Wireless Network Control of Interacting Rydberg Atoms

We identify a relation between the dynamics of ultracold Rydberg gases in which atoms experience a strong dipole blockade and spontaneous emission, and a stochastic process that models certain wireless random-access networks. We then transfer insights and techniques initially developed for these wireless networks to the realm of Rydberg gases, and explain how the Rydberg gas can be driven into crystal formations using our understanding of wireless networks. Finally, we propose a method to determine Rabi frequencies (laser intensities) such that particles in the Rydberg gas are excited with specified target excitation probabilities, providing control over mixed-state populations.

Figure 1

(left) An atom can transition between a ground, intermediate and a Rydberg state. (right) A transmitter can change between nonactive and active.

Figure 2

The Rydberg blockade prevents atoms within a radius $R$ from becoming Rydberg atoms (left). This interaction can be described using an interference graph where edges indicate which neighboring particles would block each other, which is part of the wireless network model (right). Active transmitters (black) prevent neighboring transmitters (red) from becoming active. Non-neighboring nonactive transmitters (white) can become active.

Figure 3

Dominant configurations in a (left) $9\times 5$ lattice and (middle, right) $4\times 4$ lattice with nearest-neighbor blocking.

Figure 4

Histograms of the hitting time distributions (left), and normalized average number of excited particles (right) for lattices of sizes $4\times 4$, $6\times 6$, and $8\times 8$. Here, $\mathrm{\Gamma }=2\pi \times 6\mathrm{MHz}$, ${\mathrm{\Omega }}_{\mathrm{e},i}=2\pi \times 3\mathrm{MHz}$ and ${\mathrm{\Omega }}_{\mathrm{r},i}=2\pi \times 1\mathrm{MHz}$.

Figure 5

The ${\theta }_i(\mathit{\nu },\mathit{\mu })$ for $N=9$, $b=1$, and ${\nu }_i/{\mu }_i=10$.

Figure 6

Algorithm output when $N=9$, $b=4$, $\mathrm{\Gamma }=2\pi \times 6\mathrm{MHz}$, and ${\mathrm{\Omega }}_{\mathrm{r},i}=2\pi \times 1\mathrm{MHz}$. The dotted lines indicate ${\mathbf{\Omega }}_{\mathrm{e}}^{\text{opt}}$.

Figure 7

The excitation probabilities ${\theta }_i({\mathit{\nu }}^{[n]},\mathit{\mu })$ after iterations $n=0$, 3, and 10.