Physical swap dynamics, shortcuts to relaxation, and entropy production in dissipative Rydberg gases

Ricardo Gutiérrez, Juan P. Garrahan, and Igor Lesanovsky

Phys. Rev. E 100, 012110 – Published 10 July 2019

Abstract

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.

Received 3 January 2019
Revised 13 May 2019

DOI:https://doi.org/10.1103/PhysRevE.100.012110

Physics Subject Headings (PhySH)

Cold gases in optical lattices Decoherence in quantum gases Open quantum systems

Rydberg atoms & molecules

Rabi model

Polymers & Soft MatterGeneral PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Ricardo Gutiérrez¹, Juan P. Garrahan^2,3, and Igor Lesanovsky^2,3

¹Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
²School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
³Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom

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Issue

Vol. 100, Iss. 1 — July 2019

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Images

Figure 1
Impact of excitation swaps on the dynamics of Rydberg gases. (a) An excitation swap in a 2D Rydberg gas (above) and list of relevant processes (below): (i) (de)excitations, (ii) swaps, and (iii) decay. (b) Representative trajectory of a chain of $N = 20$ atoms for $R = 4$ and $R_{c} = 1$ without exchange interactions, $U = 0$ . (c) Representative trajectory of a chain of $N = 20$ atoms for $R = 4$ and $R_{c} = 1$ with exchange interactions, $U = 1$ . Colors indicate the state of atoms following the legend in (a). In both (b) and (c) decay processes have been excluded, $κ = 0$ .
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Figure 2
Accelerating effect of swaps quantified by the persistence function. (a) Persistence as a function of time for different values of $U$ (see legend) with $R = 1.5$ (left) and $R = 4$ (right). (b) Distribution $π [{log}_{10} (τ)]$ of local persistence times $τ$ in logarithmic scale for $U = 0$ (black circles), 0.001 (cyan stars), 0.01 (red triangles), 0.1 (magenta hexagons), 1 (green squares), and 10 (blue diamonds) (the arrow shows the direction of increasing $U$ ). (c) Persistence time as a function of $R$ for different values of $U$ . Colored symbols [as in legend of panel (a)] correspond to $κ = 0$ (without decay), while gray symbols correspond to a decay rate $κ = 10^{- 6}$ . All panels show numerical results based on a chain of $N = 50$ atoms. 200 realizations starting from random initial conditions have been averaged in (a) and (c), while at least 5000 are used for the histograms in (b).
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Figure 3
Irreversibility and entropy production. (a) Cycle in configuration space. Subindices in the rates indicate the state of the neighbors of the atom undergoing the transition. The product of the transition rates depends on whether the cycle is traversed in a clockwise or a counterclockwise direction. The configuration on the top left corner has been chosen as the initial state. (b) Entropy production in a ring of $N = 4$ atoms for $R = 2$ and $R_{c} = 1$ as a function of the decay rate $κ$ . Different swap strengths $U = 0, 0.1, 1, 10$ are considered (see legend). The entropy production bound in the limit of large $U$ [see Eq. (21)] is also included (red dotted line). (c) Average number of excitations in the stationary state $〈 n 〉$ for the same parameter values as in (b).
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Figure 4
Four-state model and stationary state probabilities as functions of the overall swap rate strength. (a) Configurations, transitions, and transition rates of the model. (b) Probabilities in the stationary state as a function of the overall swap strength $U$ for $U_{g} = 5 U$ and $U_{e} = U$ . The rates are $Γ_{1} = 100, Γ_{2} = 0.01$ , and $κ = 1$ , which satisfy $Γ_{1} ≫ κ ≫ Γ_{2}$ .
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