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Abstract

In this thesis I present experimental and theoretical results showing that an ultracold gas under laser excitation to Rydberg states offers a controllable platform for studying the interesting complex dynamics that can emerge in driven-dissipative systems. The findings can be summarized according to the following three main insights: (i) The discovery of self-organized criticality (SOC) in our Rydberg system under facilitated excitation via three signatures: self-organization of the density to a stationary state; scale invariant behavior; and a critical response in terms of power-law distributed excitation avalanches. Additionally, we explore a mechanism inherent to our system which stabilizes the SOC state. We further investigate this stabilization via a controlled, variable driving of the system. These analyses can help answer the question of why scale invariant behavior is so prevalent in nature. (ii) A striking connection between the power-law growth of the Rydberg excitation number and epidemic spreading is found. Based on this, an epidemic network model is devised which efficiently describes the collective excitation dynamics. The importance of heterogeneity in the emergent Rydberg network and associated Griffiths effects provide a way to explain the observation of non-universal power laws. (iii) A novel quantum cellular automata implementation is proposed using atomic arrays together with multifrequency laser fields. This provides a natural framework to study the relation between microscopic processes and global dynamics, where special rules are found to generate entangled states with applications in quantum metrology and computing.