We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the "model A" universality class; i.e., it features a nontrivial Z2 symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line.
We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the "model A" universality class; i.e., it features a nontrivial Z2 symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line.
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.
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.
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.However, it is challenging to find systems with sufficiently controllable parameters that allow quantitatively modeling of emergent properties.Here, we study a nonequilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapor of atoms optically excited to strongly interacting Rydberg states.Electromagnetically induced transparency provides excellent control over the population dynamics and enables highresolution 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 case 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.
Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.
In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically-constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum Master equation. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include a power law growth of the density of excitations and the existence of a time-dependent Rydberg blockade radius. Our results indicate that the power-law growth of density of excitations is characterised by an exponent which decreases as the dissipation becomes weaker.
The nonequilibrium dynamics of a gas of cold atoms in which Rydberg states are off-resonantly excited is studied in the presence of noise. The interplay between interaction and off-resonant excitation leads to an initial dynamics where aggregates of excited Rydberg atoms slowly nucleate and grow, eventually reaching long-lived metastable arrangements which then relax further on much longer time scales. This growth dynamics is governed by an effective Master equation which permits a transparent and largely analytical understanding of the underlying physics. By means of extensive numerical simulations we study the many-body dynamics and the correlations of the resulting nonequilibrium states in various dimensions. Our results provide insight into the dynamical richness of strongly interacting Rydberg gases in noisy environments, and highlight the usefulness of these kinds of systems for the exploration of soft-matter-type collective behavior.