Dynamical properties of Fermi-Fermi mixtures of dipolar and nondipolar atoms

Dynamical properties of homogeneous Fermi-Fermi mixtures of dipolar and nondipolar atoms are studied at zero temperature, where dipoles are polarized by an external field. We calculate the density-density correlation functions in a ring-diagram approximation and analyze the pole structure to obtain eigenfrequencies of collective excitations. We first determine stability phase diagrams for the mixtures available in experiments:, i.e., Er-167 - Yb-173, Er-167 - Li-6, Dy-161 - Yb-173, and Dy-161 - Li-6 systems, and show that the mixtures with larger mass imbalance tend to be more unstable. We then investigate the parameter dependence of an undamped zero sound with an anisotropic real dispersion relation in the stable phase for the Dy-161 - Yb-173 mixture, and the speed of sound exhibits a critical angle of possible propagation with respect to the dipole polarization direction, above which the sound mode disappears in the particle-hole continuum. Since the sound mode is a coherent superposition of density fluctuations of dipolar and nondipolar atoms, the existence of the sound mode, e.g., the value of the critical angle, is significantly affected by the interparticle interaction through the density-density correlation between dipolar and nondipolar atoms. We have also observed such an effect of the interparticle interaction in the study of a linear response of density fluctuations to an external perturbation.