Cooper pairing and single particle properties of trapped Fermi gases

TL;DR

This paper investigates the superfluid phase of trapped atomic Fermi gases, analyzing how excitations and pairing mechanisms evolve with interaction strength and atom number, revealing shell-dependent pairing behaviors.

Contribution

It provides a detailed analysis of pairing transitions and the nature of elementary excitations in trapped Fermi gases across different interaction regimes.

Findings

Pairing occurs within the same shell at weak interactions.

Transition to inter-shell pairing at stronger interactions.

Shell structure and chemical potential influence pairing nature.

Abstract

We calculate the elementary excitations and pairing of a trapped atomic Fermi gas in the superfluid phase. The level spectra and pairing gaps undergo several transitions as the strength of the interactions between and the number of atoms are varied. For weak interactions, the Cooper pairs are formed between particles residing in the same harmonic oscillator shell. In this regime, the nature of the paired state is shown to depend critically on the position of the chemical potential relative to the harmonic oscillator shells and on the size of the mean field. For stronger interactions, we find a region where pairing occur between time-reversed harmonic oscillator states in different shells also.