The emergence of a special type of fluid-like behavior at large scales in one-dimensional (1d) quantum integrable systems, theoretically predicted in 2016, is established experimentally, by monitoring the time evolution of the insitu density profile of a single 1d cloud of 87 Rb atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsive interaction strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the 2016 theory. This contrasts with the previously existing "conventional" hydrodynamic approach-that relies on the assumption of local thermal equilibrium-, which is unable to reproduce the experimental data.

We report on local, in situ measurements of atom number fluctuations in slices of a onedimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super-to sub-Poissonian as the density is increased, which is a signature of the transition between the sub-regimes where the two-body correlation function is dominated respectively by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to subPoissonian, as expected for a 'fermionized' gas.PACS numbers: 03.75. Hh, 67.10.Ba Fluctuations witness the interplay between quantum statistics and interactions and therefore their measurement constitutes an important probe of quantum manybody systems. In particular, measurement of atom number fluctuations in ultracold quantum gases has been a key tool in the study of the Mott insulating phase in optical lattices [1], isothermal compressibility of Bose and Fermi gases [2][3][4][5], magnetic susceptibility of a strongly interacting Fermi gas [6], scale invariance of a twodimensional Bose gas [7], generation of atomic entanglement in double-wells [8], and relative number squeezing in pair-production via binary collisions [9,10].While a simple account of quantum statistics can change the atom number distribution, in a small volume of an ideal gas, from a classical-gas Poissonian to superPoissonian (for bosons) or sub-Poissonian (for fermions) distributions, many-body processes can further modify the correlations and fluctuations. For example, threebody losses may lead to sub-Poissonian fluctuations in a Bose gas [11,12]. Even without dissipation, the intrinsic interatomic interactions can also lead to sub-Poissonian fluctuations, such as in a repulsive Bose gas in a periodic lattice potential, where the energetically costly atom number fluctuations are suppressed. This effect has been observed for large ratios of the on-site interaction energy to the inter-site tunnelling energy [13,14], with the extreme limit corresponding to the Mott insulator phase [15,16]. The same physics, accounts for sub-Poissonian fluctuations observed in double-well experiments [8,17]. Sub-Poissonian fluctuations of the total atom number have been also realised via controlled loading of the atoms into very shallow traps [18].In this work, we observe for the first time subPoissonian atom number fluctuations in small slices of a single one-dimensional (1D) Bose gas with repulsive interactions, where each slice approximates a uniform system. Taking advantage of the long scale density varia- Nearly ideal Bose gasQuasi-condensate tion due to a weak longitudinal confinement, we monitor -at a given temperature -the atom number fluctuations in each slice as a function of the local density. For a weakly interacting gas, the measured fluctuations are super-Poissonian at low densities, and t...