Single-Photon Scattering in a Waveguide Coupled to a Lossy or Gain Giant Atom

TL;DR

This work analyzes single-photon transport in a 1D waveguide coupled to a giant atom with a complex on-site energy, using a generalized projection formalism to obtain exact scattering amplitudes. It reveals that gain induces spectral singularities—divergences in reflection and transmission—associated with a bound state in the continuum, while an additional time-growing bound state governs long-time dynamics. Consequently, conventional time-independent scattering breaks down in the gain regime, necessitating time-dependent wave-packet analysis which, supported by simulations, shows plateau formation and eventual exponential growth. These insights advance understanding of non-Hermitian light-matom interactions in 1D photonic systems and suggest avenues for controlled emission, routing, and sensing.

Abstract

This work investigates single-photon scattering in a one-dimensional coupled-resonator waveguide coupled to 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 a lossy giant atom absorbs the incident wave, whereas a gain giant atom 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 the existence of a stationary bound state in the continuum. Due to the presence of this bound state, the conventional time-independent scattering theory proves inadequate for such a non-Hermitian system. Furthermore, we show that the system with gain always features at least one time-growing bound state, which dominates the long-time dynamics, and we verify our time-dependent theoretical predictions via numerical simulations of Gaussian wave packet scattering.

Figures (4)

• Figure 1: Schematic diagram of a loss or gain giant atom coupled to a one-dimensional coupled-resonator waveguide modeled as a tight-binding chain.
• Figure 2: Reflection rate $R$ (red solid line), transmission rate $T$ (blue dashed line), and their sum $R+T$ (green dotted line) as functions of the photon energy $\omega_k$ for $N=2$ and $N=3$ with $g/J\approx0.812$ and $\omega_a=\omega_c=0$. Panels (a) and (c) correspond to a loss rate $\gamma/J\approx-0.215$, while panels (b) and (d) correspond to a gain rate $\gamma/J\approx0.215$. Only panel (d) employs a logarithmic vertical scale.
• Figure 3: Trajectories of the complex energies (left panels) and corresponding wave numbers (right panels) as functions of the gain rate $\gamma$. Other parameters are the same as Fig. \ref{['pic2']} (c) and (d).
• Figure 4: Scattering of a Gaussian wave packet in the waveguide by a giant atom for (a) a loss rate $\gamma/J\approx-0.215$ and (b) a critical gain rate $\gamma/J\approx0.215$ satisfying Eqs. (\ref{['sp']}). The incident wave packet is initially localized at $j_c = -500$ on a lattice of $10^4$ sites, with mean wave number $k_c=1.32$ and with parameter $\alpha = 0.02$. All other parameters are the same as Fig. \ref{['pic2']} (c) and (d). The vertical scale in (b) is logarithmic.