Title: Early warning signals of the tipping point in strongly interacting Rydberg atoms

Abstract: The identification of tipping points is essential for prediction of collapses or other sudden changes in complex systems. Applications include studies of ecology, thermodynamics, climatology, and epidemiology. However, detecting early signs of proximity to a tipping is made challenging by complexity and non-linearity. Strongly interacting Rydberg atom gases offer a model systems that offer both complexity and non-linearity, including phase transition and critical slowing down. Here, via an external probe we observe prior warning of the proximity of a phase transition of Rydberg thermal gases. This warning signal is manifested as a cessation of the variance growth with increasing probe intensity. We also observed the dynamics of the critical slowing down behavior versus different time scales, driving intensities, and atomic densities, thus providing insights into the study of a Rydberg atom system's critical behavior. Our experiment suggests that the full critical slowing down dynamics of strongly-interacting Rydberg atoms can be probed systematically, thus providing a benchmark with which to identify critical phenomena in quantum many-body systems.