  The properties of ultracold atomic Bose-Fermi mixtures in external potentials
are investigated and the existence of gap solitons of Bose-Fermi mixtures in
optical lattices demonstrated. Using a self-consistent approach we compute the
energy spectrum and show that gap solitons can be viewed as matter wave
realizations of quantum dots (anti-dots) with the bosonic density playing the
role of trapping (expulsive) potential for the fermions. The fermionic states
trapped in the condensate are shown to be at the bottom of the Fermi sea and
therefore well protected from thermal decoherence. Energy levels, filling
factors and parameters dependence of gap soliton quantum dots are also
calculated both numerically and analytically.
