Many-body interactions in a sample of ultracold Rydberg atoms with varying dimensions and densities

Ultracold highly excited atoms in a magneto-optical trap (MOT) are strongly coupled by the dipole-dipole interaction. We have investigated the importance of many-body effects by controlling the dimensionality and density of the excited sample. We excited three different cylindrical volumes of atoms in the MOT to Rydberg states. At small radius, where the sample is nearly one-dimensional, many-body interactions are suppressed. At larger radii, the sample becomes three-dimensional and many-body effects are apparent.

Figure 1

Stark map of the $31d$ states, $33p$ states, and $n=29$ manifold states that contribute to the resonances of Eq. (1). The example resonance shown in (b) depicts two interacting atoms that have been excited to $31d$ states. Via the dipole-dipole interaction, one atom is further excited to a $33p$ while the other falls to a manifold state. Both the $33p$ and $31d$ states are detected using selective field ionization. Also shown in (a) is a scan over electric field for a fixed laser intensity. The strong resonance, labeled data, is where we collected our data. The area of little interaction, labeled background, is where we collected the background.

Figure 2

(Color online) Data taken at three different excited volumes. Even though the density is higher in the smaller, one-dimensional volume, the interaction is stronger in the sparser but more three-dimensional volumes.

Figure 3

(Color online) Shown above, in (a)–(d), are $100\text{−}\mu \mathrm{m}$-long sample volumes of radii 6.5 and $20\mu \mathrm{m}$ with randomly placed atoms. Volumes (a) and (b) correspond to a $350\mu \mathrm{m}$ volume with 40 atoms, while volumes (c) and (d) correspond to such a volume with 20 atoms. In (e) we plot the fractal dimension for $350\mu \mathrm{m}$ length volumes of different radii. Note that the $6.5\mu \mathrm{m}$ radius volume remains nearly one-dimensional even to relatively high number.

Figure 4

(Color online) Results of the simulations with nine atoms are shown in (a) at $5\mu \mathrm{s}$ for two volumes of length $350\mu \mathrm{m}$. The behavior of the $5\mu \mathrm{m}$ and the $15\mu \mathrm{m}$ volumes reproduces the features of the data shown in (b).