BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model

TL;DR

This paper investigates the effects of inter-channel Pauli exclusion in a three-hyperfine-species ultracold Fermi gas near a narrow Feshbach resonance, revealing corrections of order E_F/η to the standard models and exploring related spectral and collective phenomena.

Contribution

It introduces the impact of inter-channel Pauli exclusion in a three-hyperfine-species model, extending understanding of Feshbach resonance effects beyond existing single-channel approximations.

Findings

Corrections are of order E_F/η due to inter-channel Pauli exclusion.

Modified fermionic excitation spectrum analyzed.

Brief discussion on collective modes of the system.

Abstract

We consider the behavior of an ultracold Fermi gas across a narrow Feshbach resonance, where the occupation of the closed channel may not be negligible. While the corrections to the single-channel formulae associated with the nonzero chemical potential and with particle conservation have been considered in the existing literature, there is a further effect, namely the "inter-channel Pauli exclusion principle" associated with the fact that a single hyperfine species may be common to the two channels. We focus on this effect and show that, as intuitively expected, the resulting corrections are of order $E_F/\eta$, where $E_F$ is the Fermi energy of the gas in the absence of interactions and $\eta$ is the Zeeman energy difference between the two channels. We also consider the related corrections to the fermionic excitation spectrum, and briefly discuss the collective modes of the system.