When are two fermions a simple boson? New Gross-Pitaevskii actions for cold Fermi condensates

TL;DR

This paper investigates the extent to which paired fermions in a cold Fermi gas behave like elementary bosons, developing new theoretical actions and analyzing their validity across different regimes.

Contribution

It introduces new Gross-Pitaevskii actions for the BEC regime and examines the bosonic nature of dimers beyond the Bogoliubov approximation.

Findings

Identity of dimers and bosons in the deep BEC regime at the Bogoliubov level

Failure of simple bosonic description as moving towards BCS regime

Intrinsic differences in dimer behavior beyond the Bogoliubov approximation

Abstract

The BEC regime of a cold fermi gas is characterised by coupled atoms (dimers) which, superficially, look like elementary bosons. We examine how simply-bosonic they really are; firstly, in the Bogoliubov approximation and further, through new actions for the BEC regime in which dimers are represented by coupled Gross-Pitaevskii fields. We find identity at the level of the Bogoliubov approximation in the deep BEC regime, permitting a simple Gross-Pitaevskii description. This fails rapidly as we move towards the BCS regime. However, even in the deep BEC regime there is an intrinsic difference if we go beyond the Bogoliubov approximation. To exemplify this we construct vortex solutions.