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We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluidFermi-Fermi mixture (of distinct mass) at zero temperature using energydensities for the superfluid fermions in one (1D), two (2D), and three (3D)dimensions. We also derive the dynamical time-dependent nonlinearEuler-Lagrange equation satisfied by the mixture in one dimension using thisenergy density. We obtain the linear stability conditions for the mixture interms of fermion densities of the components and the interspecies Fermi-Fermiinteraction. In equilibrium there are two possibilities. The first is that of auniform mixture of the two components, the second is that of two pure phases oftwo components without any overlap between them. In addition, a mixed and apure phase, impossible in 1D and 2D, can be created in 3D. We also obtain theconditions under which the uniform mixture is stable from an energeticconsideration. The same conditions are obtained from a modulational instabilityanalysis of the dynamical equations in 1D. Finally, the 1D dynamical equationsfor the system are solved numerically and by variational approximation (VA) tostudy the bright solitons of the system for attractive interspecies Fermi-Fermiinteraction in 1D. The VA is found to yield good agreement to the numericalresult for the density profile and chemical potential of the bright solitons.The bright solitons are demonstrated to be dynamically stable. The experimentalrealization of these Fermi-Fermi bright solitons seems possible with presentsetups.

Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation