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, $\kappa $, exceeds a critical value, $ \kappa _{ \mathrm{ cr}}$. The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary BEC with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form anti-locked ($\pi $ -phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of numbers of atoms in them, $N_{ 1}$ and $N_{ 2}$. The latter effect is characterized by the parameter $\nu \equiv (N_{ 1}-N_{ 2})/(N_{ 1}+N_{ 2}) $ (only $N_{ 1}+N_{ 2}$ is a conserved quantity), the onset of miscibility at $\kappa \geq \kappa_{ \mathrm{ cr}}$ meaning a transition to $\nu \equiv 0$. At $\kappa <\kappa_{ \mathrm{ cr}}$, $\nu $ features damped oscillations as a function of $\kappa $. We also briefly consider an asymmetric model, with a chemical-potential difference between the two components.
Categories: cond-mat.soft nlin.PS