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

TL;DR

This paper analyzes the phase diagram, stability, and soliton formation in a superfluid Fermi-Fermi mixture across different dimensions, deriving conditions for stability and demonstrating bright soliton solutions in 1D.

Contribution

It provides a comprehensive study of phase stability and soliton solutions in Fermi-Fermi mixtures, including derivation of dynamical equations and stability criteria in 1D, 2D, and 3D.

Findings

Stable uniform and phase-separated states identified in 3D.

Bright solitons are stable and can be realized experimentally.

Variational approximation matches numerical results for soliton profiles.

Abstract

We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid Fermi-Fermi mixture (of distinct mass) at zero temperature using energy densities for the superfluid fermions in one (1D), two (2D), and three (3D) dimensions. We also derive the dynamical time-dependent nonlinear Euler-Lagrange equation satisfied by the mixture in one dimension using this energy density. We obtain the linear stability conditions for the mixture in terms of fermion densities of the components and the interspecies Fermi-Fermi interaction. In equilibrium there are two possibilities. The first is that of a uniform mixture of the two components, the second is that of two pure phases of two components without any overlap between them. In addition, a mixed and a pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the conditions under which the uniform mixture is stable from an energetic consideration. The same conditions are obtained from a modulational instability analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations for the system are solved numerically and by variational approximation (VA) to study the bright solitons of the system for attractive interspecies Fermi-Fermi interaction in 1D. The VA is found to yield good agreement to the numerical result for the density profile and chemical potential of the bright solitons. The bright solitons are demonstrated to be dynamically stable. The experimental realization of these Fermi-Fermi bright solitons seems possible with present setups.