---
abstract: '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.'
author:
- Mario Salerno
title: 'Matter wave quantum dots (anti-dots) in ultracold atomic Bose-Fermi mixtures'
---

Introduction
============

The possibility to cool atomic Fermi gases below the Fermi temperature [@DeMarco] with the developement of the sympathetic cooling technique [@Hulet] has raised a significant amount of interest in theoretical and experimental studies of atomic Fermi gases embedded in Bose-Einstein condensates (BEC). Such systems have very interesting features which allow to explore a whole class of phenomena, ranging from strongly correlated effects in fermionic atomic gases to novel superfluid phases in Bose-Fermi 