  We describe interacting mixtures of ultracold bosonic and fermionic atoms in
harmonically confined optical lattices. For a suitable choice of parameters we
study the emergence of superfluid and Fermi liquid (non-insulating) regions out
of Bose-Mott and Fermi-band insulators, due to finite Boson and Fermion
hopping. We obtain the shell structure for the system and show that angular
momentum can be transferred to the non-insulating regions from
Laguerre-Gaussian beams, which combined with Bragg spectroscopy can reveal all
superfluid and Fermi liquid shells.
