超流Fermi-Fermi混合物：phase diagram，稳定性和孤子形成
Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
摘要：
利用一维、二维和三维超流费米子的能量密度，研究了零温下不同质量的Bardeen-Cooper-Schrieffer超流Fermi-Fermi混合物的相图.利用该能量密度，我们还导出了一维混合物所满足的动力学非线性Euler-Lagrange方程。我们得到的线性稳定性条件的混合物中的费米子密度的组件和种间Fermi-Fermi相互作用。在均衡中有两种可能性。第一种是两种组分的均匀混合物，第二种是两种组分的两个纯相，它们之间没有任何重叠。此外，可以在3D中创建在1D和2D中不可能的混合相和纯相。我们还从能量的角度得到了均匀混合物稳定的条件。从一维动力学方程的调制不稳定性分析中获得了相同的条件。最后，通过数值求解一维动力学方程和变分近似（VA）方法，研究了一维种间吸引Fermi-Fermi相互作用系统的亮孤子.计算结果与数值计算结果吻合较好。结果表明，亮孤子是动态稳定的。这些费米-费米亮孤子的实验实现似乎有可能与目前的设置。
英文摘要：
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.
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