Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

TL;DR

This paper investigates occupation numbers in highly polarized Fermi gases using a specific approximation, confirming the Luttinger theorem and deriving polaron energies at extreme polarization.

Contribution

It demonstrates the validity of the Luttinger theorem in strongly polarized Fermi gases within the particle-particle RPA framework and extracts polaron energies.

Findings

Luttinger theorem holds in the studied regime.

Occupation numbers calculated within the approximation.

Polaron energy obtained at extreme polarization.

Abstract

We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozieres-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy.