Magnetic-field imaging of weakly bound levels of the ground-stateNa2dimer

Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium

“…(2) with R-dependent interaction potentials and coupling terms. The R-dependent functions are found in a fit to all known Feshbach resonances and existing spectroscopic data of more deeply bound rovibrational levels of the X 1 + g and a 3 + u potentials [8][9][10][11][12]. Data from conventional spectroscopy by Kush and Hessel [39] and by Barrow et al [40] for the ground-state X 1 + g potential and by Li Li et al [41] for the lowest triplet state a 3 + u potential are also included.…”

“…We find that all the observed Feshbach resonances can be described by a single vibrational triplet level below the |1,1 + |1,1 dissociation threshold. In fact, it is the v a = 14 level with l = 0, 2, and 4 [10]. From a least-squares fit including all resonances we obtain for the rotational structure of this vibrational level three fitted energies: ε 1,0 14 /h = −4976 MHz, ε 1,2 14 /h = −3679 MHz, and ε 1,4 14 /h = −765 MHz, where the energies are given with respect to the |1,1 + |1,1 dissociation threshold.…”

“…We start the optimization process of the potentials with functions known from earlier work [10] in iteration loops containing two steps. First, the location of the Feshbach resonances and the photoassociation data from Ref.…”

“…In order to accurately and quantitatively describe both bound states and scattering processes, which include Feshbach resonances, we require the Hamiltonian for two sodium atoms in a magnetic field B (see, e.g., [10,28]). Here we use an extension that allows for a second-order spin-orbit interaction [29] and a hyperfine-contact interaction that depends on the internuclear separation R. The effect of this second correction was recently studied for Rb 2 [30].…”

“…All three are s-wave resonances, that is, caused by molecular states with rotational quantum number l = 0. In parallel, Raman spectroscopy on a molecular beam of sodium dimers to locate the least-bound rovibrational states of the ground-state potentials X 1 + g and a 3 + u has been performed [8][9][10]. Scattering lengths [9] as well as Feshbach resonance positions [10] were extracted.…”