimensional waveguide. It derives general dark-state conditions from the system Hamiltonian to show how coupling configurations and atomic parameters suppress decay. Analysis of long-time dynamics classifies the bound states into static ones with unchanging atomic excitations and oscillating ones featuring periodic exchanges of excitations between atoms and photons or between the two atoms. Under specific conditions additional quasi-dark modes appear, allowing the oscillating states to include more harmonic frequency components. These behaviors connect directly to the underlying light-matter interactions and indicate possible uses in quantum information processing.

Core claim

The system supports static bound states with persistent atomic excitations, and oscillating bound states with periodic atom-photon or atom-atom excitation exchange. Under certain conditions, oscillating bound states can contain more harmonic components owing to the emergence of additional quasi-dark modes.

What carries the argument

General dark-state conditions derived from the Hamiltonian, which classify bound states according to coupling configurations, atomic parameters, and resulting dynamical behaviors.

If this is right

  • Static bound states maintain constant atomic excitations without decay into the waveguide.
  • Oscillating bound states produce periodic atom-photon or atom-atom excitation exchange over time.
  • Additional quasi-dark modes introduce multiple harmonic components into the dynamics of certain oscillating states.
  • These features position the system as a platform for controlled light-matter interactions in quantum technologies.

Where Pith is reading between the lines

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

  • The classification of static versus oscillating behaviors could guide the design of time-dependent quantum gates using similar multi-atom setups.
  • Observing the extra harmonics from quasi-dark modes in experiment would test the link between dark-state conditions and dynamical complexity.
  • Extending the dark-state analysis to non-identical atoms or curved waveguides might uncover additional bound-state types.

Load-bearing premise

The analysis relies on specific coupling configurations and atomic parameters that permit decay suppression to be derived directly from the Hamiltonian.

What would settle it

Long-time measurements showing either constant atomic excitations or undamped periodic oscillations in atomic and photon populations at frequencies set by the system parameters would confirm the predicted bound states.

Figures

Figures reproduced from arXiv: 2508.09338 by F. J. L\"u, W. Z. Jia.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of two giant atoms coupled to an open waveg [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The Ω- [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Static bound states for two-giant-atom systems with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Time evolution of the atomic excitation probabilities of two separate giant atoms under parameters for oscillating [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Long-time evolution of the field intensity [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Time evolution of the atomic excitation probabili [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Long-time evolution of the field intensity [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) The Ω- [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) The Ω- [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

We study the bound states in the continuum (BIC) in a system of two identical two-level giant atoms coupled to a one-dimensional waveguide. By deriving general dark-state conditions, we clarify how coupling configurations and atomic parameters influence decay suppression. Through analysis of the long-time dynamical behaviors of atoms and bound photons, we carry out a detailed classification of bound states and explore the connections between these dynamical behaviors and the system's intrinsic light-matter interactions. The system supports static bound states with persistent atomic excitations, and oscillating bound states with periodic atom-photon or atom-atom excitation exchange. Under certain conditions, oscillating bound states can contain more harmonic components owing to the emergence of additional quasi-dark modes, rendering them promising platforms for high-capacity quantum information processing. These findings advance the understanding of BIC in waveguide quantum electrodynamics with multiple giant atoms and reveal their prospective applications in quantum technologies.

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

1 major / 2 minor

Summary. The paper studies bound states in the continuum (BIC) for two identical two-level giant atoms coupled to a one-dimensional waveguide. It derives general dark-state conditions from the system Hamiltonian to clarify how coupling configurations and atomic parameters suppress decay. Long-time dynamical analysis classifies the bound states into static types with persistent atomic excitations and oscillating types with periodic atom-photon or atom-atom excitation exchange; under certain conditions, additional quasi-dark modes allow oscillating states to contain more harmonic components, with suggested applications to high-capacity quantum information processing.

