Breakdown of Linearized Dispersion in Waveguide QED

Exploring interactions between quantum emitters and guided photons, waveguide quantum electrodynamics (wQED) offers a versatile platform for quantum simulation and quantum interconnect. To simplify the quantized light-matter interactions, a linearized dispersion approximation (LDA) was widely used in wQED under the conditions of weak coupling and narrow photonic bandwidth. However, a growing number of strong-coupling wQED experiments have called the validity of LDA into question. Here, by investigating giant atoms coupled to a semi-infinite waveguide, we propose a principle to judge the validity of LDA. We find that the decoherence of the atoms exhibits rich dynamical behaviors determined by different numbers of bound states in and out of the continuum (BICs and BOCs) formed in the energy spectrum of the total atom-photon system. Based on this, we show that despite the LDA can partially preserve some of BICs, it completely erases BOCs. This causes the dominant role of LDA in the atomic dynamics to break down. Providing a physical insight into the validity of LDA, our results lay a firm foundation for exploring fundamental physics and its application frontier in strong-coupling wQED platforms.