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We perform measurements of the third moment of atom number fluctuations insmall slices of a very elongated weakly interacting degenerate Bose gas. Wefind a positive skewness of the atom number distribution in the ideal gasregime and a reduced skewness compatible with zero in the quasi-condensateregime. For our parameters, the third moment is a thermodynamic quantity whosemeasurement constitutes a sensitive test of the equation of state and ourresults are in agreement with a modified Yang-Yang thermodynamic prediction.Moreover, we show that the measured skewness reveals the presence of true threebody correlations in the system.

Probing three-body correlations in a quantum gas using the measurement of the third moment of density fluctuations