Exciton dynamics in emergent Rydberg lattices

The dynamics of excitons in a one-dimensional ensemble with partial spatial order are studied. During optical excitation, cold Rydberg atoms spontaneously organize into regular spatial arrangements due to their mutual interactions. This emergent lattice is used as the starting point to study resonant energy transfer triggered by driving a $nS$ to $n^{\prime }P$ transition using a microwave field. The dynamics are probed by detecting the survival probability of atoms in the $nS$ Rydberg state. Experimental data qualitatively agree with our theoretical predictions including the mapping onto the $XXZ$ spin model in the strong-driving limit. Our results suggest that emergent Rydberg lattices provide an ideal platform to study coherent energy transfer in structured media without the need for externally imposed potentials.

Figure 1

(a) Rydberg levels and excitation scheme. In step 1 atoms are optically excited from their electronic ground state $|g\rangle$ to a highly excited state $|nS\rangle$ with effective Rabi frequency ${\Omega }_{\text{Ryd}}$. Subsequently, in step 2, a microwave field is applied that couples the $|nS\rangle$ state to a nearby $|n^{\prime }P\rangle$ level with Rabi frequency ${\Omega }_{\text{MW}}$. These states are identified as internal states of a fictitious spin-1/2 particle. (b) Quasi-one-dimensional geometry of the system. The large van der Waals potential between the $|nS\rangle$ Rydberg atoms (blue spheres) induces an exclusion volume around each excited atom characterized by the blockade radius $R_b$ larger than the transverse size of the sample. This leads to a highly structured density distribution of the Rydberg atoms after the laser excitation step. The transition dipole-dipole interaction induces a coherent spatial transfer of $\left(n^{\prime }P\right)$ excitations.

Figure 2

(a) Numerically calculated density distribution of Rydberg atoms after laser excitation as a function of the system length $L$ measured in units of the blockade radius $R_b$. (b) Survival probability $p_T\left({\Omega }_{\mathrm{MW}}\right)$ as a function of $L/R_b$ and microwave Rabi frequency ${\Omega }_{\text{MW}}$. The colormaps in panels (a) and (b) range from 0 (white) to 1 (black). (c) Cuts through the density plot shown in (b) for three different system sizes indicated by the encircled capital letters. The corresponding mean $\langle \nu \rangle$ and variance $\sqrt{\left(\Delta {\nu }^2\right)}$ of the Rydberg atom number distribution are indicated in the panels. The blue symbols show numerical results from the Hamiltonian given in Eq. (2) and the solid black lines are obtained using the effective Hamiltonian (5) valid for large ${\Omega }_{\text{MW}}$. The statistical distribution of the dipole-dipole interaction energy between atom pairs is shown in the insets. For better visibility we show the distributions as a function of $x={(\mathcal{V}{R}_b^3/{\mu }^2)}^{1/3}$, i.e., the third root of the interaction strength at the blockade distance $R_b$. The data shown in panels (b) and (c) were obtained by averaging over 400 initial configurations generated by Monte Carlo sampling. In (b) and (c) the dipole-dipole interaction strength, $V\left(R_b\right)$, for an atom pair separated by $R_b$ is $V\left(R_b\right)T=15$.

Figure 3

Experimentally measured photon retrieval probability $P$ as a function of the microwave Rabi frequency ${\Omega }_{\mathrm{MW}}$. The duration of the microwave pulse, $T=150$ ns, is fixed. Inset: (Left) Excitation scheme used in the experiment. The Rydberg $60S_{1/2}$ state is reached by a two-photon transition via the $5P_{3/2}$ state. A microwave field couples the $60S_{1/2}$ state to the $59P_{3/2}$ state. (Right) As the number of photons $\overline{n}$ in the signal field (proportional to the Rabi frequency ${\Omega }_{\mathrm{s}}$ and pulse duration) is increased, the number of retrieved photons ${\overline{n}}_{\mathrm{ret}}$ saturates in the absence of microwave driving. The data shown in the main plot are obtained well within this saturated regime (blue point). The lines are a guide to the eye.