We study the dynamics of a quantum Ising chain after the sudden introduction of a nonintegrable long-range interaction. Via an exact mapping onto a fully connected lattice of hard-core bosons, we show that a prethermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasistationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the prethermal state and the crossover to the eventual thermal one may occur algebraically.

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 explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the manybody wave functions in Hilbert space. DOI: 10.1103/PhysRevLett.118.063606 Introduction.-Rydberg gases provide a versatile platform for studies of quantum few-body and many-body phenomena with applications ranging from quantum information processing [1] to simulations of complex condensed matter systems. The experimental degree of control has reached a stage which enables efficient entanglement creation [2] and implementation of quantum Ising models [3,4]. This opens pathways towards probing magnetic structures [5][6][7][8] as well as the exploration of open many-body quantum systems [9][10][11][12][13][14][15].Of particular interest is the so-called facilitation mechanism (or antiblockade), where the excitation of an atom to a Rydberg state is strongly enhanced in the vicinity of an already excited atom [16,17]. This effect is of broad relevance and exploited in the design of quantum gates [18,19], as well as in protocols for dissipative quantum state preparation [6]. In the many-body context it effectuates an aggregation mechanism, where an initial Rydberg excitation seed triggers a dynamical growth of excitation clusters [18,[20][21][22][23] and it enables the implementation of kinetic constraints [12,24,25] thereby connecting to the physics of glass-forming substances [26][27][28].Here we perform a theoretical and experimental study of the facilitated dynamics of Rydberg excitations in a onedimensional array of optical tweezers. In a first experiment conducted with only two of them, we establish that the uncertainty of the atomic positions introduces disorder

Stochastic processes with absorbing states feature remarkable examples of non-equilibrium universal phenomena. While a broad understanding has been progressively established in the classical regime, relatively little is known about the behavior of these non-equilibrium systems in the presence of quantum fluctuations. Here we theoretically address such a scenario in an open quantum spin model which in its classical limit undergoes a directed percolation phase transition. By mapping the problem to a non-equilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin-flips alters the nature of the transition such that it becomes first-order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.