Radio Frequency Driven Nonlinear Dynamical Rydberg Dissipative Time Crystal

Strongly driven interacting Rydberg atomic media provides a powerful platform for exploring nonlinear and nonequilibrium dynamics under continuous driving and dissipation. In this work, we investigate the various regimes ranging from stable steady state response to emergence of bistability and self sustained oscillations in a Rydberg driven system in Cesium atomic vapor. We demonstrate that intrinsic dynamics evolve into a rich nonlinear response under radio-frequency (RF) heterodyne excitation. In the absence of RF driving, the system exhibits bistable optical transmission accompanied by a robust intrinsic oscillation, consistent with a dissipative time-crystal phase arising from the interplay between coherent excitation, dissipation, and long-range interactions.

By introducing an external RF field and employing heterodyne detection, we access a regime of double demodulation, where the intrinsic atomic oscillation mixes with the applied RF and local-oscillator frequencies. This mixing produces a hierarchy of intermodulation products and higher-order harmonics, revealing strong nonlinear coupling between the driven and self-organized dynamics of the atomic ensemble. As the RF drive strength is varied, the system transitions from frequency pulling and partial synchronization to regimes characterized by discrete spectral lines and comb-like structures, indicating the coexistence of multiple oscillatory modes. The findings highlight the potential of driven Rydberg systems as tunable platforms for studying nonequilibrium phase transitions and for developing atom-based RF sensing technologies rooted in intrinsic nonlinear dynamics.