See End Matter for details on our initial state.

We use a red-detuned laser beam to realize a harmonic trap, with frequencies ${\omega }_x\approx 2\pi \times 40\mathrm{Hz}$, ${\omega }_y\approx 2\pi \times 45\mathrm{Hz}$, and ${\omega }_z\approx 0$. The slight anisotropy in the $x\text{−}y$ plane limits our resolution to a distance that corresponds to $\approx 2\mathrm{\mu }\mathrm{m}$ in situ.

We use a laser beam shaped by a digital micromirror device to optically pump only a slice of the cloud into the highest hyperfine ground state and then image only the atoms in that state.

For the data in Figs. 4 and 5, we count imprints in our images within a central circle of radius $r_{\mathrm{D}}\approx 52\mathrm{\mu }\mathrm{m}$, which corresponds to in situ $S\approx 2800\mathrm{\mu }{\mathrm{m}}^2$. None of our results change (within error bars) if we reduce $r_{\mathrm{D}}$ to $\approx 34\mathrm{\mu }\mathrm{m}$, which corresponds to $S\approx 1500\mathrm{\mu }{\mathrm{m}}^2$.

We exclude clusters with fewer pixels than $N_{\min }=4$, which is sufficiently large to avoid counting noise, so $N_{\mathrm{i}}$ vanishes for $t\to \infty$; see End Matter for examples of our counting.

In both Figs. 5 and 6, we use the calibrated conversion (the average $N_{\mathrm{i}}/A$, see Fig. 4) to extract $\mathcal{L}$ from $A$. Directly using Eq. (2) does not change our results within statistical errors.