We create Bose-Einstein condensates of 87 Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the BEC and accounts for the main features of the observed behavior. 03.75.Fi, 32.80.Pj, 67.57.De Bose-Einstein condensates (BEC) in dilute atomic gases are macroscopic quantum systems which can be manipulated by a variety of experimental techniques [1]. The current development of such techniques is opening up a wealth of possibilities to explore new physics, e.g., in non-linear atom optics [2], and to study various aspects of superfluid behavior in the precisely controllable context of atomic physics [3].Atoms confined in a periodic potential share some properties with systems of electrons in crystals. Effects known from solid state physics, like Bloch oscillations and Wannier-Stark ladders, have been observed by exposing cold atoms to the dipole potential of far detuned optical lattices [4]. Macroscopic quantum interference has been observed in an experiment on a BEC confined to the antinodes of a far detuned optical lattice [5]. Bragg diffraction from a condensate has been induced in moving optical lattices [6]. This has been used, e.g., as an atom-laser outcoupler [7] and as a tool for spectroscopy of the momentum in BEC's [8]. Applications of BEC's in periodic potentials range from matter-wave transport [9] to interferometry [5] and quantum computing [10]. The question of the stability of the BEC during the evolution in optical potentials is crucial for these applications and has been addressed in theoretical works [11].In this Letter we report on some novel aspects of superfluidity in BEC's by studying their center-of-mass oscillations inside the harmonic potential of a magnetic trap in presence of a one-dimensional (1D) optical lattice. We identify different dynamical regimes by varying the initial displacement of the BEC from the bottom of the trap. For small displacements the BEC performs undamped oscillations in the harmonic potential and feels the periodic potential only through a shift in the oscillation frequency. At larger displacements we observe the onset of dissipative processes appearing through a damping in the oscillations. We can describe the experimental results in terms of an inhomogeneous superfluid having a density-dependent critical velocity. In parallel we report numerical studies of the Gross-Pitaevskii equation (GPE), which capture the main features of the observed dynamics.In our experimental setup [12] we now produce BEC's of 87 Rb atoms in the (F=1,m F = −1) state. The fundamental frequencies of our Ioffe-type magne...

We show that an explicit time-marching method previously developed for the numerical study of the dynamics of Bose-Einstein condensates can be profitably adapted to the numerical determination of their ground state. After reduction to a one-dimensional model, we first reproduce and test known results on condensates in harmonic traps and then determine the ground state of a condensate in a harmonically bound optical lattice in the range of parameters which are relevant to existing experiments.

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We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law ω = ω f [l + 4n(n + l + 2)/3] 1/2 is obtained for the vapour in the collisional regime inside a spherical trap of frequency ω f , with n the number of radial nodes and l the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account for non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix.

Abstract. We present a semiclassical two-fluid model for an interacting Bose gas confined in an anisotropic harmonic trap and solve it in the experimentally relevant region for a spin-polarized gas of 87 Rb atoms, obtaining the temperature dependence of the internal energy and of the condensate fraction. Our results are in agreement with recent experimental observations by Ensher et al .PACS numbers: 03.75.Fi, 67.40.Kh Bose-Einstein condensation (BEC) has recently been realized in dilute vapours of spin-polarized alkali atoms, using advanced techniques for cooling and trapping [1,2,3,4,5]. These condensates consist of several thousands to several million atoms confined in a well which is generated from nonuniform magnetic fields. The confining potential is accurately harmonic along the three Cartesian directions and has cylindrical symmetry in most experimental setups.The determination of thermodynamic properties such as the condensate fraction and the internal energy as functions of temperature is at present of primary interest in the study of these condensates [4,5]. The nature of BEC is fundamentally affected by the presence of the confining potential[6] and finite size corrections are appreciable, leading for instance to a reduction in the critical temperature [7,8,9,10]. Interaction effects are very small in the normal phase but become significant with the condensation-induced density increase. The correction to the transition temperature due to interactions has been recently computed by Giorgini et al [11].The temperature dependence of the condensate fraction was recently measured[5] for a sample of around 40000 87 Rb atoms, the observed lowering in transition temperature being in agreement with theoretical predictions within experimental resolution. In the same work the internal energy was measured during ballistic expansion and found to be significantly higher in the BEC phase than predicted by the ideal-gas model. While the increase is easily understood as a consequence of the interatomic repulsions, a quantitative estimate is still lacking.In this work we present a two-fluid mean-field model which is able to explain the above-mentioned effects, giving results in agreement with experiment for both the condensate fraction and the internal energy as functions of temperature.