van der Waals–stabilized Rydberg aggregates

Assemblies of Rydberg atoms subject to resonant dipole-dipole interactions exhibit Frenkel excitons. We show that van der Waals shifts can significantly modify the exciton wave function, whenever atoms approach each other closely. As a result, attractive dipole-dipole potentials and repulsive van der Waals interactions can be combined to form stable one-dimensional atom chains, akin to bound aggregates. Here the van der Waals shifts ensure a stronger homogeneous delocalization of a single excitation over the whole chain, enabling it to bind several atoms. When brought into unstable configurations, such Rydberg aggregates allow the direct monitoring of their dissociation dynamics.

Figure 1

(a) Single-body states of three Rydberg atoms are illustrated schematically. We show the $|ns\rangle$ and $|np\rangle$ states, with the transition energy $E_A=E_p-E_s$, and the absolute ground state $|g\rangle$. (b) The states $|{\pi }_i\rangle$, with $(i=1,2,3)$, are presented. For large interatomic distance relative to the crossover distance, $R>R_0$, the three $|{\pi }_i\rangle$ states are close to resonance, $D\approx \overline{D}$, and energy transfer is permitted among them with transfer parameters $J$ and $J^{\prime }$. (c) For a small interatomic distance, $R_0>R$, the states $|{\pi }_1\rangle$ and $|{\pi }_3\rangle$ have the same vdW shift of $D$, but $|{\pi }_2\rangle$ experiences a different shift $\overline{D}$, with $\overline{D}\gg D$. Hence, the $|{\pi }_2\rangle$ state is no longer resonant with $|{\pi }_{1,3}\rangle$. Now energy transfer is allowed only among the $|{\pi }_1\rangle$ and $|{\pi }_3\rangle$ states with the transfer parameter $J^{\prime }$.

Figure 2

(a) The three collective potentials, $U_k$, as a function of the interatomic distance $R$. (b, c) The site populations $|c_k^i{|}^2$ as a function of the interatomic distance $R$ in (b) the first $(k=\alpha )$ and (c) the third $(k=\gamma )$ collective states. The insets include schematically the site amplitudes at the three $|{\pi }_i\rangle$ states for the first and the third collective modes at large distances, $R>R_0$, and small distances, $R<R_0$.

Figure 3

Energy landscape of the lowest Born-Oppenheimer surface of the Rydberg trimer. For ease of interpretation we use the Jacobi coordinates $r=R_2-R_1$ and $R=R_3-R_2+r/2$. The potential exhibits a well around $R-r/2\approx r\approx 0.8$ $\mu$m and exceeds the maximum of the color bar in the region of small $r$ or $R$. Lines show a dissociating (white) and a stable (magenta) quantum classical trajectory. Big dots mark the starting position.

Figure 4

Total atom density $n$ (arb. units) in vdW–stabilized Rydberg 6-mer for three selected times.

Figure 5

Rydberg aggregate dissociation for (a, b) symmetric and (c, d) asymmetric configurations. (a) Atomic positions $R_i$ for a single dissociating trajectory, $i=1$ [red (bottom) curve], $i=2$ [magenta (middle) curve], and $i=3$ [green (top) curve]. (b) Excitation amplitudes $|c_{\alpha }^i{\left(t\right)|}^2$ for a single dissociating trajectory. (c) Total atomic density $n$ from the trajectory average; overlaid are the mean positions of the three atoms. (d) Mean excitation amplitudes $\overline{|c_{\alpha }^i{\left(t\right)|}^2}$ on the three sites. (e) Energy distribution of the final-state dimer (black solid curve) and the initial energy (red solid curve) for the same case in panel (c). The dotted lines indicate one standard error and are nearly indistinguishable from the solid ones.

Figure 6

(a) The interatomic distance trajectories for the lowest symmetric eigenstate. (b) The trajectories for the higher eigenstate. The plots are for different initial interatomic distances of 2 and 3 $\mu$m. (c) The populations $|c_k^i{|}^2$ in the lowest mode as a function of time for initial interatomic distance of 3 $\mu$m. The trajectory oscillations result in population oscillations with a period of about 0.85 $\mu$s.