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

TL;DR

This paper derives an upper bound for the pairing energy in a two-species Fermi fluid at unitarity, linking it to phase separation and superfluidity, with implications for understanding the system's phase behavior.

Contribution

It introduces a novel upper bound for the pairing energy in Fermi fluids at unitarity, connecting phase separation conditions with the superfluid gap.

Findings

Derived an explicit upper bound for  in the unitary regime.

Showed that saturation of the bound implies phase separation.

Indicated that exceeding the superfluid gap leads to phase separation.

Abstract

An upper bound is derived for $\Delta$ 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 $\Delta$ 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 $\delta \leq {5/3} (2 (2 \xi)^{2/5} - (2 \xi))$ where $\xi=\epsilon/\epsilon_{\rm FG}$, $\delta= 2 \Delta/\epsilon_{\rm FG}$; $\epsilon$ is the energy per particle and $\epsilon_{\rm FG}$ 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 $\Delta$ is the usual superfluid gap. If the superfluid gap exceeds the maximum allowed by the inequality phase separation occurs.