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This paper presents a theoretical analysis of single-photon scattering dynamics in a waveguide coupled to a "giant atom," specifically examining how non-Hermitian effects like loss and gain alter transmission coefficients and create spectral singularities. The study derives analytical expressions for these phenomena and demonstrates that gain regimes support time-growing bound states that invalidate conventional time-independent scattering theories, requiring new numerical verification methods.
Single-Photon Scattering in a Waveguide Coupled to a Giant Atom with Loss or Gain
arXiv:2512.17456v2 Announce Type: replace Abstract: This work investigates single-photon scattering in a one-dimensional coupled-resonator waveguide interacting with a giant atom with a complex on-site energy. Within the generalized projection operator formalism, we derive analytical expressions for the scattering coefficients. We find that the interference effects of a giant atom can decouple the waveguide from the atom under specific conditions, resulting in perfect transmission, distinguishing it from a small atom. Otherwise, a giant atom with loss absorbs the incident wave, whereas a giant atom with gain not only amplifies the incident wave but also leads to scattering divergence at certain energies, corresponding to spectral singularities. We explore the critical scattering dynamics associated with these singularities, and attribute the persistent wave emission to a spectral-singularity state. Furthermore, we show that the system with gain supports at least one time-growing bound state, which dominates the long-time dynamics. Due to the presence of these generalized bound states, the conventional time-independent scattering theory proves inadequate for such a non-Hermitian system in the gain regime. We verify our time-dependent theoretical predictions via numerical simulations of Gaussian wave packet scattering.
Abstract:This work investigates single-photon scattering in a one-dimensional coupled-resonator waveguide interacting with a giant atom with a complex on-site energy. Within the generalized projection operator formalism, we derive analytical expressions for the scattering coefficients. We find that the interference effects of a giant atom can decouple the waveguide from the atom under specific conditions, resulting in perfect transmission, distinguishing it from a small atom. Otherwise, a giant atom with loss absorbs the incident wave, whereas a giant atom with gain not only amplifies the incident wave but also leads to scattering divergence at certain energies, corresponding to spectral singularities. We explore the critical scattering dynamics associated with these singularities, and attribute the persistent wave emission to a spectral-singularity state. Furthermore, we show that the system with gain supports at least one time-growing bound state, which dominates the long-time dynamics. Due to the presence of these generalized bound states, the conventional time-independent scattering theory proves inadequate for such a non-Hermitian system in the gain regime. We verify our time-dependent theoretical predictions via numerical simulations of Gaussian wave packet scattering.
arXiv:2512.17456 [quant-ph]
(or arXiv:2512.17456v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.17456 Focus to learn more arXiv-issued DOI via DataCite
Phys. Scr. 101, 445106 (2026)
https://doi.org/10.1088/1402-4896/aebb01 Focus to learn more DOI(s) linking to related resources
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