Absence of BCS Condensation of Atoms in a Repulsive Fermi Gas of Atoms

TL;DR

This study demonstrates that in a repulsive ultracold Fermi gas, BCS condensation of atoms does not occur, and the observed condensate is likely composed of molecules or preformed pairs, supported by theoretical and computational analysis.

Contribution

The paper provides a theoretical demonstration that BCS condensation of atoms is absent in repulsive Fermi gases, clarifying the nature of observed condensates.

Findings

BCS condensation of atoms cannot occur in a repulsive Fermi gas.

The observed condensate is likely molecular or preformed pairs.

Effective atom-atom interaction mediated through molecules is repulsive.

Abstract

Possible Bose-Einstein condensation of molecules and Bardeen-Cooper-Schrieffer (BCS) condensation of Cooper pairs of atoms in an ultracold Fermi gas of atoms with a repulsive two-body interaction are studied by using the path integral representation of the grand partition function. From the self-consistent equations obtained in the present work for the order parameters, we have found that BCS condensation of atoms can't occur in such a Fermi gas of atoms and that the condensate observed experimentally is composed of condensed molecules or possibly of preformed Cooper pairs. To substantiate our conclusions from the self-consistent equations for the order parameters, the effective atom-atom interaction mediated through molecules has also been computed with the Foldy-Wouthuysen transformation and has been found to be repulsive, which implies a net repulsive two-body interaction between atoms and hence the absence of BCS condensation of atoms.