Quasi-particle properties of trapped Fermi gases

TL;DR

This paper develops a formalism to study how density and spin fluctuations influence quasi-particle properties and the critical temperature of pairing in trapped Fermi gases, emphasizing the role of trap geometry and level structure.

Contribution

It introduces a consistent approach to analyze fluctuation effects on quasi-particles and pairing in trapped Fermi gases near Feshbach resonances, considering different trap geometries.

Findings

Density and spin fluctuations significantly affect quasi-particle properties.

Discrete level structure plays a crucial role in determining the critical temperature.

The formalism applies to both harmonic traps and infinite potential wells.

Abstract

We develop a consistent formalism in order to explore the effects of density and spin fluctuations on the quasi-particle properties and on the pairing critical temperature of a trapped Fermi gas on the attractive side of a Feshbach resonance. We first analyze the quasi-particle properties of a gas due to interactions far from resonance (effective mass and lifetime, quasi-particle strength and effective interaction) for the two cases of a spherically symmetric harmonic trap and of a spherically symmetric infinite potential well. We then explore the effect of each of these quantities on $T_c$ and point out the important role played by the discrete level structure.