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arXiv:1903.12181 · Physical Review A

Controlling excitation avalanches in driven Rydberg gases

Kai Klocke, Michael Buchhold

Published May 24, 2019• 6 citations
arXivHTMLPDF

Abstract

Recent experiments with strongly interacting, driven Rydberg ensembles have introduced a promising setup for the study of self-organized criticality (SOC) in cold atom systems. Based on this setup, we theoretically propose a control mechanism for the paradigmatic avalanche dynamics of SOC in the form of a time-dependent drive amplitude. This gives access to a variety of avalanche dominated, self-organization scenarios, prominently including self-organized criticality, as well as sub- and supercritical dynamics. We analyze the dependence of the dynamics on external scales and spatial dimensionality. It demonstrates the potential of driven Rydberg systems as a playground for the exploration of an extended SOC phenomenology and their relation to other common scenarios of SOC, such as, e.g., in neural networks and on graphs.

DOI
10.1103/physreva.99.053616

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Recent experiments with strongly interacting, driven Rydberg ensembles have introduced a promising setup for the study of self-organized criticality (SOC) in cold atom systems. Based on this setup, we theoretically propose a control mechanism for the paradigmatic avalanche dynamics of SOC in the form of a time-dependent drive amplitude. This gives access to a variety of avalanche dominated, self-organization scenarios, prominently including self-organized criticality, as well as sub- and supercritical dynamics. We analyze the dependence of the dynamics on external scales and spatial dimensionality. It demonstrates the potential of driven Rydberg systems as a playground for the exploration of an extended SOC phenomenology and their relation to other common scenarios of SOC, such as, e.g., in neural networks and on graphs.
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Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many, seemingly unrelated systems, such as forest fires, virus spreading or atomic excitation dynamics. SOC describes the buildup of large-scale and long-range spatio-temporal correlations as a result of only local interactions and dissipation. The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes. We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example: driven Rydberg atoms. To this end, we generalize existing GNN simulation approaches to predict dynamics for the internal state of the node. We show that we can accurately reproduce the MC dynamics as well as generalize along the two important axes of particle number and particle density. This paves the way to model much larger systems beyond the limits of traditional MC methods. While the exact system is inspired by the dynamics of Rydberg atoms, the approach is quite general and can readily be applied to other systems.
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From financial markets and neuronal activity in the brain to the way forest fires and diseases spread, the dynamics of complex systems are governed by critical events and emergent phenomena that are exceedingly difficult to understand or predict from underlying principles. We recently discovered that a gas of ultracold atoms continuously driven to strongly-interacting Rydberg states by an off-resonant laser field displays all the hallmarks of complex systems dynamics in a highly-controllable experimental system: (i) At early times we observe rapid growth of Rydberg excitations that has a striking correspondence with the spreading of diseases empirically observed in epidemics [1]; (ii) At later times we find that the system evolves toward a self-organised critical (SOC) state [2], a phenomenon that has been conjectured to explain the abundance of scale-invariant systems found in nature. I will discuss how these experiments can be understood in terms of an emergent atomic network that bridges the gap between mathematical models and empirical observations. This provides the opportunity to identify general principles governing non-equilibrium dynamics and to learn how seemingly universal properties emerge from microscopic physical details. References: [1] T. M. Wintermantel et al., Epidemic growth and Griffiths effects on an emergent network of excited atoms. Nature Communications 12, 103 (2021) [2] S. Helmrich et al., Signatures of self-organized criticality in an ultracold atomic gas. Nature 577, 481-486 (2020)
Efficient operation of neural networks has been linked to criticality in their underlying non-equilibrium excitation dynamics. However, obtaining experimental evidence of this conjecture remains challenging due to limited control and undersampling in biological systems. Here, we experimentally explore neural network criticality using an ultracold Rydberg gas as a highly controllable simulator. We highlight the similarity of the excitation spreading via Rydberg facilitation and the synaptic connection of spiking activity of neurons, giving rise to distinct absorbing and active phases. We systematically explore and resolve criticality criteria, including power-law scaling of excitation avalanches and the emergence of universal avalanche shape collapse. Crucially, we implement a controlled gain mechanism to compensate for atom loss, mimicking metabolic resource replenishment and stabilizing the system in a controlled non-equilibrium steady state. We find peak temporal correlations at the critical point and stochastic oscillations with dragon king avalanches in the active phase, consistent with predictions for systems orbiting criticality. Our work establishes facilitated Rydberg gases as a platform for investigating criticality, resource dynamics, and emergent oscillations in neural networks.
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