Probing Three-Body Correlations in a Quantum Gas Using the Measurement of the Third Moment of Density Fluctuations

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.

Figure 1

(a) Scheme of the imaging setup. The probe laser crosses the atomic cloud (red dot) before its reflection from the chip surface and detection on a CCD camera. (b) Typical in situ absorption image; the scale on the color bar shows the optical density. The pixel size in the object plane is $\Delta =4.5\mu \mathrm{m}$. (c) Typical longitudinal density profile (solid curve), together with the mean profile (dashed red curve).

Figure 2

Measured third moment (open circles) of the atom number fluctuations versus the mean atom number per pixel, for temperatures of 376 nK (a) and 96 nK (b). The insets show the corresponding atom number variances. The error bars are the statistical errors. Graphs (c) and (d) show the skewness $s_m$ corresponding to (a) and (b), respectively. The theoretical predictions, scaled by ${\kappa }_2=0.55$ and ${\kappa }_3=0.34$ for (a) and (c), and by ${\kappa }_2=0.52$ and ${\kappa }_3=0.31$ for (b) and (d), are shown for comparison: solid lines, the modified Yang-Yang prediction; dashed lines, the ideal Bose-gas prediction; dash-dotted lines on (b) and (d), the quasicondensate prediction; dotted lines, the shot-noise limit $⟨N⟩$.

Figure 3

The measured three-body integral ${\mathcal{H}}_m$ versus $⟨N⟩$, corresponding to the data of Figs. 2a, 2b, respectively. The solid (dash-dotted) curves are the thermodynamic predictions from the modified Yang-Yang (quasicondensate) model.