We study the rotation of a 87Rb Bose-Einstein condensate confined in a quadratic plus quartic potential. This trap configuration allows one to increase the rotation frequency of the gas above the trap frequency. In such a fast rotation regime we observe a dramatic change in the appearance of the quantum gas. The vortices which were easily detectable for a slower rotation become much less visible, and their surface density is well below the value expected for this rotation frequency domain. We discuss some possible tracks to account for this effect.

We have observed high-contrast matter wave interference between 30 Bose-Einstein condensates with uncorrelated phases. Interferences were observed after the independent condensates were released from a one-dimensional optical lattice and allowed to overlap. This phenomenon is explained with a simple theoretical model, which generalizes the analysis of the interference of two condensates.

We have observed phase defects in quasi-2D Bose-Einstein condensates close to the condensation temperature. Either a single or several equally spaced condensates are produced by selectively evaporating the sites of a 1D optical lattice. When several clouds are released from the lattice and allowed to overlap, dislocation lines in the interference patterns reveal nontrivial phase defects.PACS numbers: 03.75. Lm, 32.80.Pj, 67.40.Vs Low dimensional bosonic systems have very different coherence properties than their three dimensional (3D) counterparts. In a spatially uniform one dimensional (1D) system, a Bose-Einstein condensate (BEC) cannot exist even at zero temperature. In two dimensions (2D) a BEC exists at zero temperature, but phase fluctuations destroy the long range order at any finite temperature. At low temperatures the system is superfluid and the phase fluctuations can be described as bound vortexantivortex pairs. At the Kosterlitz-Thouless (KT) transition temperature [1,2,3] the unbinding of the pairs becomes favorable and the system enters the normal state.In recent years, great efforts have been made to study the effects of reduced dimensionality in trapped atomic gases [4]. In both 1D and 2D, the density of states in a harmonic trap allows for Bose-Einstein condensation at finite temperature. In contrast to 1D and elongated 3D systems [5,6,7,8,9,10,11,12,13], the coherence properties of 2D atomic BECs have so far been explored only theoretically [14,15,16,17]. In previous experiments, quasi-2D BECs [6,18,19,20] or ultracold clouds [21] were produced in specially designed "pancake" trapping potentials. The sites of a 1D optical lattice usually also fulfill the criteria for 2D trapping [22,23,24,25]; the difficulty in these systems is to suppress tunneling between the sites, and to address or study them independently [26,27].In this Letter, we report the production of an array of individually addressable quasi-2D BECs. By selectively evaporating the atoms from the sites of a 1D optical lattice, we can produce either a single or several equally spaced condensates. The distinct advantage of this approach is that it opens the possibility to study the phase structures in quasi-2D BECs interferometrically. We have observed interference patterns which clearly reveal the presence of phase defects in condensates close to the ideal gas Bose-Einstein condensation temperature. We discuss the possible underlying phase configurations.Our experiments start with an almost pure 87 Rb condensate with 4 × 10 5 atoms in the F = m F = 2 hyperfine state, produced by radio-frequency (rf) evaporation in a cylindrically symmetric Ioffe-Pritchard (IP) magnetic trap. The trapping frequencies are ω z /2π = 12 Hz axially, and ω ⊥ /2π = 106 Hz radially, leading to cigar-shaped condensates with a Thomas-Fermi length of 90 µm and a diameter of 10 µm.After creation of the BEC we ramp up the periodic potential of a 1D optical lattice, which splits the 3D condensate into an array of independent quasi-2D BECs (see Fig. 1(a) and [24]...

In this short review we present our recent results concerning the rotation of atomic Bose-Einstein condensates confined in quadratic or quartic potentials, and give an overview of the field. We first describe the procedure used to set an atomic gas in rotation and briefly discuss the physics of condensates containing a single vortex line. We then address the regime of fast rotation in harmonic traps, where the rotation frequency is close to the trapping frequency. In this limit the Landau Level formalism is well suited to describe the system. The problem of the condensation temperature of a fast rotating gas is discussed, as well as the equilibrium shape of the cloud and the structure of the vortex lattice. Finally we review results obtained with a quadratic + quartic potential, which allows to study a regime where the rotation frequency is equal to or larger than the harmonic trapping frequency.