Local vs non-local dynamics in cavity-coupled Rydberg atom arrays

Locality is a transversal principle that governs quantum dynamics of many-body systems. However, for cavity embedded systems, such fundamental notion is hindered by the presence of non-local cavity modes, leaving space for new possible dynamical behaviors. Here, we investigate the real-time dynamics of low-energy excitations in one dimensional Rydberg atom arrays coupled to a global cavity mode. We derive an effective description in terms of a Tavis-Cummings-Ising model, whose phase diagram features ordered and disordered phases. The non-local nature of the cavity mode drastically affects the emergent meson and string dynamics. Mesons hybridize coherently with the cavity photons, leading to composite meson-polaritons excitations. Strings, differently from local interacting theories, acquire a finite kinetic energy thanks to non-local cavity-mediated interactions between the underlying domain-walls. We then conclude by presenting a new concrete experimental blueprint for a cavity QED Rydberg atom array simulator where the physics outlined in this work can be realized.