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

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