# Bosonic characters of atomic Cooper pairs across resonance

## TL;DR

This paper investigates the bosonic nature of atomic Cooper pairs in a Fermi gas across different interaction regimes, highlighting how their wave functions exhibit bosonic characteristics depending on the definition used and interaction strength.

## Contribution

It compares two definitions of Cooper pair wave functions and analyzes their bosonic properties across the BEC-BCS crossover in a uniform Fermi gas.

## Key findings

- Pairs with ODLRO are more bosonic than pair-projected pairs on the BCS side.
- At strong coupling, over 90% of atoms form molecular condensates.
- Both definitions converge in the strongly interacting regime.

## Abstract

We study the two-particle wave function of paired atoms in a Fermi gas with tunable interaction strengths controlled by Feshbach resonance. The Cooper pair wave function is examined for its bosonic characters, which is quantified by the correction of Bose enhancement factor associated with the creation and annihilation composite particle operators. An example is given for a three-dimensional uniform gas. Two definitions of Cooper pair wave function are examined. One of which is chosen to reflect the off-diagonal long range order (ODLRO). Another one corresponds to a pair projection of a BCS state. On the side with negative scattering length, we found that paired atoms described by ODLRO are more bosonic than the pair projected definition. It is also found that at $(k_F a)^{-1} \ge 1$, both definitions give similar results, where more than 90% of the atoms occupy the corresponding molecular condensates.