Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide
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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BibTeX
@misc{liu2026perfect,
title = {{Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide}},
author = {T. Y. Liu and X. Y. Li and W. Y. Hu and T. Z. Luan and Cheng Shang and H. Z. Shen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08343},
eprint = {2610.08343},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08343},
}
RIS
TY - UNPB
TI - Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide
AU - T. Y. Liu
AU - X. Y. Li
AU - W. Y. Hu
AU - T. Z. Luan
AU - Cheng Shang
AU - H. Z. Shen
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08343
UR - https://arxiv.org/abs/2610.08343
AB - 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.
ER -