Newton’s Cradle and Entanglement Transport in a Flexible Rydberg Chain

In a regular, flexible chain of Rydberg atoms, a single electronic excitation localizes on two atoms that are in closer mutual proximity than all others. We show how the interplay between excitonic and atomic motion causes electronic excitation and diatomic proximity to propagate through the Rydberg chain as a combined pulse. In this manner entanglement is transferred adiabatically along the chain, reminiscent of momentum transfer in Newton’s cradle.

Figure 1

(a) Sketch of the initial total density distribution of $N=5$ Rydberg atoms. (b) Visualization of the electronic state $|{\pi }_1⟩$. (c) Trapping of the electronic excitation in the repulsive exciton state by a perturbation of the regular chain. Shown are the populations $p_n=|⟨{\pi }_n|{\phi }_{\mathrm{rep}}(\mathbf{R})⟩{|}^2$ as a function of $a/x_0$.

Figure 2

Nuclear dynamics in the case $N=3$. The time evolution of the total atomic density $n(x,t)$ (a) is shown together with a comparison of Tully’s surface hopping calculations (black solid line) with the full quantum evolution (red dashed line) in the other panels. (b) Spatial slice $n(x,t_0)$, with $t_0$ as indicated by the first vertical white lines in (a). Arbitrary units. (c) Relative population $n_2=\int d\mathbf{R}|{\tilde{\varphi }}_2(\mathbf{R}){|}^2$ ($n_2=|{\tilde{c}}_2{|}^2$ in Tully’s algorithm) on the adiabatic surface (index 2) that is energetically nearest to the initial repulsive one. This is a measure of the propensity of nonadiabatic transitions. The deviation of curves in (b) and (c) is shown magnified in the insets. (d) Initial repulsive state.

Figure 3

Dynamics of atomic motion and excitation transfer. (a) Total atomic density averaged over ${10}^5$ realizations. We actually plot $\sqrt{n}$. (b) Mean trajectories of the individual atoms (white) and electronic excitation probabilities (diabatic populations) $|c_m{|}^2$, $c_m=\sum _m{O}_{nm}^T{\tilde{c}}_m$. The latter are encoded as the width of the copper shading surrounding each trajectory. (c) Population on the adiabatic surface “rep” (black line) and individual diabatic populations. (d) Purity $P=\mathrm{Tr}[{\widehat{\sigma }}^2]$ of the reduced electronic density matrix $\widehat{\sigma }$ (solid green line) and bipartite entanglement $E_{n,n+1}$ for neighboring atoms as defined in the text. The dotted line indicates 1.