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

TL;DR

This paper explores the phase diagram of ultracold four-component fermionic mixtures, revealing a non-Abelian symmetry-locked superfluid phase that can occur under realistic experimental conditions.

Contribution

It introduces the concept of a two-flavors superfluid symmetry-locking (TSFL) phase in fermionic mixtures with unequal interactions, expanding understanding of symmetry-locked states.

Findings

Extended TSFL phase region in the phase diagram.

TSFL phase persists with moderate repulsive intra-pair interactions.

Explicit estimates show realization in Yb isotopic mixtures without fine-tuning.

Abstract

The occurrence of non-Abelian symmetry-locked states in ultracold fermionic mixtures with four components is investigated. We study the phase diagram in the presence of an attractive interaction between the species of two pairs of the mixture, and general (also repulsive) interactions between the species of each pair. This system is physically realized, e.g., in mixtures of two different earth-alkaline species, both of them with two hyperfine levels selectively populated. We find an extended region of the diagram exhibiting a two-flavors superfluid symmetry-locking (TSFL) phase. This phase is present also for not too large repulsive intra-pair interactions and it is characterized by a global non-Abelian symmetry group obtained by locking together 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 be achieved also without tuning the interactions between $\mathrm{Yb}$ atoms.