Abstract:
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.

Abstract:
We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with a standard deviation small compared to the typical energy per atom, dominated by the interaction energy. Numerical solutions of the Gross-Pitaevskii equation reproduce well our observations. We propose a scenario for disorder-induced trapping of the condensate in agreement with our observations.

Abstract:
The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.

Abstract:
We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with a standard deviation small compared to the typical energy per atom, dominated by the interaction energy. Numerical solutions of the Gross-Pitaevskii equation reproduce well our observations. We propose a scenario for disorder-induced trapping of the condensate in agreement with our observations.

Abstract:
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Due to the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.

Abstract:
We analyze the localization of a Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE). We first derive the 1D GPE from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wavefuction and space-time dependent transverse width) which reduce to the 1D GPE under strict conditions. Then, by using the 1D GPE we report the suppression of localization in the interacting BEC when the repulsive scattering length between bosonic atoms is sufficiently large.

Abstract:
Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasi-condensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the Time Evolving Block Decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure \emph{in situ} to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give new insight into the dynamics of strongly correlated many-body systems.

Abstract:
We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a 1D optical lattice. A clear separation of these two regimes is obtained performing measurements at different temperatures of the atomic sample. The timescales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability.

Abstract:
We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions.

Abstract:
We investigate correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87-Rb Bose-Einstein condensate into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of seven smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated phase coherent 1D mean-field regime and the strongly correlated Tonks-Girardeau regime.