Superfluid amplitude fluctuations above $T_c$ in a unitary Fermi gas

We study the transport properties of a Fermi gas with strong attractive interactions close to the unitary limit. In particular, we compute the spin diffusion lifetime of the Fermi gas due to superfluid fluctuations above the BCS transition temperature $T_c$. To calculate the spin diffusion lifetime we need the scattering amplitudes. The scattering amplitudes are dominated by the superfluid fluctuations at temperatures just above $T_c$. The normal scattering amplitudes are calculated from the Landau parameters. These Landau parameters are obtained from the local version of the induced interaction model for computing Landau parameters. We also calculate the leading order finite temperature correction to the diffusion lifetime. A calculation of the spin diffusion coefficient is presented in the end. Upon choosing a proper value of $F_0^a$, we are able to present a good match between the theoretical result and the experimental measurement, which indicates the presence of the superfluid fluctuations near $T_c$.

Figure 1

Diagrammatic representation of the integral equations for the Landau parameters $F$ and the scattering amplitudes $a$. (a) represents the equation for Landau parameters decomposed into direct and induced terms; (b) sums all the reducible diagrams. It represents the equation relating $F$ to the scattering amplitudes $a$.

Figure 2

The Landau parameter $F_0^a$ vs $-{\left(k_F{a}_s\right)}^{-1}$ curve.

Figure 3

Spin diffusion coefficient curve from low to high temperature. The black solid curve is the low temperature expansion of $D$ at $F_0^a=1.7$; the dashed line is the classical limit of $D$; the blue curve represents the summation of the two limits; the red dots with error bars are the experimental data [10].

Figure 4

The calculated spin diffusion lifetime curves with different $F_0^a$ values.