We report on the Bose-Einstein condensation of potassium atoms, whereby quantum degeneracy is achieved by sympathetic cooling with evaporatively cooled rubidium. Because of the rapid thermalization of the two different atoms, the efficiency of the cooling process is high. The ability to achieve condensation by sympathetic cooling with a different species may provide a route to the production of degenerate systems with a larger choice of components.

We employ radio-frequency spectroscopy on weakly bound 6 Li2 molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold 6 Li atoms based on a multi-channel quantum scattering model. We determine the singlet and triplet scattering lengths to be as = 45.167(8)a0 and at = −2140(18)a0 (1 a0 = 0.0529177 nm), and the positions of the broad Feshbach resonances in the energetically lowest three s−wave scattering channels to be 83.41 (15) [2,3,4,5,6] and the studies of the crossover physics from a molecular Bose-Einstein condensate to atomic Cooper pairs in the Bardeen-CooperSchrieffer state (BEC-BCS crossover) [5,7,8]. These studies are of general importance in physics as the ultracold Fermi gas provides a unique model system for other strongly interacting fermionic systems [9].In spin mixtures of 6 Li atoms, a broad Feshbach resonance in the energetically lowest s-wave channel [10] allows for precise interaction tuning. This, together with the extraordinary stability of the system against inelastic decay [2,11], makes 6 Li the prime candidate for BEC-BCS crossover studies. Precise knowledge of the magnetic-field dependent scattering properties is crucial for a quantitative comparison of the experimental results with crossover theories. Of particular importance is the precise value of the magnetic field where the s−wave scattering diverges. At this unique point, the strongly interacting fermionic quantum gas is expected to exhibit universal properties [12]. Previous experiments explored the 6 Li resonance by measuring inelastic decay [13], elastic collisions [14,15], and the interaction energy [16], but could only locate the exact resonance point to within a range between 80 mT and 85 mT.An ultracold gas of weakly bound molecules is an excellent starting point to explore the molecular energy structure near threshold [17]. Improved knowledge on the exact 6 Li resonance position was recently obtained in an experiment that observed the controlled dissociation of weakly bound 6 Li 2 molecules induced by magnetic field ramps [18]. These measurements provided a lower bound of 82.2 mT for the resonance position. Studies of systematic effects suggested an upper bound of 83.4 mT. Within this range, however, we observe the physical behavior of the ultracold gas still exhibits a substantial dependence on the magnetic field [8]. In this Letter, we apply radiofrequency (rf) spectroscopy [17,19] on weakly bound molecules to precisely determine the interaction parameters of cold 6 Li atoms. Together with a multi-channel quantum scattering model, we obtain a full characterization of the two-body scattering properties, essential for BEC-BCS crossover physics.The relevant atomic states are the lowest three sublevels in the 6 Li ground state manifold, denoted by |1 , |2 and |3 . Within the magnetic field range investigated in this experiment, these levels form a triplet of st...

