Localization and scattering of a photon in quasiperiodic qubit arrays

We study the localization and scattering of a single photon in a waveguide coupled to qubit arrays with quasiperiodic spacings. As the quasiperiodic strength increases, localized subradiant states with extremely long lifetime appear around the resonant frequency and form a continuum band. In stark contrast to the fully disordered waveguide QED where all states are localized, we analytically find that the fraction of localized states is up to \(3-sqrt{5}\)/2 when the modulation frequency is \(1+sqrt{5}\)/2. The localized and delocalized states can be related to excitation in flat and curved inverse energy bands under the approximation of large-period modulation. When the quasiperiodic strength is weak, an extended subradiant state can support the transmission of a photon. However, as the quasiperiodic strength increases, localized subradiant states can completely block the transmission of a single photon in resonance with the subradiant states, and enhance the overall reflection. At a fixed quasiperiodic strength, we also find mobility edge in transmission spectrum, below and above which the transmission is either turned on and off as system size increases. Our work give new insights into the localization in non-Hermitian systems.