Popov approximation for composite bosons in the BCS-BEC crossover

TL;DR

This paper develops an improved fermionic theory for the BCS-BEC crossover, bridging the fermionic and bosonic descriptions with Popov and Bogoliubov approximations, to better match recent experimental results.

Contribution

It introduces successive improvements to the fermionic theory, enabling accurate descriptions of composite bosons in the BCS-BEC crossover using Popov and Bogoliubov approximations.

Findings

Enhanced theoretical framework for BCS-BEC crossover

Better agreement with experimental data on trapped Fermi atoms

Unified description of fermionic and bosonic regimes

Abstract

Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for point-like bosons. This work bears on the recent experimental advances on the BCS-BEC crossover with trapped Fermi atoms, which show the need for accurate theoretical descriptions of BEC side of the crossover.