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 propose creation of a molecular Bose-Einstein condensate (BEC) by loading an atomic BEC into an optical lattice and driving it into a Mott insulator (MI) with exactly two atoms per site. Molecules in a MI state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the MI is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.PACS numbers: 03.75. Fi, 42.50.Ct The generation of Bose Einstein condensates (BEC) of dilute atomic gases has resulted in a remarkable series of experiments demonstrating various properties of quantum degenerate gases [1]. One of the next major goals in this effort is the realization of a molecular BEC. A promising route towards a molecular condensate is the conversion of an atomic BEC to molecules via photoassociation, a process discussed so far for conditions of quasihomogeneous trapping of atomic gases [2,3,4,5]. In this Letter we describe a novel path to create condensates of composite atomic objects, in particular a molecular BEC, based on photoassociation via a Mott insulator state of bosonic atoms trapped in an optical lattice [6,7]. This provides an efficient way of generating a molecular BEC, avoiding some of the problems encountered in the quasihomogeneous case [2]. It also touches upon fundamental questions related to the formation of a BEC by "melting" of a Mott-insulator (MI) state in a quantum phase transition, as opposed to the familiar growth from a thermal cloud of atoms [8].Experimental advances in manipulating BECs [1], and in particular the loading of a BEC into an optical lattice generated by interfering laser beams have recently led to a seminal experiment by I. Bloch and collaborators [7]. They demonstrated a quantum phase transition from a BEC or superfluid (SF) state into a MI by varying the lattice laser intensity, as proposed theoretically in [6]. While a SF phase has long range order, the MI phase corresponds to the loading of a precise number of atoms into each lattice site, i.e. Fock state occupation of lattice sites. Among the proposed applications of this new atomic quantum phase are the study of ultracold controlled collisions and quantum computing with neutral atoms [9]. In the present context, the MI phase opens the possibility to efficiently create a molecular BEC in the following four steps: (i) an atomic BEC is loaded into an optical lattice, (ii) the depth V 0 of the optical lattice is increased to create a MI with exactly two particles per lattice site, (iii) a molecular MI state is produced by two-color photoassociation of the atoms under tight trapping conditions, and (iv) by decreasing the depth of the optical lattice the MI state is "melted", and thus a molecular BEC is created in a quantum phase transition.At the end of step (i) above, we have an ensemble of bosonic atoms illuminated by orthogonal, standing wave laser fields tuned far from atomic resonance. These laser fields generate a potential...

When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can to a good approximation ignore the high energy states and thereby obtain an effective two-mode model. Here, we show that the regime in which the two-mode model is valid can be extended by adding an on-site three-body interaction term and a three-body interaction-induced tunneling term to the two-mode Hamiltonian. These terms effectively account for virtual transitions to the higher energy states. We determine appropriate strengths of the three-body terms by an optimization of the minimal value of the wave function overlap within a certain time window. Considering different initial states with three or four atoms, we find that the resulting model accurately captures the dynamics of the system for parameters where the two-mode model without the three-body terms is poor. We also investigate the dependence of the strengths of the three-body terms on the barrier height and the atom-atom interaction strength. The optimal three-body interaction strengths depend on the initial state of the system.