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

Chao Feng,Yu Chen

Fig. 5 (Color online) In (a) and (b) we give the Bogoliubov spectrum for Bose gases mixed with Fermi gases in deep lattice. The chemical potential of the Fermi gases is $\mu=0.1t$ and $\mu=0.5t$ ($t<0$) in (a) and (b) respectively. In (c), the blue dot-dashed line is for the Bogoliubov spectrum of the interacting Bose gases alone, while the black dashed line and the red solid line are Bogoliubov spectrum of Bose gases mixed with lattice fermions along $\Gamma MK\Gamma$ route in the first Brilluin zone.