Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases

Sanders, Jaron; Jonckheere, Matthieu; Kokkelmans, Sjjmf Servaas

doi:10.1103/physrevlett.115.043002

Cited by 19 publications

(43 citation statements)

References 25 publications

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“…1(a) and 1(b) [1D chain and a 2D square lattice, respectively] that irreversible deposition processes indeed dominate the growth regime, similar to what was suggested recently in Ref. [28]. Deviations become apparent in the long-time limit when the system approaches its stationary state: for the reversible process this is the fully random state, lim t→∞ c(t) = 1/2, while for the deposition process it is the (absorbing) state of a full lattice, lim t→∞ c(t) = 1.…”

Section: Effective Dynamicssupporting

confidence: 77%

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

2015

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The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power-law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a selfsimilar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations -often referred to as the blockade radius -is not a static but rather a dynamic quantity.

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Section: Effective Dynamicssupporting

confidence: 77%

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

2015

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“…The essential feature of these gases is that once an atom is in its Rydberg state, it prevents neighboring atoms from reaching their Rydberg state. By modeling the dynamics of the excitation process as an exploration process on a relation graph (specifically, the canonical Erdös-Rényi (ER) graph), the statistical properties of the proportion of atoms ultimately in the Rydberg state were studied in [18]. This article formalizes and generalizes the heuristical arguments provided there.…”

Section: Introductionmentioning

confidence: 99%

Scaling Limits and Generic Bounds for Exploration Processes

2017

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We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become explored. Given an initial number of vertices $N$ growing to infinity, we study statistical properties of the proportion of explored nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the \emph{jamming constant}, through a diffusion approximation for the exploration process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e. random sequential adsorption. As opposed to homogeneous random graphs, these do not allow for a reduction in dimensionality. Instead we build on a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and obtain generic bounds: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, we give two trajectorial interpretations of our bounds by constructing two coupled processes that have the same fluid limits.Comment: 25 pages, 3 figure

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“…For the resonant case = 0 (in practice, γ ), the interactions between an atom and its neighbors lead to a blockade constraint resulting in anticorrelated dynamics [9,16]: The more excited atoms there are in the vicinity, the smaller i , leading to a spatially inhomogeneous local excitation rate and an overall slowing down of the relaxation process as the number of excitations in the systems grows. The interparticle distance below which this blockade constraint becomes important is given by the (incoherent) blockade radius r b = (C 6 / γ ) 1 6 .…”

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confidence: 99%

Experimental observation of controllable kinetic constraints in a cold atomic gas

et al. 2016

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Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. In situations where relaxation requires highly constrained local particle rearrangements, such as in glassy systems, this dynamics can be difficult to analyze from first principles. The essential physical ingredients, however, can be captured by idealized lattice models with so-called kinetic constraints. While so far constrained dynamics has been considered mostly as an effective and idealized theoretical description of complex relaxation, here we experimentally realize a many-body system exhibiting manifest kinetic constraints and measure its dynamical properties. In the cold Rydberg gas used in our experiments, the nature of the kinetic constraints can be tailored through the detuning of the excitation lasers from resonance. The system undergoes a dynamics which is characterized by pronounced spatial correlations or anticorrelations, depending on the detuning. Our results confirm recent theoretical predictions, and highlight the analogy between the dynamics of interacting Rydberg gases and that of certain soft-matter systems. DOI: 10.1103/PhysRevA.93.040701 Complex collective relaxation in many-body systems is often accompanied by a dramatic slowdown of diffusion processes and the emergence of nonergodic and glassy phases [1][2][3][4]. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion. Local rearrangements are highly constrained, giving rise to collective-and often slow-relaxation. These features can be seen to be the consequence of effective kinetic constraints in the dynamics [5]. A kinetic constraint is a condition on the rate for a local transition dependent on the local environment: The transition and its reverse-irrespective of whether they are energetically favorable or unfavorable-can only occur if the constraint is satisfied. Kinetic constraints [6] can severely restrict relaxation in situations where local particle arrangements make satisfying them unlikely, which is typical of fluid systems with excluded volume interactions such as dense colloids or supercooled liquids [1][2][3][4]. When a constraint is satisfied, however, the transition is allowed and a local rearrangement is "facilitated" [5,6]. Kinetic constraints naturally give rise [7] to collective and spatially heterogeneous relaxation, and are used to describe situations where the correlation properties of the dynamics go beyond those of the static stationary state, a salient feature of glassy systems [4].Steric hindrances and dynamic facilitation are argued to play a central role in the behavior of glass formers [5]. However, it can be difficult [8] to establish unambiguously the relation between microscopic processes and emerging kinetic constraints, or between idealized models with explicit kinetic constraints and actual physical systems. In this Rapid Communication we establish such a direct connection by reporting the experimental observation of correlated...

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Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases

Cited by 19 publications

References 25 publications

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

Scaling Limits and Generic Bounds for Exploration Processes

Experimental observation of controllable kinetic constraints in a cold atomic gas

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