  It is challenging to probe ergodicity breaking trends of a quantum many-body
system when dissipation inevitably damages quantum coherence originated from
coherent coupling and dispersive two-body interactions. Rydberg atoms provide a
test bed to detect emergent exotic many-body phases and non-ergodic dynamics
where the strong Rydberg atom interaction competes with and overtakes
dissipative effects even at room temperature. Here we report experimental
evidence of a transition from ergodic towards ergodic breaking dynamics in
driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by
the long-time phase oscillation, which is attributed from the formation of
Rydberg excitation clusters in limit cycle phases. The broken symmetry in the
limit cycle is a direct manifestation of many-body interactions, which is
verified by tuning atomic densities in our experiment. The reported result
reveals that Rydberg many-body systems are a promising candidate to probe
ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of
non-equilibrium phase transition.
