Coboson many-body formalism for cold-atom dimers
Yia-Chung Chang1, Monique Combescot2, Shiue-Yuan Shiau3*
1Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, CNRS, Paris, France
2Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan
3Physics Department, National Cheng Kung University, Tainan, Taiwan
* presenting author:Shiue-Yuan Shiau,
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.

Keywords: cold atom, coboson formalism, scattering length, Bose-Einstein condensation