Feshbach resonances in 6 Li were experimentally studied and theoretically analyzed. In addition to two previously known s-wave resonances, we found three p-wave resonances. Four of these resonances are narrow and yield a precise value of the singlet scattering length, but do not allow us to accurately predict the location of the broad resonance near 83 mT. Its position was previously measured in a molecule-dissociation experiment for which we, here, discuss systematic shifts. [2,4,6,7,8,9,10].In 6 Li these experiments have been carried out in the vicinity of the s-wave Feshbach resonance near 830 G [2,4,7,8,9,10] (1 G = 10 −4 Tesla). The quantitative interpretation of these experiments and the characterization of the BEC-BCS crossover require a precise knowledge of the resonance location. However, its determination is not trivial since the resonance width is extremely large (180 G), and the line shape is strongly affected by many body effects. In our previous work we determined the position of this resonance by the onset of molecule dissociation to be 822 ± 3 G [7].In this paper we report on a detailed study of Feshbach resonances in 6 Li with the goal of accurately characterizing the interaction potential of two 6 Li atoms. Three resonances in the |1 and |2 states which are p-wave resonances have been observed [11]. The positions of these Feshbach resonances together with the location of a narrow s-wave resonance in the |1 + |2 mixture near 543 G are used for a precise determination of the singlet swave scattering length. These results, however, do not constrain the position of the broad resonance, which also depends on the triplet scattering length. An improved measurement of its location is presented and the magnitude and the origin of possible systematic errors are discussed.The experimental setup has been described in Ref. [12].Up to 4 × 10 7 quantum degenerate 6 Li atoms in the |F,m F = |3/2, 3/2 state were obtained in a magnetic trap by sympathetic cooling with 23 Na. The 6 Li atoms were then transferred into an optical dipole trap (ODT) formed by a 1064 nm laser beam with a maximum power of 9 W. In the optical trap three different samples were prepared: A single radio-frequency sweep transferred the atoms to state |1 (|F,m F = |1/2, 1/2 at low field). Another Landau-Zener sweep at an externally applied magnetic field of 565 G could then be used to either prepare the entire sample in state |2 (|1/2, −1/2 at low field) or create an equal mixture of atoms in state |1 and |2 . Except for the measurement of the broad s-wave Feshbach resonance, all resonances were observed by monitoring magnetic field dependent atom losses. Atom numbers were obtained from absorption images taken at zero field. The externally applied field was calibrated by driving microwave transitions from state |2 to state |5 (|3/2, 1/2 at low field) and from state |1 to state |6 (|3/2, 3/2 at low field) for several magnetic fields close to the resonance positions. For spin polarized samples either in state |1 or |2 swave scattering is forb...

We have observed Feshbach resonances in collisions between ultracold 52Cr atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of 52Cr and thus the absence of a Fermi-contact interaction leads to regularly spaced resonance sequences. By comparing resonance positions with multichannel scattering calculations we determine the s-wave scattering length of the lowest (2S+1)Sigma(+)(g) potentials to be 112(14) a(0), 58(6) a(0), and -7(20) a(0) for S=6, 4, and 2, respectively, where a(0)=0.0529 nm.

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances focusing on the specific 40 Ca + + Na system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of the charge-neutral ultracold systems.Advances in trapping, cooling, manipulation and readout of single atoms and ions have led over recent years to a range of fundamental as well as applied investigations on the quantum properties of such systems. Nowadays, an increasing number of experimental groups worldwide are starting experiments with combined charged-neutral systems in various configurations [1]. While the theory of atom-ion collisions is well established for high collision energies [2,3], a theoretical description in the ultracold domain is still largely missing.This letter presents the first study of magnetic Feshbach resonances and the first fully quantum study of the radiative charge exchange process for ultracold atomion systems that includes effects of Feshbach and shape resonances. Here we consider only two-body collisions in free space, a necessary prelude to further studies incorporating effects of ion micromotion or trap confinement. We develop a reliable yet manageable effective model of atom-ion collisions by applying multichannel quantum defect theory (MQDT) [4,5,6] based on the long range ion-induced-dipole potential that varies as r −4 at large ion-atom distance r [7,8]. This powerful tool has proven effective as a few-parameter approach for describing scattering and bound states in electron-ion core [4], electron-atom [9] and neutral atom systems [10]. Although the literature on the subject is rich, here we discuss some details of MQDT illustrating how it works in the ultracold domain, so we can reveal the new and interesting ultracold ion-atom physics. We adapt MQDT to the atom-ion realm, utilizing the analytical solutions for the r −4 asymptotic potential [9,11] and applying the frame transformation [10,12] at short distances to reduce the number of quantum defect parameters in the model. We verify the model predictions by comparing to our own numerical close-coupled calculations, taking 40 Ca + − 23 Na [13] as a reference system.We describe the S-state atom and S-state ion collisions with the close-coupled radial Schrödinger equationHere, µ = m i m a /(m i + m a ) denotes the reduced mass, W(r) is the interaction matrix, and F(r) is the matrix of radial solutions. The wave function for N scattering channels reads Ψ i (r) = N j=1 A j Y j (r)F ij (r)/r where Y j (r) denotes the angular par...

We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold ^{39}K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the nonuniversal coupling of two scattering channels. Instead, our observed ratio of the three-body parameter with the van der Waals radius is approximately the same universal ratio as for broader resonances. This unexpected observation suggests the presence of a new regime for three-body scattering at narrow resonances.

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