Extended Data Fig. 3: Structure factor close to q = 0.

We show experimental power spectra of different spin and density degrees of freedom close to q = 0 (green diamonds). The grey diamonds represent the fluctuations of a coherent spin state with comparable atom numbers. We compare to thermal Bogoliubov theory predictions for the same parameters as displayed in Fig. 4 but with q = 0 (green line; grey band indicates 68% confidence interval of statistical and systematic uncertainties). Experimentally, we find that for momenta in the range of 0.02 μm⁻¹ to 0.1 μm⁻¹ the fluctuations are higher than for the thermal predictions for all observables (except the transversal spin F_⊥). The length scale of these fluctuations is in accordance with observable localized long-lived non-linear excitations which are not present in the thermalized data of Fig. 4.