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arXiv · 2610.08343

Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide

T. Y. Liu·X. Y. Li·W. Y. Hu·T. Z. Luan·Cheng Shang·H. Z. Shen
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Abstract

Bound states in structured reservoirs require exact interference conditions and are therefore sensitive to imperfections in the coupling geometry. In this paper, we study a two-level giant atom coupled at multiple points to a mirror-terminated semi-infinite waveguide. The exact atom-photon bound state requires both cancellation of the outgoing radiation amplitude and dispersive matching to the atomic detuning. Generalized delay-equation dynamics, continued-pole spectra, and real-space photon fields verify this criterion for coupling-strength, position, and coupling-phase imperfections. For representative realizations, retuning restores one-, two-, and three-root responses after strength errors and one- and two-root responses after position errors. The specified position-imperfect three-root configuration fails because its $2π$ root is no longer dark, consistent with a $58.77\%$ spectral mismatch. Ensembles of 1000 realizations at each error amplitude show near-unity target-state recovery for strength errors, unity recovery of the specified one- and two-root targets but no three-root recovery for position errors, and no nontrivial exact recovery for independent phase errors. Optimized phase-imperfect responses instead retain finite linewidths. Root matching with realization-dependent control retuning therefore constitutes a compensation procedure, rather than generic passive robustness against arbitrary disorder.

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T. Y. Liu, X. Y. Li, W. Y. Hu, T. Z. Luan, Cheng Shang, H. Z. Shen. 2026-10-06. Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide. https://arxiv.org/abs/2610.08343

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