Engineering anisotropic Dicke model with dipole-dipole interaction for Rydberg atom arrays in an optical cavity

Abstract The anisotropic Dicke model offers a platform for exploring plentiful 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 adiabatic state preparation of 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 quantum simulation of light-matter interactions and exploration of exotic many-body phases.