Significance. If the results hold, the work provides a useful dynamical classification of bound states in a two-giant-atom waveguide-QED system and connects these behaviors to the underlying light-matter interactions. The emphasis on tunable oscillating states with extra harmonics could inform designs for quantum technologies, extending standard waveguide-QED treatments to giant atoms with multiple coupling points.

major comments (1)
  1. [Derivation of dark-state conditions and subsequent dynamical classification] The central classification of static versus oscillating bound states rests on algebraic conditions for zero-decay eigenmodes obtained from the two-giant-atom Hamiltonian. These conditions on the coupling phases e^{ikx} and atomic detuning hold exactly only when inter-atom separation and individual coupling-point spacings satisfy discrete relations (e.g., multiples of λ/4) that produce perfect destructive interference. For generic separations the imaginary part of the self-energy is not nulled, so the claimed general dark states become decaying resonances; this restriction propagates to the long-time dynamics and the attribution of extra harmonic components to quasi-dark modes.
minor comments (2)
  1. [Abstract] The abstract states that the system supports static and oscillating bound states but does not indicate the range of validity of the dark-state conditions; the main text should explicitly state the discrete separation requirements.
  2. [Hamiltonian and dark-state derivation] Notation for the coupling phases and self-energy should be introduced with a clear reference to the Hamiltonian before the dark-state conditions are derived.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below, clarifying the scope of our derivations while acknowledging the need for greater precision on the conditions for exact dark states.

read point-by-point responses

  1. Referee: [Derivation of dark-state conditions and subsequent dynamical classification] The central classification of static versus oscillating bound states rests on algebraic conditions for zero-decay eigenmodes obtained from the two-giant-atom Hamiltonian. These conditions on the coupling phases e^{ikx} and atomic detuning hold exactly only when inter-atom separation and individual coupling-point spacings satisfy discrete relations (e.g., multiples of λ/4) that produce perfect destructive interference. For generic separations the imaginary part of the self-energy is not nulled, so the claimed general dark states become decaying resonances; this restriction propagates to the long-time dynamics and the attribution of extra harmonic components to quasi-dark modes.

    Authors: We agree that exact nulling of the imaginary part of the self-energy, and thus true bound states in the continuum, occurs only when the coupling phases satisfy the discrete relations corresponding to separations that are multiples of λ/4 (or equivalent). Our derivation obtains the algebraic conditions on phases and detuning from the Hamiltonian precisely to identify those regimes where decay is fully suppressed. The term 'general' in the manuscript refers to the form of these conditions across different coupling configurations, not to their validity for arbitrary separations. For generic separations the states are resonances, as the referee notes, and our long-time dynamical classification and discussion of quasi-dark modes apply specifically to the parameter regimes where the derived conditions are satisfied. We will revise the manuscript to state explicitly that perfect destructive interference and exact dark states require these discrete separations, while retaining the general algebraic framework for when such states exist. This clarification will also be added to the discussion of oscillating states and extra harmonic components. revision: partial

Circularity Check

0 steps flagged

Derivations from standard Hamiltonian are self-contained with no circular reductions

full rationale

The paper begins with the standard waveguide-QED Hamiltonian for two identical two-level giant atoms and derives dark-state conditions algebraically by setting the imaginary part of the self-energy to zero. Classification into static and oscillating bound states follows from solving the resulting eigenmodes and examining long-time atomic and photonic dynamics. No parameters are fitted to data and then relabeled as predictions, no self-citation chains carry the central claims, and no ansatz or uniqueness theorem is smuggled in from prior author work. The algebraic conditions on coupling phases and detunings are obtained directly from the equations of motion without reducing to the input assumptions by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard waveguide-QED modeling assumptions and parameter choices for coupling configurations; no new entities are postulated.

free parameters (1)
  • coupling configurations and atomic parameters
    These are varied to derive general dark-state conditions and influence decay suppression.
axioms (1)
  • domain assumption Two identical two-level giant atoms coupled to a one-dimensional waveguide
    This is the foundational model setup invoked throughout the abstract for deriving bound-state conditions.

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Reference graph

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