We have investigated the expansion of a Bose-Einstein condensate of strongly magnetic chromium atoms. The long-range and anisotropic magnetic dipole-dipole interaction leads to an anisotropic deformation of the expanding chromium condensate which depends on the orientation of the atomic dipole moments. Our measurements are consistent with the theory of dipolar quantum gases and show that a chromium condensate is an excellent model system to study dipolar interactions in such gases.

We analyze the scattering of bright solitons in dipolar Bose-Einstein condensates placed in uncon-nected layers. Whereas for short-range interactions unconnected layers are independent, a remarkable consequence of the dipole interaction is the appearance of novel nonlocal interlayer effects. In particular, we show that the interlayer interaction leads to an effective molecular potential between disconnected solitons, inducing a complex scattering physics between them, which includes inelastic fusion into soliton-molecules, and strong symmetric and asymmetric inelastic resonances. In addition , a fundamentally new 2D scattering scenario in matter-wave solitons is possible, in which inelastic spiraling occurs, resembling phenomena in photorrefractive materials. Finally, we consider the scattering of unconnected 1D solitons and discuss the feasibility in current on going experiments. Up to very recently, typical experiments on ultra cold gases involved particles interacting dominantly via a short-range isotropic potential, which, due to the very low energies involved, is fully determined by the corresponding s-wave scattering length. However, recent experiments on cold molecules [1], Rydberg atoms [2], and atoms with large magnetic moment [3], open a fascinating new research area, namely that of dipolar gases, for which the dipole-dipole interaction (DDI) plays a significant or even dominant role. The DDI is long-range and anisotropic (partially attractive), and leads to fundamentally new physics in condensates [4, 5, 6], degenerated Fermi gases [7], and strongly-correlated atomic systems [8]. It leads to the Einstein-de Haas effect in spinor con-densates [9], and may be employed for quantum computation [10], and ultra cold chemistry [11]. Recently, time-of-flight experiments in Chromium have allowed for the first observation ever of dipolar effects in quantum gases [12]. Interestingly, the physics of short-range interacting Bose-Einstein condensates (BECs) at low temperatures is given by a nonlinear Schrödinger equation (NLSE) with cubic local nonlinearity, similar to the one appearing in other systems, in particular in Kerr media in nonlinear optics. In 1D, nonlinearity allows for solitonic solutions [13], which have been observed in BEC [14]. However, bright solitons are unstable in 2D and 3D. In periodic potentials multidimensional discrete solitons are possible [15], but they do not move in a multidimensional way, although the use of optical lattices has been proposed to move 2D and 3D discrete solitons along a free direction [16]. Other interesting possibility to stabilize high dimensional solitons is to use Feshbach resonances to manage spatially and/or temporally the scattering length [17]. Due to the DDI, a dipolar BEC is described by a NLSE with nonlocal cubic nonlinearity [4, 5, 6], opening an interesting cross-disciplinary link between BEC and other nonlocal nonlinear media, as e.g. plasmas [18], where the nonlocal response is induced by heating and ioniza-tion, and nematic liquid crystals, where it is ...

We study the expansion of a dilute ultracold sample of fermions initially trapped in a anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similarly to what happens with Bose-Einstein condensates. Viceversa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.Since the first experiments on trapped Bose-Einstein condensates the imaging of the expanding cloud, following the sudden switching off of the confining potential, has provided crucial information on the novel features exhibited by atomic gases in conditions of quantum degeneracy. These include, in particular, the bimodal structure of an expanding Bose gas at finite temperature and the anisotropy of the asymptotic profile of the condensate [1,2]. In the Thomas-Fermi limit, where the Gross-Pitaevskii equations coincide with the hydrodynamic theory of superfluids, the anisotropy of the expanded gas reflects the anisotropy of the pressure force which is stronger in the direction of tighter confinement [3]. The predictions of the hydrodynamic equations and of the consequent scaling behaviour exhibited by BoseEinstein condensates during the expansion have been investigated by several authors ( [4], [5], [6]), providing excellent agreement with experiments [7,8] and pointing out the difference with respect to the expansion of a non condensed gas. In the latter case, in the collisionless regime, the density profile approaches an isotropic shape, independent of the initial deformation of the gas.In this letter we study the problem of the expansion of an ultracold sample of fermions initially trapped in an anisotropic harmonic trap. We will show that also in the case of fermions the expansion of the gas provides valuable information about the state of the system and the role of interactions. We will consider a gas of atoms interacting with attractive forces. This is a natural requirement for the realization of Cooper-pairs and hence for the achievement of the superfluid phase [9]. Such interactions are naturally present in some fermionc species like 6 Li and can otherwise be obtained by changing the scattering length profiting of the presence of a Feshbach resonance.The description of the expansion of a cold fermionic gas in the normal and superfluid phase requires different theoretical approaches. For the normal phase we use the formalism of the Landau-Vlasov equations, while in the superfluid phase we study the expansion using the hydrodynamic theory of superfluids.We consider the case of two different fermionic states, hereafter called 1 and 2, initially confined in a harmonic trap. We assume that the two species are pres...

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wavefunction. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.

We study dipolar relaxation in both ultra-cold thermal and Bose-condensed chromium atom gases. We show three different ways to control dipolar relaxation, making use of either a static magnetic field, an oscillatory magnetic field, or an optical lattice to reduce the dimensionality of the gas from 3D to 2D. Although dipolar relaxation generally increases as a function of a static magnetic field intensity, we find a range of non-zero magnetic field intensities where dipolar relaxation is strongly reduced. We use this resonant reduction to accurately determine the S = 6 scattering length of chromium atoms: a6 = 103 ± 4a0. We compare this new measurement to another new determination of a6, which we perform by analysing the precise spectroscopy of a Feshbach resonance in d-wave collisions, yielding a6 = 102.5 ± 0.4a0. These two measurements provide by far the most precise determination of a6 to date. We then show that, although dipolar interactions are long-range interactions, dipolar relaxation only involves the incoming partial wave l = 0 for large enough magnetic field intensities, which has interesting consequences on the stability of dipolar Fermi gases. We then study ultra-cold chromium gases in a 1D optical lattice resulting in a collection of independent 2D gases. We show that dipolar relaxation is modified when the atoms collide in reduced dimensionality at low magnetic field intensities, and that the corresponding dipolar relaxation rate parameter is reduced by a factor up to 7 compared to the 3D case. Finally, we study dipolar relaxation in presence of radio-frequency (rf) oscillating magnetic fields, and we show that both the output channel energy and the transition amplitude can be controlled by means of rf frequency and Rabi frequency. Strong dipole-dipole interactions arise when an atomic or molecular species carries a strong permanent magnetic or electric dipole moment. Good candidates therefore include heteronuclear molecules with large electric dipole moments (which were recently produced at large phasespace densities [7]), or atoms with large electronic spin (so far erbium [8], dysprosium [9] and chromium). Up to now, chromium is the only species with large dipole moment for which a quantum degenerate gas has been produced [10,11]. Smaller dipolar effects were also observed in a BEC of potassium for which the scattering length can be precisely tuned to zero by means of a Feshbach resonance [12].Interesting new physics comes at play when one also considers the spin degree of freedom. Spin dynamics of optically trapped multi-component Bose-Einstein Condensates (also known as spinor condensates) [13] has been observed [14]. Coherent oscillations between the spin components is driven by centrally symmetric short range exchange interactions, and the total magnetization in the system is conserved. In [15] a first dipolar effect was observed on the spin texture of a Rb spinor condensate. Dipole-dipole interaction will introduce additional new features in spin dynamics as it couples the spin degree of fre...