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 $g^{(2)}(\tau )$ 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.

Figure 1

Experimental setup and $g_N^{(2)}(\tau )$ measurements (a) Scheme of the experiment. A cigar-shaped cloud of ${}^{87}\mathrm{Rb}$ atoms is excited by a resonant laser beam propagating perpendicularly to its long axis. The light emitted by the cloud is collected either along its axis (${\widehat{u}}_z$, shown) or in a perpendicular direction (${\widehat{u}}_{\perp }$, not shown) by two avalanche photodiodes (APD1,2) arranged in a Hanbury-Brown and Twiss configuration. A time tagger (TT) records the photon arrival times. Inset: example of intensity $⟨\widehat{I}(t)⟩$ collected along ${\widehat{u}}_z$. Red: steady state where $g_N^{(2)}(\tau )$ is calculated. (b) $g_N^{(2)}(\tau )$ along ${\widehat{u}}_z$ for a dilute cloud, compared to the Siegert relation (dashed line). (c) $g_N^{(2)}(\tau )$ in the dense regime measured along ${\widehat{u}}_z$ (red line), violating the Siegert relation. Light blue line: collection along ${\widehat{u}}_{\perp }$.

Figure 2

Evidence for a negligible average field. (a) Intensity $⟨\widehat{I}⟩$ measured along ${\widehat{u}}_z$ in steady state versus atom number $N$. Error bars are standard error on the mean (SEM). Dashed line: linear and a quadratic scalings. (b) $|g_N^{(1)}(\tau )|$ with $\mathrm{\Omega }\simeq 4.5\mathrm{\Gamma }$ (red line) and expectation for a single atom (black line).

Figure 3

Atom number $N$ dependence of correlations (a) $g_N^{(2)}(\tau )$ versus $\tau$ and $N$. (b) $g_N^{(2)}(0)$ obtained by averaging $g_N^{(2)}(\tau )$ in the interval $-2\mathrm{ns}⩽\tau ⩽2\mathrm{ns}$. (c) Connected correlation $\mathit{C}(0)$ as defined in the main text. Inset: example of $\mathit{C}(\tau )$. The error bars are SEM.