Phase Separation and an upper bound for $Δ$ for Fermi fluids in the Phase Separation and an upper bound for $Δ$ for Fermi fluids in the unitary regime

Abstract

An upper bound is derived for $Δ$ for a cold dilute fluid of equal amounts of two species of fermion in the unitary regime $k_f a \to \infty$ (where $k_f$ is the Fermi momentum and $a$ the scattering length, and $Δ$ is a pairing energy: the difference in energy per particle between adding to the system a macroscopic number (but infinitesimal fraction) of particles of one species compared to adding equal numbers of both. The bound is $δ\leq {5/3} (2 (2 ξ)^{2/5} - (2 ξ))$ where $ξ=ε/ε_{\rm FG}$, $δ= 2 Δ/ε_{\rm FG}$; $ε$ is the energy per particle and $ε_{\rm FG}$ is the energy per particle of a noninteracting Fermi gas. If the bound is saturated, then systems with unequal densities of the two species will separate spatially into a superfluid phase with equal numbers of the two species and a normal phase with the excess. If the bound is not saturated then $Δ$ is the usual superfluid gap. If the superfluid gap exceeds the maximum allowed by the inequality phase separation occurs.