  A mixture of ultracold bosons and fermions placed in an optical lattice
constitutes a novel kind of quantum gas, and leads to phenomena, which so far
have been discussed neither in atomic physics, nor in condensed matter physics.
We discuss the phase diagram at low temperatures, and in the limit of strong
atom-atom interactions, and predict the existence of quantum phases that
involve pairing of fermions with one or more bosons, or, respectively, bosonic
holes. The resulting composite fermions may form, depending on the system
parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an
insulator with fermionic domains. We discuss the feasibility for observing such
phases in current experiments.
