Structured Emission and Entanglement Dynamics of a Giant Atom in a Photonic Creutz Ladder

We explore the spontaneous emission dynamics of a giant atom coupled to a photonic Creutz ladder, focusing on how flat-band frustration and synthetic gauge fields shape atom–photon interactions. The Creutz ladder exhibits perfectly flat bands, Aharonov–Bohm caging, and topological features arising from its nontrivial hopping structure. By embedding the giant atom at multiple spatially separated sites, we reveal interference-driven emission control and the formation of nonradiative bound states. Using both spectral and time-domain analyses, we uncover strong non-Markovian dynamics characterized by persistent oscillations, long-lived entanglement, and recoherence cycles. The emergence of bound-state poles in the spectral function is accompanied by spatially localized photonic profiles and directionally asymmetric emission, even in the absence of band dispersion. Calculations of von Neumann entropy and atomic purity confirm the formation of coherence-preserving dressed states in the flat-band regime. Furthermore, the spacetime structure of the emitted field displays robust zig-zag interference patterns and synthetic chirality, underscoring the role of geometry and topology in photon transport. Our results demonstrate how flat-band photonic lattices can be leveraged to engineer tunable atom–photon entanglement, suppress radiative losses, and create structured decoherence-free subspaces for quantum information applications.