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The occurrence of non-Abelian symmetry-locked states in ultracold fermionicmixtures with four components is investigated. We study the phase diagram inthe presence of an attractive interaction between the species of two pairs ofthe mixture, and general (also repulsive) interactions between the species ofeach pair. This system is physically realized, e.g., in mixtures of twodifferent earth-alkaline species, both of them with two hyperfine levelsselectively populated. We find an extended region of the diagram exhibiting atwo-flavors superfluid symmetry-locking (TSFL) phase. This phase is presentalso for not too large repulsive intra-pair interactions and it ischaracterized by a global non-Abelian symmetry group obtained by lockingtogether two independent invariance groups of the corresponding normal state.Explicit estimates are reported for the mixture of the fermionic isotopes$^{171}\mathrm{Yb}$-$^{173}\mathrm{Yb}$, indicating that the TFSL phase can beachieved also without tuning the interactions between $\mathrm{Yb}$ atoms.

Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions