Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The cross-over into two-dimensional and onedimensional condensates was observed by a change in aspect ratio and saturation of the release energy when the number of trapped atoms was reduced.New physics can be explored when the hierarchy of physical parameters changes. This is evident in dilute gases, where the onset of Bose-Einstein condensation occurs when the thermal deBroglie wavelength becomes longer than the average distance between atoms. Dilutegas condensates of density n in axially-symmetric traps are characterized by four length scales: Their radius R ⊥ , their axial half-length R z , the scattering length a which parameterizes the strength of the two-body interaction, and the healing length ξ = (4πna) −1/2 . In almost all experiments on Bose-Einstein condensates, both the radius and length are determined by the interaction between the atoms and thus, R ⊥ , R z ≫ ξ ≫ a. In this regime, a BEC is three-dimensional and is well-described by the socalled Thomas-Fermi approximation [1]. A qualitatively different behavior of a BEC is expected when the healing length is larger than either R ⊥ or R z since then the condensate becomes restricted to one or two dimensions, respectively. New phenomena that may be observed in this regime are for example quasi-condensates [2-4] and a Tonk's gas of impenetrable bosons [4][5][6].In this Letter, we report the experimental realization of cigar-shaped one-dimensional condensates with R z > ξ > R ⊥ and disk-shaped two-dimensional condensates with R ⊥ > ξ > R z . The cross-over from 3D to 1D or 2D was explored by reducing the number of atoms in condensates which were trapped in highly elongated magnetic traps (1D) and disk-shaped optical traps (2D) and measuring the release energy. In harmonic traps, lower dimensionality is reached when µ 3D = 4π 2 a n/m < ω t . Here, ω t is the trapping frequency in the tightly confining dimension(s) and µ 3D is the interaction energy of a weakly interacting BEC, which in 3D corresponds to the chemical potential. Other experiments in which the interaction energy was comparable to the level spacing of the confining potential include condensates in onedimensional optical lattices [8] and the cross-over to an ideal-gas (zero-D) condensate [7], both at relatively low numbers of condensate atoms.Naturally, the number of interacting atoms in a lowerdimensional condensate is limited. The peak interaction energy of a 3D condensate of N atoms with mass m is given by1/2 are the oscillator lengths of the harmonic potential. The cross-over to 1D and 2D, defined by µ 3D = ω t or equivalently ξ = l t occurs if the number of condensate atoms becomeswhere we have used the scattering length (a = 2.75 nm) and mass of 23 Na atoms to derive the numerical factor. Our traps feature extreme aspect ratios resulting in N 1D > ...

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.PACS numbers: 03.75.Lm, 64.60.My The characteristic feature of Bose-Einstein condensation is the accumulation of a macroscopic number of particles in the lowest quantum state. Condensate fragmentation, the macroscopic occupation of two or more quantum states, is usually prevented by interactions [1], but may happen in spinor condensates [2,3]. However, multiple condensates may exist in metastable situations. Let's assume that an equilibrium condensate has formed in one quantum state, but now we modify the system allowing for one even lower state. How does the original condensate realize that it is in the wrong state and eventually migrate to the true ground state of the system? What determines the time scale for this equilibration process? This is the situation which we experimentally explore in this paper using a double-well potential.The process we study is relevant for at least four different questions.(1) The description of the formation of the condensate is a current theoretical frontier and requires finite-temperature quantum kinetic theories. There are still discrepancies between theoretical predictions and experimental results [4,5]. Our double-well system has the advantage of being an almost closed system (little evaporation) with well defined initial conditions and widely adjustable time scales (through the height of the barrier). (2) Spinor condensates show rich ground states and collective excitations due to the multi-component order parameter [2]. Several groups have observed longlived metastable configurations [6,7,8,9] and speculated about transport of atoms from one domain to another via the thermal cloud [6,8]. The double-well potential allows us to characterize such distillation processes in their simplest realization. (3) The incoherent transport observed here in a double well-potential imposes stringent limitations on future experiments aiming at the observation of coherent transport in Josephson junctions [10,11,12]. (4) Our observation of condensate growth in one potential well due to the addition of thermal atoms realizes the key ideas of proposals on how to achieve a continuous atom laser [13] which is different from the experiment where condensates were replenished with transported condensates [14]. The whole system has equilibrated. V denotes the height of the potential barrier between the two wells, which is measured with respect to the bottom of the left well, and ∆U the trap depth difference between the two wells.The scheme of the experiment is shown in Fig....

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.