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, exceeds a critical value, ΰcr. 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 (Ï€ -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 Î≡ (N1 â N2) â• (N1 + N2) (only N1 + N2 is a conserved quantity), the onset of miscibility at ΰ⩠Îcr meaning a transition to Î≡0. At Î< Îcr, Î features damped oscillations as a function of Î. 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 Î is suddenly switched from zero to a value exceeding Îcr, are considered too. In the latter case, the system features oscillatory relaxation to the mixed state. © 2006 The American Physical Society.