Reciprocal Floquet thermalization in a one-dimensional Rydberg atom array

Periodically driven Floquet quantum systems hold great promise for engineering exotic quantum phases and matter, but are often limited by rapid thermalization. In this work, we propose and demonstrate a square-wave-modulated Floquet engineering protocol to steer and study the thermalization dynamics in one-dimensional Rydberg atom arrays. We identify a reciprocal Floquet thermalization mechanism, which is triggered when the combination of laser detuning and Rydberg atom interactions inversely matches the Floquet period. The level statistics show narrow peaks when the reciprocal condition is met, while thermalization is suppressed between two adjacent peaks. We extract signatures of thermalization and its suppression from the stroboscopic evolution of the atomic population. Critically, thermalization occurs in a disorder-free regime, with rapid equilibration achieved within the Rydberg lifetime and experimentally accessible initial states. Our study establishes a robust framework for exploring thermalization-to-localization transitions and designing effective Hamiltonians, and highlights the unique potential of the Rydberg atom array setting for quantum simulations.