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

TL;DR

This paper investigates the collective excitations and stability of homogeneous Fermi-Fermi mixtures of dipolar and non-dipolar atoms at zero temperature, revealing how mass imbalance and interactions influence sound modes and stability.

Contribution

It provides a detailed analysis of the dynamical properties, stability phase diagrams, and anisotropic zero sound behavior in experimentally relevant dipolar mixtures, highlighting the impact of inter-particle interactions.

Findings

Larger mass imbalance leads to increased instability.

Existence of an anisotropic zero sound mode with a critical propagation angle.

Inter-particle interactions significantly affect the sound mode and density fluctuations.

Abstract

Dynamical properties of homogeneous Fermi-Fermi mixtures of dipolar and non-dipolar 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: $^{167}$Er-$^{173}$Yb, $^{167}$Er-$^{6}$Li, $^{161}$Dy-$^{173}$Yb, and $^{161}$Dy-$^{6}$Li 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 $^{161}$Dy-$^{173}$Yb 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 non-dipolar atoms, the existence of the sound mode, e.g., the value of the critical angle, is significantly affected by the inter-particle interaction through the density-density correlation between dipolar and non-dipolar atoms. We have also observed such an effect of the inter-particle interaction in the study of a linear response of density fluctuations to an external perturbation.