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

Chao Feng,Yu Chen

Fig. 4 (Color online) The static structure factor in momentum space $\chi_0({q})$. In these figures we only show the largest region of the static structure factor. In (a), the chemical potential is $\mu=t$; In (b), the chemical potential is $\mu=0.5t$; and in (c), the chemical potential is $\mu=0.1t$. The brighter color is for larger $\chi({q})$, and the darker color is for smaller $\chi({q})$. Three axes are $q_x$, $q_y$, and $q_z$ direction, from $-\pi$ to $\pi$. Beyond this range, the static structure factor is almost zero, suppressed by the band gap.