Fig. 1: Physical system for studying epidemic growth and dynamics on complex networks.

a Experiments are performed on a two-dimensional gas containing N ~ 3 × 10⁴ potassium atoms driven by an off-resonant laser field. The gas is initially prepared with a small number of seed excitations (blue disks), which then evolves according to the microscopic processes depicted in sub-figure b, giving rise to growing excitation clusters that spread throughout the system. After different exposure times t, the Rydberg atoms are field ionized and detected on a microchannel plate detector (MCP), where the incident ions create voltage spikes (blue trace). b Each atom can be treated as a two-level system with a ground state \(\left|g\right\rangle\) (gray disks) and excited Rydberg state \(\left|r\right\rangle\) (larger blue disks). Excited atoms can decay with rate Γ or facilitate additional excitations with rate κ at a characteristic distance R_fac (determined by the laser detuning Δ) analogous to the transmission of an infection. c The dynamics of this system can be described by a susceptible-infected-susceptible (SIS) model on an emergent heterogeneous network. Each node i represents a discrete cell of the coarse-grained system, which can be infected (with excitation, blue) or susceptible (without excitation, white) and is connected to neighboring nodes according to the adjacency matrix a_ij. The infection probability of each node is weighted by the number of atoms in that cell that can undergo facilitated excitation N_i (indicated by the numerical labels on each node). Disconnected nodes with N_i = 0, corresponding to vacant cells, are depicted with dashed lines. d Exemplary data and numerical simulations (solid line) showing two different stages of dynamics: rapid growth followed by saturation. Error bars represent the standard error of the mean over typically 16 experiment repetitions.