  Abstract Far-from equilibrium dynamics that lead to self-organization are
highly relevant to complex dynamical systems not only in physics, but also in
life-, earth-, and social sciences. It is challenging however to find systems
with sufficiently controllable parameters that allow quantitatively modelling
of emergent properties. Here, we study a non-equilibrium phase transition and
observe signatures of self-organized criticality in a dilute thermal vapour of
atoms optically excited to strongly interacting Rydberg states.
Electromagnetically induced transparency (EIT) provides excellent control over
the population dynamics and enables high-resolution probing of the
driven-dissipative dynamics, which also exhibits phase bistability. Increased
sensitivity compared to previous work allows us to reconstruct the complete
phase diagram including in the vicinity of the critical point. We observe that
interaction-induced energy shifts and enhanced decay only occur in one of the
phases above a critical Rydberg population. This limits the application of
generic mean-field models, however a modified, threshold-dependent approach is
in qualitative agreement with experimental data. Near threshold, we observe
self-organized dynamics in the form of population jumps that return the density
to a critical value.
