Superfluid and Fermi liquid phases of Bose-Fermi mixtures in optical lattices

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.