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arXiv:0708.0752 · Physical Review A

Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s -wave scattering lengths

Masaaki Kitagawa, Katsunari Enomoto, Kentaro Kasa, Yoshiro Takahashi, R. Ciuryło, Pascal Naidon, Paul S. Julienne

Published Jan 28, 2008• 225 citations
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Abstract

By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the $s$-wave scattering lengths of all 28 pairs of the seven stable isotopes. The $s$-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for $^{168}\text{Y}\text{b}$, 3.38(11) nm for $^{170}\text{Y}\text{b}$, $\ensuremath{-}0.15(19)\text{ }\text{nm}$ for $^{171}\text{Y}\text{b}$, $\ensuremath{-}31.7(3.4)\text{ }\text{nm}$ for $^{172}\text{Y}\text{b}$, 10.55(11) nm for $^{173}\text{Y}\text{b}$, 5.55(8) nm for $^{174}\text{Y}\text{b}$, and $\ensuremath{-}1.28(23)\text{ }\text{nm}$ for $^{176}\text{Y}\text{b}$. The coefficient of the lead term of the long-range van der Waals potential of the ${\text{Yb}}_{2}$ molecule is ${C}_{6}=1932(30)$ atomic units $({E}_{h}{a}_{0}^{6}\ensuremath{\approx}9.573\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{J}\text{ }{\text{nm}}^{6})$.

DOI
10.1103/physreva.77.012719

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By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the sss-wave scattering lengths of all 28 pairs of the seven stable isotopes. The sss-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for 168Yb^{168}\text{Y}\text{b}168Yb, 3.38(11) nm for 170Yb^{170}\text{Y}\text{b}170Yb, \ensuremath−0.15(19) nm\ensuremath{-}0.15(19)\text{ }\text{nm}\ensuremath−0.15(19) nm for 171Yb^{171}\text{Y}\text{b}171Yb, \ensuremath−31.7(3.4) nm\ensuremath{-}31.7(3.4)\text{ }\text{nm}\ensuremath−31.7(3.4) nm for 172Yb^{172}\text{Y}\text{b}172Yb, 10.55(11) nm for 173Yb^{173}\text{Y}\text{b}173Yb, 5.55(8) nm for 174Yb^{174}\text{Y}\text{b}174Yb, and \ensuremath−1.28(23) nm\ensuremath{-}1.28(23)\text{ }\text{nm}\ensuremath−1.28(23) nm for 176Yb^{176}\text{Y}\text{b}176Yb. The coefficient of the lead term of the long-range van der Waals potential of the Yb2{\text{Yb}}_{2}Yb2​ molecule is C6=1932(30){C}_{6}=1932(30)C6​=1932(30) atomic units (Eha06\ensuremath≈9.573\ifmmode×\else\texttimes\fi10\ensuremath−26 J nm6)({E}_{h}{a}_{0}^{6}\ensuremath{\approx}9.573\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{J}\text{ }{\text{nm}}^{6})(Eh​a06​\ensuremath≈9.573\ifmmode×\else\texttimes\fi10\ensuremath−26 J nm6).
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 $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$. 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.u. On the other hand 87{}^{87}87Rb170{}^{170}170Yb 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{}^{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)].
We perform two-photon photoassociation spectroscopy of the heteronuclear CsYb molecule to measure the binding energies of near-threshold vibrational levels of the $X{\phantom{\rule{3.33333pt}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ molecular ground state. We report results for 133Cs170Yb^{133}\mathrm{Cs}^{170}\mathrm{Yb}133Cs170Yb, 133Cs173Yb^{133}\mathrm{Cs}^{173}\mathrm{Yb}133Cs173Yb, and 133Cs174Yb^{133}\mathrm{Cs}^{174}\mathrm{Yb}133Cs174Yb, in each case determining the energy of several vibrational levels including the least-bound state. We fit an interaction potential based on electronic structure calculations to the binding energies for all three isotopologs and find that the ground-state potential supports 77 vibrational levels. We use the fitted potential to predict the interspecies sss-wave scattering lengths for all seven Cs+Yb isotopic mixtures.
Photoassociation spectroscopy, based on forming of molecules from colliding atoms in the presence of light, is a priceless tool for the study of atomic interactions. It enables direct measurements of bound state energies, both in excited and ground state molecules. Applications include determinations of s -wave scattering lengths, as well as atomic state lifetimes. In this work we present the results of our research on the mass-scaling behaviour of molecular bound state energies and collisional properties in spin-singlet atoms. We will concentrate on two such species: strontium and ytterbium, both of which offer several stable isotopes, enabling mass tuning of the system's properties.
We report photoassociation spectroscopy of 174Yb^{174}\mathrm{Yb}174Yb for the $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{1}P_{1}$ transition at $1\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$, where only the sss-wave scattering state contributes to the spectra. The wave function of the sss-wave scattering state is obtained from the photoassociation efficiency, and we determine that the C6{C}_{6}C6​ potential coefficient is $2300\ifmmode\pm\else\textpm\fi{}250\text{ }\text{ }\mathrm{a}.\mathrm{u}.$ and the sss-wave scattering length is $5.53\ifmmode\pm\else\textpm\fi{}0.11\text{ }\text{ }\mathrm{nm}$. Based on these parameters, we discuss the scattering properties of sss- and ddd-wave states.
Low-lying rovibrational levels of Yb2{}_{2}2​ molecules are measured by photoassociation to an accuracy of about 500 Hz. The measurements, in combination with a potential model that includes some beyond-Born-Oppenheimer effects, produce a determination of the sss-wave scattering lengths with error bars which are over two orders of magnitude better than previous determinations.
The triplet s-wave scattering length of 6Li^{6}\mathrm{Li}6Li is determined using two-photon photoassociative spectroscopy of the diatomic a3{\mathrm{}}^{3}3${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ state of 6Li2^{6}\mathrm{Li}_{2}6Li2​. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)a0{\mathrm{a}}_{0}a0​, where a0{\mathrm{a}}_{0}a0​ is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving 6Li^{6}\mathrm{Li}6Li and 7Li^{7}\mathrm{Li}7Li determined from this and our previous spectroscopic investigations is given.