Switching Exciton Pulses Through Conical Intersections

Exciton pulses transport excitation and entanglement adiabatically through Rydberg aggregates, assemblies of highly excited light atoms, which are set into directed motion by resonant dipole-dipole interaction. Here, we demonstrate the coherent splitting of such pulses as well as the spatial segregation of electronic excitation and atomic motion. Both mechanisms exploit local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The intersection provides a sensitive knob controlling the propagation direction and coherence properties of exciton pulses. The fundamental ideas discussed here have general implications for excitons on a dynamic network.

Figure 1

(a) Orthogonal atom chains with one Rydberg dimer each. Atoms 0 and 1 initially share an excitation, due to which atom 1 reaches the conical intersection at $x_{\mathrm{CI}}$. The origin of the coordinate system is set to the mean initial position of atom 0. (b) The repulsive energy surface $U_{\text{rep}}$ (red) and middle surface $U_{\text{mid}}$ (green) of the trimer subunit (atoms 1, 2, and 3) near the CI. (c),(d) Forces on atom 2 (solid lines) and atom 3 (dashed lines), for the repulsive surface [red, (c)] and middle surface [green, (d)]. The insets show atomic positions and the excitation distribution ($d_n$, see text) of exciton states and forces for the indicated values of $\mathrm{\Delta }{x}_{12}$, which denotes the distance between atom 1 and the vertical chain. The parameter $p$ controls the degree of symmetry of the trimer, where $p=1$ corresponds to an isosceles trimer configuration.

Figure 2

Normalized total atomic density for atomic motion on two BO surfaces; overlayed are selected trajectories of the quantum classical method. (a) Horizontal density $n(x,t)$ (see [25]) of atoms 0 and 1. The dashed white line marks the $x$ position of the vertical chain. (b) Vertical density $n(y,t)$ of atoms 2 and 3. In (a) and (b) we actually plot $\sqrt{n(x,t)}$, $\sqrt{n(y,t)}$. (c) Purity of reduced electronic state, see [25]. Our calculations are for lithium atoms excited to principal quantum number $\nu =44$ with a transition dipole moment of $\mu =1000\mathrm{a}.\mathrm{u}.$. The parameters of the initial atomic configuration were $a_1=2.16\mu \mathrm{m}$, $a_2=5.25\mu \mathrm{m}$, and $d=8.5\mu \mathrm{m}$. To sample the nuclear wave function, we have propagated $10^5$ trajectories [36] with a standard deviation of ${\sigma }_x=0.5\mu \mathrm{m}$ for the atomic positions. Here, we have used $C_6=0$ for simplicity.

Figure 3

Use of the trimer subunit with conical intersection as an exciton switch. Depending on the geometry, we can realize three qualitatively different scenarios: (a) asymmetric, repulsive surface; (b) asymmetric, middle surface; (c) symmetric, repulsive and middle surface. Each plot shows $\sqrt{n(y,t)}$ as in Fig. 2. When atoms reach the white horizontal lines ($r_{\text{coll}}$, $6.6\mu \mathrm{m}$ beyond the initial $y$ position of atoms 3, 6), we extract the level of bipartite entanglement, listed in Fig. 4. The parameters, different from those of Fig. 2, are $\nu =80$ (hence, $\mu =3374\mathrm{a}.\mathrm{u}.$), $a_1=6\mu \mathrm{m}$, $d=22\mu \mathrm{m}$, and $C_6\approx -7.6\times 10^{20}\mathrm{a}.\mathrm{u}.$ as derived in [25]. Also, see [25] for videos of representative single trajectories.

Figure 4

Geometry and entanglement switching for the three scenarios of Fig. 3. Atom numbering and control parameters $a_2$, $\mathrm{\Delta }y$ are defined in the sketch on the left. The entanglement measure ${\overline{E}}_{ij}$ is defined in [25].