Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation

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.

Figure 1

(a) Relevant atomic levels and interaction energy shifts. Atoms are excited with an off-resonant laser with detuning $\Delta <0$ and Rabi frequency $\Omega$. The interaction with an excited atom (red) shifts the transition of a second atom, positioned at the facilitation radius $r_{\mathrm{fac}}$ into resonance. (b) Shape of the rate function $\Gamma \left(r\right)$ for two atoms (one is excited and positioned at the origin) for $r_{\mathrm{fac}}=\frac{R}{2},\frac{3R}{5},\frac{7R}{10},...,R$. (c) Facilitation dynamics in two dimensions. A single atom facilitates the excitation of (blue) atoms within a shell (gray region) of width $\Delta r$. Upon a subsequent excitation on this shell the facilitation region is changed to an ellipsoid. Note the deviation of the facilitation region in step 2 (3) from that of two (three) overlapping circles.

Figure 2

Snapshots of a two-dimensional system with $N=200\times 200$ atoms. The interaction parameter is $R=10$ and the facilitation radius is $r_{\mathrm{fac}}=\frac{7R}{10}$. Red dots correspond to excited atoms. Blue dots correspond to atoms where state changes in the next step are facilitated, i.e., where the corresponding rate for a state change is larger than $0.1$.

Figure 3

(a) Effective mean-field potential $V\left(p\right)$ [see Eq. (4)] for a two-dimensional gas and $r_{\mathrm{fac}}=\frac{R}{2},\frac{3R}{5},...,R$. (b) Time evolution of the density in one ($N={10}^6$), two ($N=1000\times 1000$), and three ($N=200\times 200\times 200$) dimensions. The solid lines represent data for $R=10$. Broken lines in $2d$ show data for $R=30$ and $r_{\mathrm{fac}}=\frac{R}{2},\frac{3R}{5},...,R$ (here $N=3000\times 3000$).

Figure 4

Density and Mandel $Q$-parameter (see text) as a function of time for a three-dimensional system with $R=10$. Shown are data for $r_{\mathrm{fac}}=\frac{R}{2}$ ($N=30\times 30\times 30$) and $r_{\mathrm{fac}}=\frac{7R}{10}$ ($N=50\times 50\times 50$). Broken lines sketch power-law approximations to the time-dependence of the excitation density in four different regimes.