Miscibility in a degenerate fermionic mixture induced by linear coupling

Abstract

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, $\ensuremath{\kappa}$, exceeds a critical value, ${\ensuremath{\kappa}}_{\mathrm{cr}}$. 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 ($\ensuremath{\pi}$-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, ${N}_{1}$ and ${N}_{2}$. The latter effect is characterized by the parameter $\ensuremath{\nu}\ensuremath{\equiv}({N}_{1}\ensuremath{-}{N}_{2})∕({N}_{1}+{N}_{2})$ (only ${N}_{1}+{N}_{2}$ is a conserved quantity), the onset of miscibility at $\ensuremath{\kappa}\ensuremath{\geqslant}{\ensuremath{\kappa}}_{\mathrm{cr}}$ meaning a transition to $\ensuremath{\nu}\ensuremath{\equiv}0$. At $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{\mathrm{cr}}$, $\ensuremath{\nu}$ features damped oscillations as a function of $\ensuremath{\kappa}$. 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 $\ensuremath{\kappa}$ is suddenly switched from zero to a value exceeding ${\ensuremath{\kappa}}_{\mathrm{cr}}$, are considered too. In the latter case, the system features oscillatory relaxation to the mixed state.