as a function of $\chi_{bf}$, for parameter values $\chi_{b}=1, \varepsilon=3, N_b=1,  N_f=20$. The top horizontal line represents the bottom of the fermionic band while the insets are enlargement of rectangles a,b, where level crossing and avoid crossing occur, respectively. Right Panel. Wavefunctions of the gap soliton (thick line) and of trapped fermionic states (ordered by decreasing energy from the top) at $\chi_{bf}=-30$. Other parameters are fixed as in the right panel. The vertical dotted line and the periodic potential at the bottom (scaled by a factor $60$) were drawn to identify the symmetry of the wavefunctions. A vertical offset among curves was introduced to avoid overlapping. All plotted quantities are in normalized units.[]{data-label="fig6"}](fig6a.eps "fig:"){width="4.4cm" height="4.8cm"} ![Left panel. Energy levels of the fermionic bound states inside the condensate as a function of $\chi_{bf}$, for parameter values $\chi_{b}=1, \varepsilon=3, N_b=1,  N_f=20$. The top horizontal line represents the bottom of the fermionic band while the insets are enlargement of rectangles a,b, where level crossing and avoid crossing occur, respectively. Right Panel. Wavefunctions of the gap soliton (thick line) and of trapped fermionic states (ordered by decreasing energy from the top) at $\chi_{bf}=-30$. Other parameters are fixed as in the right panel. The vertical 