Trapped fermions with density imbalance in the BEC limit

TL;DR

This paper investigates the behavior of imbalanced two-component trapped fermions in the BEC limit, deriving coupled equations to describe their density profiles and scattering properties relevant to recent experiments.

Contribution

It introduces a set of coupled equations incorporating scattering lengths to analyze density profiles of imbalanced fermions in the BEC regime.

Findings

Derived coupled equations for composite bosons and excess fermions.

Obtained density profiles using Thomas-Fermi approximation.

Relevant to recent experimental setups with trapped fermionic atoms.

Abstract

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the BEC limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms