2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138037We study an atomic Bose-Fermi mixture in an optical lattice which is confined using an optical trap. We obtain the Mott ground states of such a system in the limit of deep optical lattice and discuss the effect of quantum fluctuations on these states. We also study the superfluid-insulator transitions of bosons and metal-insulator transition of fermions in such a mixture within a slave-rotor mean-field approximation, and obtain the corresponding phase diagram. We discuss experimental implications of our results.Final version; Aceepted for publication in PRAStrongly Correlated Electronstext