We investigate the behavior of a weakly interacting nearly one-dimensional (1D) trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based on exact solutions obtained using the Yang-Yang thermodynamic formalism, in a regime where other, approximate theoretical approaches fail. We use Bose-gas focusing [Shvarchuck et al., Phys. Rev. Lett. 89, 270404 (2002)] to probe the axial momentum distribution of the gas, and find good agreement with the in situ results.PACS numbers: 03.75. Hh, 05.30.Jp, 05.70.Ce Reducing the dimensionality in a quantum system can have dramatic consequences. For example, the 1D Bose gas with repulsive delta-function interaction exhibits a surprisingly rich variety of physical regimes that is not present in 2D or 3D [1,2]. This 1D Bose gas model is of particular interest because exact solutions for the manybody eigenstates can be obtained using a Bethe ansatz [3]. Furthermore, the finite-temperature equilibrium can be studied using the Yang-Yang thermodynamic formalism [4,5,6], a method also known as the thermodynamic Bethe ansatz. This formalism is the unifying framework for the thermodynamics of a wide range of exactly solvable models. It yields solutions to a number of important interacting many-body quantum systems and as such provides critical benchmarks to condensed-matter physics and field theory [6]. The specific case of the 1D Bose gas as originally solved by Yang and Yang [4] is of particular interest because it is the simplest example of the formalism. The experimental achievement of ultracold atomic Bose gases in the 1D regime [7] has attracted renewed attention to the 1D Bose gas problem [8] and is now providing previously unattainable opportunities to test the Yang-Yang thermodynamics.In this paper, we present the first direct comparison between experiments and theory based on the Yang-Yang exact solutions. The comparison is done in the weakly interacting regime and covers a wide parameter range where conventional models fail to quantitatively describe in situ measured spatial density profiles. Furthermore, we use Bose-gas focusing [9] to probe the equilibrium momentum distribution of the 1D gas, which is difficult to obtain through other means.For a uniform 1D Bose gas, the key parameter is the dimensionless interaction strength γ = mg/ 2 n, where m is the mass of the particles, n is the 1D density, and g is the 1D coupling constant. At low densities or large coupling strength such that γ ≫ 1, the gas is in the strongly interacting or Tonks-Girardeau regime [10]. The opposite limit γ ≪ 1 corresponds to the weakly interacting gas. Here, for temperatures below the degeneracy temperature T d = 2 n 2 /2mk B , one distinguishes two regimes [11]. (i) For sufficiently low temperatures, T ≪ √ γT d , the equilibrium state is a quasi-condensate with suppressed density fluctuations. The system can be treated by the mean-field approach and by the Bogoliubov theory of excitations. The 1D c...

We present the implementation of tailored trapping potentials for ultracold gases on an atom chip. We realize highly elongated traps with box-like confinement along the long, axial direction combined with conventional harmonic confinement along the two radial directions. The design, fabrication and characterization of the atom chip and the box traps is described. We load ultracold ( 1 µK) clouds of 87 Rb in a box trap, and demonstrate Bose-gas focusing as a means to characterize these atomic clouds in arbitrarily shaped potentials. Our results show that box-like axial potentials on atom chips are very promising for studies of one-dimensional quantum gases.

We experimentally investigate the properties of radio-frequency-dressed potentials for Bose-Einstein condensates on atom chips. The three-dimensional potential forms a connected pair of parallel waveguides. We show that rf-dressed potentials are robust against the effect of small magnetic-field variations on the trap potential. Long-lived dipole oscillations of condensates induced in the rf-dressed potentials can be tuned to a remarkably low damping rate. We study a beam-splitter for Bose-Einstein condensates and show that a propagating condensate can be dynamically split in two vertically separated parts and guided along two paths. The effect of gravity on the potential can be tuned and compensated for using a rf-field gradient.

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