  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.
