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 and antidots 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.
In recent years ultracold atomic gases have emerged as a new and promising platform for exploring the physics of quantum many-body systems, allowing researchers to revisit fundamental problems of condensed-matter physics such as superconductivity or magnetism. By trapping ultracold atoms in the periodic potential created by interfering laser beams (a so-called optical lattice), it has indeed become possible to engineer very clean ?materials? whose parameters can be tuned in a wide range. This bottom-up approach comes very close to Feynman?s idea of a ?quantum simulator?, an