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Physical Review A

Determination of collisional properties of cold Na atoms from analysis of bound-state photoassociation and Feshbach resonance field data

Frank A. van Abeelen, BOUDEWIJN J. VERHAAR

Published Jan 1, 1999• 54 citations
Publisher

Abstract

We review the information on the interactions between cold ground-state Na atoms following from ${\mathrm{Na}}_{2}$ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths ${a}_{S}$ and ${a}_{T},$ ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$

DOI
10.1103/physreva.59.578

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We review the information on the interactions between cold ground-state Na atoms following from Na2{\mathrm{Na}}_{2}Na2​ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length a1,\ensuremath−1{a}_{1,\ensuremath{-}1}a1,\ensuremath−1​ of Na atoms in the ∣1,\ensuremath−1〉|1,\ensuremath{-}1〉∣1,\ensuremath−1〉 hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths aS{a}_{S}aS​ and aT,{a}_{T},aT​, a1,\ensuremath−1,{a}_{1,\ensuremath{-}1},a1,\ensuremath−1​, scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find aS=(19.1\ifmmode±\else\textpm\fi2.1)a0,aT=(65.3\ifmmode±\else\textpm\fi0.9)a0,{a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},aS​=(19.1\ifmmode±\else\textpm\fi2.1)a0​,aT​=(65.3\ifmmode±\else\textpm\fi0.9)a0​, and a1,\ensuremath−1(B=0)=(55.4\ifmmode±\else\textpm\fi1.2)a0.{a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.a1,\ensuremath−1​(B=0)=(55.4\ifmmode±\else\textpm\fi1.2)a0​.
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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,{a}_{\mathrm{singlet}}{=19.20(30)a}_{0},asinglet​=19.20(30)a0​, and atriplet=62.51(50)a0,{a}_{\mathrm{triplet}}{=62.51(50)a}_{0},atriplet​=62.51(50)a0​, where 1a0=0.0529177{1a}_{0}=0.05291771a0​=0.0529177 nm.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.
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 sss-, eight ddd-, and three ggg-wave Feshbach resonances, including a more precise determination of two known sss-wave resonances, and one sss-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.
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The experimental characterization of the electronic states correlated to the asymptote of ground state Na (3S) and Rb (5S) atoms was expanded by spectroscopic data on $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels using a high resolution Fourier transform spectroscopy technique. The hyperfine splitting of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels was partially resolved and analyzed for both Na85Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{85}\mathrm{Rb}Na85Rb and Na87Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{87}\mathrm{Rb}Na87Rb isotopomers. Transitions to high lying levels of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states were recorded simultaneously which enables one to determine long range parameters of the molecular potentials. Coupled channels calculations based on the Fourier grid method were finally applied for deriving accurate potential energy curves of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states capable of a reliable description of cold collisions between Na and Rb atoms in their ground states. Scattering lengths and Feshbach resonances were calculated for some quantum states.