Hartree shift and pairing gap in ultracold Fermi gases in the framework of low-momentum interactions

TL;DR

This paper investigates the Hartree shift and pairing gap in ultracold Fermi gases near the BCS-BEC crossover using low-momentum interactions and diagrammatic perturbation theory, achieving good agreement with established theories and experiments.

Contribution

It introduces a diagrammatic approach with self-consistency to compute the Hartree shift and pairing gap, extending results to the unitary regime and discussing potential applications.

Findings

Results agree with Gor'kov-Melik-Barkhudarov corrections in weak coupling.

Hartree shift matches Galitskii results in weak coupling.

Reasonable agreement with experiments and quantum Monte-Carlo near unitarity.

Abstract

In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum dependent interaction that reproduces the s-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well-converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte-Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.