From the Bogoliubov-de Gennes equations for superfluid fermions to the Gross-Pitaevskii equation for condensed bosons

TL;DR

This paper derives the Gross-Pitaevskii equation for condensed bosons from the Bogoliubov-de Gennes equations for superfluid fermions, including three-body corrections, relevant to ultracold atom experiments.

Contribution

It presents a derivation of the Gross-Pitaevskii equation from fermionic superfluid equations in the strong-coupling limit, incorporating three-body effects.

Findings

Derived the Gross-Pitaevskii equation from Bogoliubov-de Gennes equations.

Included three-body corrections to the equation.

Applicable to ultracold fermionic atom experiments.

Abstract

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.