We observe bound states just below the dissociation limit and shape and Feshbach resonances between the ground state hyperfine asymptotes by Raman spectroscopy on a molecular beam of sodium dimers. The rotational selectivity of a two-photon transition gives access to specific states of nuclear motion and thus to cold collision properties of two colliding atoms. Modeling of the collisional resonance structures requires a multichannel treatment of the nuclear dynamics that uses highly accurate $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potentials. These potentials are constructed from bound levels just below the ground state asymptote measured in this experiment and bound state information available in the literature. We also present simulations of the spectrum between the ground state hyperfine asymptotes. The good agreement shows that accurate potentials obtained from bound state information are able to reproduce scattering properties of two colliding sodium atoms. From this analysis we find for the scattering lengths ${a(f=2)=a}_{1,\ensuremath{-}1}{=52.98(40)a}_{0},$
asinglet=19.20(30)a0, and
atriplet=62.51(50)a0, where
1a0=0.0529177 nm.
eshbach resonances play a central role in the manipulation of the interparticle interaction in ultracold atomic gases. The Asymptotic Bound-state Model (ABM) [1,2] is a powerful and easy-to-use tool to predict properties of these Feshbach resonances. This model exploits the fact that only the least bound states in the interaction potential determine the low energy interaction properties. These bound states are coupled by hyperfine and Zeeman interactions, and the intersection of these coupled bound states with the scattering threshold determine the position of these Feshbach resonances. The high accuracy of this model was clearly demonstrated when assigning 13 resonances in the 6Li-40K mixture by using only two bound state parameters [1]. Here we discuss the extension of the ABM by the including threshold effects, which allow for the prediction of the resonance width as well.
We have studied magnetic Feshbach resonances in an ultracold sample of Na prepared in the absolute hyperfine ground state. We report on the observation of three
s-, eight
d-, and three
g-wave Feshbach resonances, including a more precise determination of two known
s-wave resonances, and one
s-wave resonance at a magnetic field exceeding 200 mT. Using a coupled-channels calculation we have improved the sodium ground-state potentials by taking into account these new experimental data and derived values for the scattering lengths. In addition, a description of the molecular states leading to the Feshbach resonances in terms of the asymptotic-bound-state model is presented.