Perfect Bound States and non-Markovian Dynamics for Imperfect Giant Atoms in a Semi-Infinite Waveguide
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4587501127, G8315128151
OpenAlex ID: W7220963301