Establishing the Presence of Coherence in Atomic Fermi Superfluids: Spin-Flip and Spin-Preserving Bragg Scattering at Finite Temperatures

Abstract

We show how in ultracold Fermi gases the difference between the finite temperature $T$ structure factors, called ${S}_{\ensuremath{-}}(\ensuremath{\omega},\mathbf{q})$, associated with spin and density, reflects coherent order at all $\ensuremath{\omega}$, $\mathbf{q}$, ${k}_{F}a$, and $T$. This observation can be exploited in two photon Bragg scattering experiments on gases which are subject to variable attractive interactions. Our calculations incorporate spin and particle number conservation laws which lead to compatibility at general $T$ with two $f$-sum rules. Because of its generality a measurement of ${S}_{\ensuremath{-}}(\ensuremath{\omega},\mathbf{q})$ can be a qualitative, direct, in situ approach for establishing superfluid order.