Three-body crossover from a Cooper triple to bound trimer state in three-component Fermi gases near a triatomic resonance

TL;DR

This paper explores the transition from Cooper pairs to Cooper triples and then to bound trimers in a three-component Fermi gas near a triatomic resonance, revealing a three-body crossover analogous to BCS-BEC in two-component gases.

Contribution

It introduces a theoretical framework for understanding the competition between pair and triple formations and maps out the phase diagram near a triatomic resonance.

Findings

Identification of a phase transition from Cooper pairs to Cooper triples.

Prediction of a shift in the three-body threshold scattering length due to Cooper triples.

Demonstration of a three-body crossover similar to BCS-BEC crossover.

Abstract

We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length $a_{-}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.