Effective Hamiltonian study of excitations in a boson- fermion mixture with attraction between components

TL;DR

This paper develops an effective Hamiltonian approach to analyze collective excitations in a boson-fermion ultracold mixture, revealing how interactions influence stability and oscillation modes.

Contribution

It introduces an analytical framework for studying excitations in boson-fermion mixtures with attractive interactions, linking collapse phenomena to collective mode behavior.

Findings

Analytical solutions for collective modes in the mixture.

Identification of conditions leading to collapse.

Dependence of oscillation frequencies on scattering length and atom number.

Abstract

An effective Hamiltonian for the Bose subsystem in the mixture of ultracold atomic clouds of bosons and fermions with mutual attractive interaction is used for investigating collective excitation spectrum. The ground state and mode frequencies of the $^{87}$Rb and $^{40}$K mixture are analyzed quantitatively at zero temperature. We find analytically solutions of the hydrodynamics equations in the Thomas- Fermi approximation. We discuss the relation between the onset of collapse and collective modes softening and the dependence of collective oscillations on scattering length and number of boson atoms.