Abstract
We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f-sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.
Highlights
Ultra-cold Fermi gas has been the focus of a lot of research investigations due to its highly controllable attractive interaction[1,2,3,4,5,6]
An alternative approach based on measuring the collective (Nambu-Goldstone) mode though the Bragg spectroscopy has been carried out experimentally to establish the phase coherence of unitary Fermi gases [8]
Due to the inhomogeneity of the clouds of Fermi gases, the integrated Bragg spectroscopy is difficult to extract useful information to indicate the existence of the condensate
Summary
Ultra-cold Fermi gas has been the focus of a lot of research investigations due to its highly controllable attractive interaction[1,2,3,4,5,6]. A decade ago, the superfluidity of Fermi gases has been proved experimentally by the observation of the vortex lattices[7] This method still requires a fast sweep of the attractive interaction between the fermions to the deep Bose-Einstein condensation (BEC) limit, in order to see the density depletion in the vortex core. An alternative approach based on measuring the collective (Nambu-Goldstone) mode though the Bragg spectroscopy has been carried out experimentally to establish the phase coherence of unitary Fermi gases [8]. We adopt an G0G pair fluctuation theory to compute the density response function of unitary Fermi gases. We show that a gauge invariant linear response theory of which the approximation exactly matches the approximation used in the thermodynamic calculation can be constructed.
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