Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
We study dipolar relaxation in both ultracold thermal and Bose-condensed Cr 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 three-dimensional (3D) to two-dimensional (2D). Although dipolar relaxation generally increases as a function of a static magnetic-field intensity, we find a range of nonzero magnetic-field intensities where dipolar relaxation is strongly reduced. We use this resonant reduction to accurately determine the
S=6 scattering length of Cr atoms: ${a}_{6}=103\ifmmode\pm\else\textpm\fi{}4{a}_{0}$. We compare this new measurement to another new determination of
a6, which we perform by analyzing the precise spectroscopy of a Feshbach resonance in
d-wave collisions, yielding ${a}_{6}=102.5\ifmmode\pm\else\textpm\fi{}0.4{a}_{0}$. 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 ultracold Cr gases in a one-dimensional (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 the presence of rf oscillating magnetic fields, and we show that both the output channel energy and the transition amplitude can be controlled by means of the rf frequency and Rabi frequency.
The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, the observed rate of inelastic collisions was strongly enhanced in a sodium Bose-Einstein condensate when the scattering length was tuned to both larger or smaller values than the off-resonant value. These strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates.
Abstract. Ultra-cold atomic systems provide a new setting where to investigate the role of longrange interactions. In this paper we will review the basics features of those physical systems, in particular focusing on the case of Chromium atoms. On the experimental side, we report on the observation of dipolar effects in the expansion dynamics of a Chromium Bose-Einstein condensate. By using a Feshbach resonance, the scattering length characterising the contact interaction can be strongly reduced, thus increasing the relative effect of the dipole-dipole interaction. Such experiments make Chromium atoms the strongest candidates at present for the achievement of the strong dipolar regime. On the theoretical side, we investigate the behaviour of ultra-cold dipolar systems in the presence of a periodic potential. We discuss how to realise this situation experimentally and we characterise the system in terms of its quantum phases and metastable states, discussing in detail the differences with respect to the case of zero-range interactions.
We present an accurate quantum mechanical study of molecule–molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ g – ) molecules at cold (∼0.1 K) and ultracold (∼10 –6 K) temperatures. Our calculations show that magnetic spin relaxation in molecule–molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T =0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 × 10 –11 cm –3 s –1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule–molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.