Polaron-Polariton in subwavelength atomic arrays

We study how atomic motion modifies the collective dipolar excitations and light–matter interactions of subwavelength atomic arrays. Working in the Lamb–Dicke regime, we derive an effective polaron–polariton description that captures correlated spin–phonon dynamics beyond common "fast" and "frozen" motion limits. By comparing analytic polaron predictions with numerical simulations of transport and reflectivity, we reveal regimes where collective excitations remain surprisingly robust against motion, as well as conditions where phonon emission strongly boosts decay of subradiant states or facilitates populating them. Our results show how atomic center-of-mass motion alters the open-system dynamics of atomic arrays and suggest new ways to harness subradiant modes and optomechanical effects in emerging experiments.