Isotopic tuning of scattering lengths of ultracold Yb atoms

The species Yb has 5 stable spinless bosonic isotopes and two fermionic ones, $^{171}$Yb with I=1/2 and $^{173}$Yb with I=5/2. Two-color photoassociation spectroscopy of ultracold Yb atomic gases has been used to measure the binding energies of 7 J=0 and 5 J=2 bound states near the dissociation threshold of the homonuclear molecular dimers $^{170}$Yb$_{2}$, $^{171}$Yb$_{2}$, $^{172}$Yb$_{2}$, $^{173}$Yb$_{2}$, $^{174}$Yb$_{2}$, and $^{176}$Yb$_{2}$. Fitting 3 binding energies from $^{174}$Yb$_{2}$ and $^{176}$Yb$_{2}$ determines the C$_{6}$ and$_{ }$C$_{8}$ van der Waals constants and the absolute number of bound states in the single ground state potential. Our mass-scaled model then accurately predicts the binding energies of the other 9 measured levels, and determines accurate scattering lengths of all 28 different isotopic combinations, including $^{168}$Yb. As the reduced mass varies from 168/2 to 176/2, the scattering lengths vary through a complete cycle from --$\infty $ to +$\infty $. Thus, scattering length can be widely ``tuned'' by varying isotopic composition. Since all 6 species from mass 170 to 176 can be brought to the quantum degenerate regime, this gives a wide variety of mixtures for new studies of ultracold quantum gases and lattices.