Correlated Exciton Transport in Rydberg-Dressed-Atom Spin Chains

We investigate the transport of excitations through a chain of atoms with nonlocal dissipation introduced through coupling to additional short-lived states. The system is described by an effective spin-$1/2$ model where the ratio of the exchange interaction strength to the reservoir coupling strength determines the type of transport, including coherent exciton motion, incoherent hopping, and a regime in which an emergent length scale leads to a preferred hopping distance far beyond nearest neighbors. For multiple impurities, the dissipation gives rise to strong nearest-neighbor correlations and entanglement. These results highlight the importance of nontrivial dissipation, correlations, and many-body effects in recent experiments on the dipole-mediated transport of Rydberg excitations.

Figure 1

Transport of excitations (red spheres) through a chain of optically dressed atoms with site index $j$ (green spheres). (a) Excitonic motion arises through coherent long range exchange interactions $J$ and through dissipative processes mediated by a tailored reservoir coupling. The blockade radius $R_c$ refers to the distance over which the dipole-dipole interactions significantly affect the states of neighboring atoms. (b) Each site is represented by an atom, which can be in either the impurity Rydberg state $|p⟩$ or the auxiliary states $|g⟩$, $|e⟩$, or $|s⟩$. Dipolar interactions result in exchange between $|s⟩$ and $|p⟩$ Rydberg states. States $|g⟩\leftrightarrow |e⟩$ and $|e⟩\leftrightarrow |s⟩$ are coupled with Rabi frequencies $\omega$ and $\mathrm{\Omega }$, respectively. The state $|e⟩$ spontaneously decays to the $|g⟩$ state with the rate ${\mathrm{\Gamma }}_e$. The state space ${\widehat{H}}_e$ comprising $|e⟩$ or $|s⟩$ excitations can be adiabatically eliminated, resulting in an effective spin-$1/2$ model for the impurity and dressed states.

Figure 2

(a) Distance dependence of the effective coupling rates $J$ (solid line), $\mathrm{\Gamma }$ (dashed line), and $\gamma$ (dotted line) for a single impurity with $m=3$ in units of the two-level-atom scattering rate $K={\omega }^2/{\mathrm{\Gamma }}_e$. (b) Mean square displacement of the propagating excitation $⟨x^2⟩$ for a chain of $N=121$ sites obtained from simulations for three values of the dimensionless interaction strength: $V(a)=R_c^3/a^3=50$ (triangles), $V(a)=1$ (circles), and $V(a)=0.02$ (squares). The solid lines show the approximate analytic scalings in the three regimes described in the text. (c)–(e) Enlarged density plots showing the impurity probability distribution at short times for (c) coherent transport with $V(a)=0.02$, (d) diffusive transport with $V(a)=1$, and (e) transport in the blockade regime $V(a)=50$. Bright colors indicate high probability density.

Figure 3

Two exciton dynamics and density-density correlations $g^{(2)}$ for $\mathrm{\Gamma }=1$, $\mathrm{\Omega }=2$, $K=0.05$, $m=3$, and varying $V(a)$. (a) Probability density as a function of time for $V(a)=1$ showing normal diffusion. (b) Equal time correlation function $g^{(2)}(0,k)$ for the same parameters. The colors correspond to $g^{(2)}>1$ (dark red), $g^{(2)}<1$ (blue), and $g^{(2)}=1$ (white). (c) Equal time density-density correlation function at steady state as a function of $V(a)$ [same color scale as in (b)]. (d) Nearest-neighbor correlation function $g^{(2)}(0,1)$ versus $V(a)$ showing bunching around $V(a)\approx 1$.