Clock shifts in a Fermi gas interacting with a minority component: a soluble model

TL;DR

This paper presents an exactly solvable model for the absorption spectrum of a Fermi gas with a heavy minority component, highlighting the significance of vertex corrections and the limitations of ladder approximations.

Contribution

It introduces a closed-form solution for the spectrum in the heavy minority limit and emphasizes the role of vertex corrections and many-particle effects.

Findings

Vertex corrections qualitatively alter the absorption spectrum.

Large line shifts are not necessarily due to resonant interactions.

Ladder approximation fails for degenerate majority components with large mass ratios.

Abstract

We consider the absorption spectrum of a Fermi gas mixed with a minority species when majority fermions are transferred to another internal state by an external probe. In the limit when the minority species is much more massive than the majority one, we show that the minority species may be treated as static impurities and the problem can be solved in closed form. The analytical results bring out the importance of vertex corrections, which change qualitatively the nature of the absorption spectrum. It is demonstrated that large line shifts are not associated with resonant interactions in general. We also show that the commonly used ladder approximation fails when the majority component is degenerate for large mass ratios between the minority and majority species and that bubble diagrams, which correspond to the creation of many particle--hole pairs, must be taken into account. We carry out detailed numerical calculations, which confirm the analytical insights and we point out the connection to shadowing phenomena in nuclear physics.