Calculation of the even-odd energy difference in superfluid Fermi systems using the pseudopotential theory

TL;DR

This paper extends pseudopotential theory to superfluid Fermi systems at the Feshbach resonance, calculating the energy difference when adding an atom and introducing universal parameters for quasiparticle states.

Contribution

It develops a novel extension of pseudopotential theory to Bogoliubov-de Gennes equations for superfluid Fermi systems, including universal parameters for quasiparticle states.

Findings

Results agree with Monte-Carlo calculations for small systems

Method applicable to larger particle numbers

Defined universal numbers for quasiparticle state widths

Abstract

The pseudopotential theory is extended to the Bogoliubov-de Gennes equations to determine the excess energy when one atom is added to the trapped superfluid Fermi system with even number of atoms. Particular attention is paid to systems being at the Feshbach resonance point. The results for relatively small particle numbers are in harmony with the Monte-Carlo calculations, but are also relevant for systems with larger particle numbers. Concerning the additional one quasiparticle state we define and determine two new universal numbers to characterize its widths.