Collisional oscillations of trapped boson-fermion mixtures approaching collapse

TL;DR

This paper investigates the collective oscillation modes of trapped boson-fermion mixtures with attractive interactions, revealing mode frequency shifts as the system approaches collapse, using hydrodynamic and RPA methods.

Contribution

It provides a detailed analysis of mode frequency shifts in boson-fermion mixtures near collapse, comparing hydrodynamic and RPA approaches and identifying characteristic softening and blue shifts.

Findings

Fermionic modes exhibit a significant blue shift near collapse.

Bosonic modes soften as the mixture approaches instability.

Surface modes are largely unaffected by interspecies interactions.

Abstract

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions.