Effects of fermion-boson interaction in neutral atomic systems

TL;DR

This paper explores how fermion-boson interactions affect collective excitations in helium mixture films, revealing mode interactions, quantum coherence possibilities, and corrections to theoretical models, with implications for atomic mixture systems.

Contribution

It introduces a detailed analysis of mode interactions and vertex corrections in fermion-boson helium mixtures, highlighting new collective behaviors and theoretical insights.

Findings

Level repulsion between zero sound and third sound modes

Potential observation of quantum coherence between helium components

Vertex corrections modify Landau Fermi liquid parameters

Abstract

We investigate the collective excitations of $^3$He-$^4$He mixture films at zero temperature within random phase approximation and linear response theory. In low concentration region of $^3$He, a level repulsion between zero sound and third sound mode is derived, which opens the possibility to observe quantum mechanical coherence between $^3$He particle-hole pair and the condensate of $^4$He. We also investigate the $^3$He-$^4$He vertex corrections in ladder approximation and show that the third branch, the combined mode of fermionic particle-hole pair and the third sound quanta, provides a unique correction to Landau $f$ function. Some implications to the fermion-boson mixture of alkali atoms in a potential trap is discussed.