Direct observation of quantum phonon fluctuations in a one dimensional Bose gas

We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small sub-volumes of a weakly interacting ultracold atomic 1D cloud are studied using \textit{in situ} absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the \textit{quantum quasicondensate} regime, the ratio of chemical potential to thermal energy is $\mu/ k_B T\simeq4$, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a non-local analysis at variable observation length, we observe a clear deviation from a classical field prediction, which reveals the emergence of dominant quantum fluctuations at short length scales, as the thermodynamic limit breaks down.