Simultaneous Onset of Condensation of Molecules and Atoms in an Attractive Fermi Gas of Atoms

TL;DR

This paper derives self-consistent equations showing that Bose-Einstein condensation of molecules and BCS pairing of atoms in an attractive Fermi gas occur simultaneously, with the critical temperature influenced by molecule number and atom-molecule coupling.

Contribution

It presents a theoretical framework demonstrating the simultaneous onset of BEC and BCS in an attractive Fermi gas, highlighting the role of atom-molecule interactions.

Findings

BEC and BCS order parameters are proportional, indicating simultaneous onset.

The critical temperature increases with the number of molecules.

Atom-molecule coupling enhances the critical temperature.

Abstract

The self-consistent equations for the order parameters of Bose-Einstein condensation (BEC) of molecules and Bardeen-Cooper-Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms have been derived within the Hartree-Fock-Bogoliubov approximation from the path integral representation of the grand partition function. We have found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We have also found that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.