Damping of long wavelength collective modes in spinor Bose-Fermi mixtures

TL;DR

This paper investigates how fermionic excitations induce damping of bosonic collective modes in spinor Bose-Fermi mixtures, revealing state-dependent damping effects and implications for experimental observations.

Contribution

It introduces an effective field theory describing damping mechanisms of bosonic modes in spinor Bose-Fermi mixtures, highlighting state-dependent damping effects due to fermionic excitations.

Findings

Fermionic excitations cause damping of bosonic Goldstone modes.

Density and spin modes are damped in polar superfluids.

Density mode remains undamped in ferromagnetic superfluids.

Abstract

Using an effective field theory we describe the low energy bosonic excitations in a three dimensional ultra-cold mixture of spin-1 bosons and spin-1/2 fermions. We establish an interesting fermionic excitation induced generic damping of the usual undamped long wavelength bosonic collective Goldstone modes. Two states with bosons forming either a ferromagnetic or polar superfluid are studied. The linear dispersion of the bosonic Bogoliubov excitations is preserved with a renormalized sound velocity. For the polar superfluid we find both gapless modes (density and spin) are damped, whereas in the ferromagnetic superfluid we find the density (spin) mode is (not) damped. We argue quite generally that this holds for any mixture of bosons and fermions that are coupled through at least a density-density interaction. We discuss the implications of our many-body interaction results for experiments on Bose-Fermi mixtures.