Three-component Fermi gas with SU(3) symmetry: BCS-BEC crossover in three and two dimensions

TL;DR

This paper investigates the BCS-BEC crossover in a three-component SU(3) symmetric Fermi gas, analyzing key physical properties in both three and two dimensions, revealing dimension-dependent behaviors and signatures of hyperfine component loss.

Contribution

It provides a detailed analysis of the BCS-BEC crossover in a three-component Fermi gas with SU(3) symmetry, including calculations of pairing gap, population imbalance, condensate fraction, and sound velocity in different dimensions.

Findings

In 3D, the condensate fraction approaches 1 at strong coupling.

In 2D, the condensate fraction nears 1 only at very large interaction strengths.

Sound velocity indicates the disappearance of a hyperfine component in 2D.

Abstract

We analyze the BCS-BEC crossover for a Fermi gas made of neutral atoms in three hyperfine states with a SU(3) invariant attractive interaction. By solving the extended BCS equations for the total number of particles and the pairing gap, we calculate at zero temperature the pairing gap, the population imbalance, the condensate fraction and the first sound velocity of the uniform system as a function of the interaction strength in both three and two dimensions. Contrary to the three-dimensional case, in two dimensions the condensate fraction approaches the value 1 only for an extremely large interaction strength and, moreover, the sound velocity gives a clear signature of the disappearance of one of the three hyperfine components.