  We realize simultaneous quantum degeneracy in mixtures consisting of the
alkali and alkalineearth-like atoms Li and Yb. This is accomplished within an
optical trap by sympathetic cooling of the fermionic isotope 6Li with
evaporatively cooled bosonic 174Yb and, separately, fermionic 173Yb.Using
cross-thermalization studies, we also measure the elastic s-wave scattering
lengths of both Li-Yb combinations, |a6Li-174Yb| = 1.0\pm0.2 nm and
|a6Li-173Yb| = 0.9\pm0.2 nm. The equality of these lengths is found to be
consistent with mass-scaling analysis. The quantum degenerate mixtures of Li
and Yb, as realized here, can be the basis for creation of ultracold molecules
with electron spin degrees of freedom, studies of novel Efimov trimers, and
impurity probes of superfluid systems.
