Engineering an anisotropic Dicke model of Rydberg atom arrays in an optical cavity with dipole–dipole interactions

The anisotropic Dicke model offers a platform for the exploration of numerous quantum many-body phenomena. Here, we propose a Floquet-engineered scheme to realize such a system with strong dipole–dipole interactions using Rydberg atom arrays in an optical cavity. By periodically modulating the microwave fields, the anisotropic parameter can be precisely controlled and tuned between zero and one, enabling the system to transition smoothly from being purely dominated by rotating-wave terms to being exclusively governed by counter- rotating wave excitations. Leveraging this tunability, we demonstrate enhanced preparation of adiabatic superradiant and superradiant solid phases where symmetry-protected energy gaps suppress undesired level crossings. Our approach, combining Rydberg interactions and cavity-mediated long-range correlations, establishes a versatile framework for the quantum simulation of light–matter interactions and the exploration of exotic many-body phases.