  We study degenerate mixtures of "heavy" bosons and "light" superfluid bosons
using a variational polaron transformation. We consider the Mott
insulator-superfluid transition of the heavy species and find that at $T=0$
interaction favors the superfluid phase of the heavy species. Our analytic
results agree well with numerically exact quantum Monte Carlo simulations in
two dimensions. We then show that in three dimensions the variational polaron
transformation can be combined with a Gutzwiller approximation to give good
results.
