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...
