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

The anisotropic Dicke model reveals the important role that counter-rotating wave terms play in the coupling between light and two level atoms. It is intriguing to generate the model to the strongly correlated many body case, where the competition between atomic interaction and light-atom coupling will induce exotic phenomenon. In this paper, we provide a periodically driving method for engineering an anisotropic Dicke model with strong dipole-dipole interaction between atoms based on Rydberg atom arrays in cavity. By modulating the pumping laser, the ratio of counter-rotating wave terms to rotating ones could be tuned from zero to infinity. As an illustrative example, the superiority of this tunability in the adiabatic state preparation is revealed. Our engineered model provides an extensive foundation for subsequet research of quantum simulation, many-body physics and even information processing.