Miscibility in a degenerate fermionic mixture induced by linear coupling

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, κ, exceeds a critical value, κcr. The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary Bose-Einsten condensate with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form antilocked (π-phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of the numbers of atoms in them, N₁ and N₂. The latter effect is characterized by the parameter ν≡(N₁-N₂)∕(N₁+N₂) (only N₁+N₂ is a conserved quantity), the onset of miscibility at κκcr meaning a transition to ν≡0. At κ<κcr, ν features damped oscillations as a function of κ. We also briefly consider an asymmetric model, with a chemical-potential difference between the two components. The relation between the imbalance in the spin population, induced by the linear coupling, and the developing spatial structure resembles the known Larkin-Ovchinnikov-Fulde-Ferrell states in the Fermi mixture. Dynamical states, when κ is suddenly switched from zero to a value exceeding κcr, are considered too. In the latter case, the system features oscillatory relaxation to the mixed state.