We study a bosonic version of the Kondo lattice model with an on-site
repulsion in the conduction band, implemented with alkali atoms in two bands of
an optical lattice. Using both weak and strong-coupling perturbation theory, we
find that at unit filling of the conduction bosons the superfluid to Mott
insulator transition should be accompanied by a magnetic transition from a
ferromagnet (in the superfluid) to a paramagnet (in the Mott insulator).
Furthermore, an analytic treatment of Gutzwiller mean-field theory reveals that
quantum spin fluctuations induced by the Kondo exchange cause the otherwise
continuous superfluid to Mott-insulator phase transition to be first order. We
show that lattice separability imposes a serious constraint on proposals to
exploit excited bands for quantum simulations, and discuss a way to overcome
this constraint in the context of our model by using an experimentally realized
non-separable lattice. A method to probe the first-order nature of the
transition based on collapses and revivals of the matter-wave field is also
discussed.
