Hartree-Fock-Bogoliubov theory versus local-density approximation for superfluid trapped fermionic atoms

TL;DR

This paper compares Hartree-Fock-Bogoliubov and local-density approximation methods for superfluid trapped fermionic atoms, introducing a new regularization technique and analyzing their agreement across different system sizes and temperatures.

Contribution

A new regularization method for HFB equations is proposed, improving simplicity and convergence, and the comparison with LDA highlights shell effects and temperature-dependent discrepancies.

Findings

HFB and LDA agree well for large atom numbers at zero temperature

Shell effects are significant in small systems and not captured by LDA

Discrepancies increase at non-zero temperature near the critical point

Abstract

We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature the two calculations are in quite good agreement, which, however, is deteriorated at non-zero temperature, especially near the critical temperature. In this case the different behavior can be explained within the Ginzburg-Landau theory.