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arXiv:1309.3131 · Physical Review A

Scattering lengths in isotopologues of the RbYb system

Mateusz Borkowski, Piotr Szymon Żuchowski, R. Ciuryło, Paul S. Julienne, Dariusz Kędziera, Ł. M. Mentel, Paweł Tecmer, Frank Münchow, Cristian Bruni, Axel Görlitz

Published Nov 20, 2013• 64 citations
arXivHTMLPDF

Abstract

We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold ${}^{87}$Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the $s$-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$. For example, the ${}^{87}$Rb${}^{174}$Yb system is characterized by a large positive scattering length of $+880(120)$ a.u., while ${}^{87}$Rb${}^{173}$Yb has $a=\ensuremath{-}626(88)$ a.u. On the other hand ${}^{87}$Rb${}^{170}$Yb has a very small scattering length of $\ensuremath{-}11.5(2.5)$ a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including ${}^{85}$Rb the variation of the interspecies scattering lengths is much smoother ranging from $+39.0(1.6)$ a.u. for ${}^{85}$Rb${}^{176}$Yb to $+230(12)$ a.u. in the case of ${}^{85}$Rb${}^{168}$Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is ${C}_{6}=2837(13)$ a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].

DOI
10.1103/physreva.88.052708

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We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold 87{}^{87}87Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the sss-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from \ensuremath−\ensuremath∞\ensuremath{-}\ensuremath{\infty}\ensuremath−\ensuremath∞ to +\ensuremath∞+\ensuremath{\infty}+\ensuremath∞. For example, the 87{}^{87}87Rb174{}^{174}174Yb system is characterized by a large positive scattering length of +880(120)+880(120)+880(120) a.u., while 87{}^{87}87Rb173{}^{173}173Yb has a=\ensuremath−626(88)a=\ensuremath{-}626(88)a=\ensuremath−626(88) a.u. On the other hand 87{}^{87}87Rb170{}^{170}170Yb has a very small scattering length of \ensuremath−11.5(2.5)\ensuremath{-}11.5(2.5)\ensuremath−11.5(2.5) a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including 85{}^{85}85Rb the variation of the interspecies scattering lengths is much smoother ranging from +39.0(1.6)+39.0(1.6)+39.0(1.6) a.u. for 85{}^{85}85Rb176{}^{176}176Yb to +230(12)+230(12)+230(12) a.u. in the case of 85{}^{85}85Rb168{}^{168}168Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is C6=2837(13){C}_{6}=2837(13)C6​=2837(13) a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].
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