Demonstration of a Strong Rydberg Blockade in Three-Atom Systems with Anisotropic Interactions

We study the Rydberg blockade in a system of three atoms arranged in different two-dimensional geometries (linear and triangular configurations). In the strong blockade regime, we observe high-contrast, coherent collective oscillations of the single excitation probability and an almost perfect van der Waals blockade. Our data are consistent with a total population in doubly and triply excited states below 2%. In the partial blockade regime, we directly observe the anisotropy of the van der Waals interactions between $|nD⟩$ Rydberg states in the triangular configuration. A simple model that only uses independently measured two-body van der Waals interactions fully reproduces the dynamics of the system without any adjustable parameter. These results are extremely promising for scalable quantum information processing and quantum simulation with neutral atoms.

Figure 1

(a) Relevant energy levels of a three-atom system with van der Waals interactions $V_{ij}$. In the blockade regime, the ground state $|ggg⟩$ is resonantly coupled to the symmetric collective state $(|ggr⟩+|grg⟩+|rgg⟩)/\sqrt{3}$. (b) Scheme of the experimental setup. Arbitrary geometries of two-dimensional arrays of dipole traps are obtained by imprinting a phase map $\phi$ with the SLM. (c) Trap geometry. Three single-atoms are trapped in microscopic optical tweezers separated by $R=4\mu \mathrm{m}$ in a linear (top) and by $R=8\mu \mathrm{m}$ in a triangular arrangement (bottom). The quantization axis $\widehat{z}$ is set by a 3G external magnetic field.

Figure 2

(a) Representative single-atom Rabi flopping to the $|82D_{3/2}⟩$ state for the central atom in the linear arrangement. Single-atom Rabi frequencies $\mathrm{\Omega }\simeq 2\pi \times 0.8\mathrm{MHz}$, and damping rates $\gamma \simeq 0.3\mu {\mathrm{s}}^{-1}$ for all three atoms are obtained from fits (solid lines) to the solution of the OBEs for a single two-level atom. (b) Probability of single (blue circles), double (red triangles), and triple (green squares) Rydberg excitation as a function of the excitation pulse area in the linear arrangement. The collective enhancement of the Rabi frequency by $\sqrt{3}$ clearly appears in the data. Solid lines are the result of the model described in the text without any adjustable parameter. (c) Same as (b) but for the triangular geometry.

Figure 3

Angular dependence of the effective interaction energy $V_{\text{eff}}$ for two atoms in $|82D_{3/2}⟩$ at $R=12\mu \mathrm{m}$, with $\theta$ the angle between the internuclear axis and the quantization axis $\widehat{z}$. Red squares indicate the measured energy shifts $V_{13}$, $V_{23}$, and $V_{12}$ used for the simulation of three-atom dynamics in the partial blockade regime (see Fig. 4). In the inset, the angular dependence of the interaction for the spherically symmetric $|82S_{1/2}⟩$ state is shown for comparison. Error bars represent one standard deviation confidence intervals in the fits.

Figure 4

Probabilities of detection of double Rydberg excitation $P_{rrg}$, $P_{rgr}$, $P_{grr}$, and triple excitation $P_{rrr}$ versus excitation pulse area $\mathrm{\Omega }\tau$ for driving Rabi frequencies $\mathrm{\Omega }=2\pi \times 0.8\mathrm{MHz}$ (a), and $\mathrm{\Omega }=2\pi \times 1.6\mathrm{MHz}$ (b) in the triangular configuration. The distance between the traps is $R=12\mu \mathrm{m}$. The ratio between effective pairwise interaction energies is $V_{13}/V_{12}\sim 3$ for $\theta =60°$. Solid lines are the solution of the OBEs without any adjustable parameter.