as a model for an optical lattice. We assume $m_b=m_f=m$, $V_{ext}^b= V_{ext}^f=V_{trap}$ and normalize Eqs. (\[bose-fermi-eqns\]) by measuring space in units of $k_L^{-1}$, time in units of $\hbar/E_r$ ($E_r=\hbar^2
k_L^2/2m$ is the lattice recoil energy) and rescaling wavefunctions according to $\psi_b \rightarrow (g_{{b}_0} N_b /2
\pi E_r {a_{\perp}}^2)^{1/2} \psi_b$, $\psi_f\rightarrow
(g_{{bf}_0}/2\pi E_r {a_{\perp}^2})^{1/2})^{1/2}) \psi_f $. This leads to the same normalized equations (\[norm-eqns\]) but with $V=\varepsilon \cos(2x)$, where $\varepsilon=V_0/E_r$. With this normalization the relation between the dimensionless number of bosons $N_b$ and the physical one is $N_p=(k_L
a_{\perp}^2/a_{b})N_b$ (typical values are in the range of $10^3-10^5$ atoms, for $a_{\perp}\approx 10^{-6} m, k_L=10^7
m^{-1}, a_{b}= 1 \div 50 \cdot 10^{-10}m$). In the following we show the existence of gap-solitons in BFM and suggest them as matter wave quantum dots (anti-dots) (the anti-dot case will be discussed elsewhere [@msalerno]).

![Time evolution of the OS (left panel) and IS (right panel) BFM densities in Fig. \[fig3\]a and Fig. \[fig3\]b obtained from direct numerical integrations of Eqs. (\[bose-fermi-eqns\]) on a line of length $L=40 \pi$. Space and time are in normalized units.[]{data-label="fig4"}](fig4a.eps "fig:"){width="4.3cm" height="4.8cm"} ![Time evolution of the OS (left panel) and IS (right panel) BFM densities in Fig. \[fig3\]a and Fig. \[fig3\]b obtained 