Exploring self-organized criticality in driven cold gases

Recent experiments with strongly interacting, driven Rydberg ensembles have unambiguously demonstrated aspects of self-organized criticality (SOC) in the dynamics of the Rydberg pseudospins. Such experiments present a means for precise control of the microscopics from which SOC emerges and offer a new playground for the exploration of SOC with cold atoms. Here we simulate the dynamics of such Rydberg ensembles through numerical integration of the corresponding effective field theory. In particular, we discuss an experimentally feasible loading scheme by which the prototypical avalanche dynamics can be maintained and controlled. This gives access to three distinct dynamical regimes: i) a subcritical regime of periodically occurring avalanches ii) an extended SOC regime featuring scale invariance and fractal real-space structures, and iii) a supercritical regime with constant avalanche activity. This relates Rydberg atom dynamics with SOC in neural networks, where similar scenarios have been observed. We sharpen this connection by analyzing the dependence of SOC on the size and dimensionality of the ensembles.