Finite temperature excitations of a trapped Bose-Fermi mixture

TL;DR

This paper investigates the collective excitations of a trapped Bose-Fermi mixture at finite temperature, analyzing how coupling and temperature influence excitation frequencies, damping, and phase separation signatures.

Contribution

It provides a self-consistent calculation of excitation frequencies and damping rates in a Bose-Fermi mixture at finite temperature, including effects of coupling and phase separation.

Findings

Dipole mode remains near trapping frequency across temperatures.

Damping rates of monopole and quadrupole modes vary with coupling.

Signatures of spatial separation are observed in damping behavior.

Abstract

We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random phase approximation and linear response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.