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    From flat to narrow bands: Engineering quantum emission in a one-dimensional Lieb lattice

    Zhiyong Liu, Yue Sun, and Ying Hu*

    • State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

    • *Contact author: huying@sxu.edu.cn

    Phys. Rev. A 113, 053713 – Published 11 May, 2026

    DOI: https://doi.org/10.1103/scl3-s18t

    Abstract

    We develop a comprehensive theoretical framework that unifies quantum emission dynamics in one-dimensional Lieb lattices, bridging the gap between ideal flat-band coherence and realistic narrow-band dissipation. By coupling an emitter to sublattices with finite flat-band wave-function overlap, we activate a collective, size-independent interaction fundamentally distinct from dispersive-band processes. Controllably breaking lattice symmetry transforms the flat band into a narrow dispersive band, enabling a continuous crossover from non-Markovian to Markovian dynamics governed by the competition between coupling strength and engineered bandwidth. Crucially, we derive explicit scaling laws that provide a quantitative blueprint for tuning spontaneous emission from coherent trapping to Markovian decay. Our work provides a unified framework that connects idealized flat-band physics to emerging narrow-band platforms such as moiré photonic crystals, offering a practical toolkit for interpreting experiments and engineering quantum emission in structured photonic environments.

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