Condensate formation with three-component ultracold fermions

TL;DR

This paper explores Bose-Einstein condensation and population imbalance in a three-component ultracold Fermi gas across the BCS-BEC crossover, providing explicit formulas and density profiles in both 2D and 3D systems.

Contribution

It introduces explicit mean-field formulas for key properties and analyzes the BCS-BEC crossover in three-component Fermi systems, including trapped configurations.

Findings

Derived formulas for densities, gap, and condensate fraction.

Analyzed BCS-BEC crossover in 2D and 3D systems.

Calculated density profiles in trapped gases.

Abstract

We investigate the formation of Bose-Einstein condensation and population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions and also in two dimensions. Within the mean-field theory, we derive explicit formulas for number densities, gap order parameter, condensate density and condensate fraction of the uniform system, and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers. In addition, we study this Fermi mixture trapped by a harmonic potential: we calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.