# Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length

## TL;DR

This paper investigates the collective oscillations and parametric resonances in superfluid Fermi-Bose mixtures with oscillating scattering lengths, comparing PDE and ODE models, and applies findings to recent experiments with lithium isotopes.

## Contribution

It introduces a detailed analysis of collective modes and parametric resonances in Fermi-Bose mixtures with time-varying interactions, bridging PDE and ODE modeling approaches.

## Key findings

- Identification of parametric resonances under periodic scattering length variation
- Comparison of PDE and ODE models for mixture dynamics
- Application to experiments with $^{6}$Li and $^{7}$Li atoms

## Abstract

Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic $^{6}$Li and bosonic $^{7}$Li atoms, which approximately have the same masses, is discussed.