Reciprocal Floquet Thermalization in one dimensional Rydberg atom array

Periodically driven Floquet quantum systems hold great promise for engineering exotic quantum phases and matter, but are often hindered by thermalization. In this work, we propose and demonstrate a square wave modulated Floquet engineering protocol to steer and study thermalization dynamics in one dimensional Rydberg atom arrays. We identify a novel reciprocal Floquet thermalization mechanism, which is triggered when combination of laser detuning and the Rydberg atom interaction and Floquet period are reciprocal pairs. This leads to many-body quantum chaos, evidenced by level spacing distribution and inverse participation ratio. Signatures of the thermalization can be found from stroboscopic evolution of the atom population, which saturates to that of the thermal ensemble state. Critically, the thermalization occurs in the disorder-free regime, with rapid equilibration achieved within the Rydberg lifetime and experimentally accessible initial states. Our study establishes a robust framework for manipulating out-of-equilibrium dynamics in many-body interacting spin systems. This approach opens pathways for exploring thermalization-to-localization transitions and designing effective Hamiltonians, and highlight the unique potential of the Rydberg atom array setting for quantum simulation.