Tunable Range Interactions and Multi-Roton Excitations for Bosons in a Bose-Fermi Mixture with Optical Lattices *

Chao Feng,Yu Chen

Fig. 3 (Color online) In (a), we show the Bogoliubov spectrum for $V_P=-2E_r$ case. $g_{B}n_{B}/E_r=4.05$ and $g_{BF}^2/E_r^2=0.0045$. Red color is small energy value and violet color is for large energy value. In (b), we show the dispersion of bosons in a path from $\Gamma$ point to $M$ point, to $K$ point then return to $\Gamma$ point. A reference dispersion is presented in dashed line when we turn off the boson-fermion interactions.