Coboson many-body formalism for cold atom dimers with attraction between different fermion species only

TL;DR

This paper develops a coboson many-body formalism for cold atom dimers with attraction only between different fermion species, simplifying the analysis of their interactions and many-body effects like Bose-Einstein condensation.

Contribution

It introduces a new formalism that models interactions of heteronuclear fermion pairs using fermion exchange and provides analytical results for key many-body parameters.

Findings

Interaction occurs through fermion exchange only.

Analytical expressions for N-coboson normalization and energy.

Formalism facilitates studying complex many-body phenomena.

Abstract

Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we here develop evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the $N$-coboson normalization factor and the $N$-coboson ground-state energy within the Born approximation, in terms of the Born dimer-dimer scattering length. This formalism opens the route toward approaching complex many-body effects, such as Bose-Einstein condensation, through a new perspective.