Non-Gaussian Correlations in the Steady State of Driven-Dissipative Clouds of Two-Level Atoms

We report experimental measurements of the second-order coherence function $g^{\left(2\right)}\left(\tau \right)$ of the light emitted by a laser-driven dense ensemble of ${}_{87}\mathrm{Rb}$ atoms. We observe a clear departure from the Siegert relation valid for Gaussian chaotic light. Measuring intensity and first-order coherence, we conclude that the violation is not due to the emergence of a coherent field. This indicates that the light obeys non-Gaussian statistics, stemming from non-Gaussian correlations in the atomic medium. More specifically, the steady state of this driven-dissipative many-body system sustains high-order correlations in the absence of first-order coherence. These findings call for new theoretical and experimental explorations to uncover their origin, and they open new perspectives for the realization of non-Gaussian states of light.