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

TL;DR

This paper presents a theoretical framework for controlling quantum emission in one-dimensional Lieb lattices, enabling tunable dynamics from flat-band coherence to narrow-band dissipation.

Contribution

It introduces a unified model linking flat-band physics to narrow-band platforms, with explicit scaling laws for emission control.

Findings

Derived scaling laws for tuning spontaneous emission.

Demonstrated continuous crossover from non-Markovian to Markovian dynamics.

Provided a practical toolkit for quantum emission engineering in structured photonic systems.

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 wavefunction 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 moir$\rm\acute{e}$ photonic crystals, offering a practical toolkit for interpreting experiments and engineering quantum emission in structured photonic environments.