[論文レビュー] Localization and scattering of a photon in quasiperiodic qubit arrays

Xinyin Zhang, Yongguan Ke+5 more|arXiv (Cornell University)|Jan 29, 2026

Quantum Mechanics and Non-Hermitian Physics被引用数 0

ひとこと要約

The paper studies how a photon scatters in a waveguide coupled to quasiperiodically spaced qubit arrays and reveals a continuum of localized subradiant states and a mobility edge in transmission.

ABSTRACT

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.

研究の動機と目的

• Understand how quasiperiodic spacing affects localization of single excitations in a qubit array coupled to a waveguide.
• Link excitation localization properties to photon scattering and transmission.
• Identify how quasiperiodic strength influences subradiant states and transmission features.
• Characterize the existence of a mobility edge in the transmission spectrum.

提案手法

• Three-part Hamiltonian: H_R = H_A + H_F + H_I for quasiperiodic qubit spacings.
• Transfer-matrix method in real space to obtain reflection and transmission of a single photon.
• Green function method in momentum space to relate scattering to subradiant eigenstates via G(ω) and H_eff.
• Large-period modulation approximations to connect localized/delocalized states to flat/curved inverse energy bands.
• Fraction of localized states derived from periodic approximation using Fibonacci/Renyi-like rational approximants.

実験結果

リサーチクエスチョン

• RQ1 How does quasiperiodic modulation affect localization of single-excitation states in a waveguide QED system?
• RQ2 What is the relationship between localized/delocalized subradiant states and photon reflection/transmission?
• RQ3 Can a mobility edge in transmission emerge in a quasiperiodic WQED system, and how does it depend on system size and frequency?

主な発見

• Localized subradiant states form a continuum around the resonant frequency as quasiperiodic strength grows.
• The fraction of localized states can reach (3−√5)/2 when the modulation frequency is (1+√5)/2.
• Localized states block photon transmission at resonance, while delocalized subradiant states can support transmission.
• The overall reflection increases with quasiperiodic strength due to enhanced localization.
• There exists a transmission mobility edge, showing localization transition as photon frequency changes and system size varies.
• The two analytical methods (transfer-matrix and Green function) yield identical results, linking scattering to subradiant-state properties.