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Physical Review Research

Griffiths phase in a facilitated Rydberg gas at low temperatures

Daniel Brady, Jana Bender, Patrick Mischke, Simon Ohler, Thomas Niederprüm, Herwig Ott, Michael Fleischhauer

Published Jan 16, 2024• 6 citations
Publisher

Abstract

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. Motivated by experiments, we theoretically analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. In the high-temperature limit, a homogeneous mean-field behavior is recovered, while characteristic effects of heterogeneity can be seen in a frozen gas. At high temperatures, the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdős-Rényi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdős-Rényi network taking into account Rydberg blockade. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013052

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arXiv:2007.07697•Nature Communications•Jan 4, 2021•25 citations
The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. Motivated by experiments, we theoretically analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. In the high-temperature limit, a homogeneous mean-field behavior is recovered, while characteristic effects of heterogeneity can be seen in a frozen gas. At high temperatures, the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdős-Rényi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdős-Rényi network taking into account Rydberg blockade. Published by the American Physical Society 2024
The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte-Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. In this paper, we analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. While in the high-temperature limit a homogeneous mean-field behaviour is recovered, characteristic effects of heterogeneity can be seen in a frozen gas. At large temperatures the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdös-Renyi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdös-Renyi network taking into account Rydberg blockade. Furthermore, we expand upon an existing macroscopic Langevin equation to more accurately describe the density of Rydberg atoms in the frozen and finite temperature regimes.
The excitation spread caused by Rydberg facilitation in a gas of laser-driven atoms is an interesting model system for studying epidemic dynamics. We derive a mean-field approach to describe this facilitation process in the limits of high and low temperatures, which takes into account Rydberg blockade and the network character of excitation spreading in a low-temperature gas. As opposed to previous mean-field models, our approach accurately predicts all stages of the facilitation dynamics from the initial fast epidemic growth, an extended saturation period, to the final relaxation phase.
Understanding the universal properties of nonequilibrium phase transitions of spreading processes is a challenging problem. This applies in particular to irregular and dynamically varying networks. We here investigate an experimentally accessible model system for such processes, namely, the absorbing-state phase transition (ASPT) of Rydberg-excitation spreading, known as Rydberg facilitation, in a laser-driven gas of mobile atoms. It occurs on an irregular graph, set by the random atom positions in the gas, and, depending on temperature, changes its character from static to dynamic. By studying the behavior of the order parameter in the work of Brady . [], we showed numerical evidence for a crossover from directed percolation (DP) universality through various phases of anomalous directed percolation (ADP) to mean-field (MF) behavior when the temperature of the gas is increased. As the behavior of the order parameter is not sufficient to uniquely determine the universality class, we here analyze the distribution of avalanches—characteristic of nonequilibrium critical behavior—to fully characterize the ASPT. Performing extended numerical calculations and experiments on a cold Rb 87 atom gas, we confirm our earlier numerical findings and our phenomenological model that maps the dynamic network to a static one with power-law tails of the distribution of excitation distances. Furthermore, we discuss the influence of dissipation, present in the experiment and a necessary ingredient for the self-organization of the system to the critical point. In particular, we study the potential modification of the universality class by losses as a function of dissipation strength.
The facilitation of Rydberg excitations in a gas of atoms provides an ideal model system to study epidemic evolution on (dynamic) networks and self-organization of complex systems to the critical point of a nonequilibrium phase transition. Using Monte Carlo simulations and a machine learning algorithm we show that the universality class of this phase transition can be tuned but is robust against decay inherent to the self-organization process. The classes include directed percolation (DP), the most common class in short-range spreading models, and mean-field (MF) behavior, but also different types of anomalous directed percolation (ADP), characterized by rare long-range excitation processes. In a frozen gas, ground state atoms that can facilitate each other form a static network, for which we predict DP universality. With atomic motion the network becomes dynamic by long-range (Lévy-flight type) excitations. This leads to continuously varying critical exponents, varying smoothly between DP and MF values, corresponding to the ADP universality class. These findings also explain the recently observed critical exponent of Rydberg facilitation in an ultracold gas experiment [Helmrich et al., Nature (London) 577, 481 (2020)NATUAS0028-083610.1038/s41586-019-1908-6], which was in between DP and MF values.
Abstract Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.
Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.