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

Chao Feng,Yu Chen

Fig. 2 (Color online) Induced interaction in momentum space $V_{\rm ind}({q})$. The momentum space is restricted to the cubic region $q_{i=x,y,z}\in[0,\pi/\lambda]$. In (a), (b), (c), (d), we show $V_{\rm ind}({q})$ for different fermion optical lattice strength. $V_P=-E_r$ in (a), $V_P=-2E_r$ in (b), $V_P=-3E_r$ in (c) and $V_P=-5E_r$ in (d). The chemical potential $\mu$ is mixed as $0.1t$. The corner in the center of each figure is ${Q}_\pi=(\pi,\pi,\pi)/\lambda$ point.