Static structure factor of a strongly correlated Fermi gas at large momenta

Understand

We theoretically investigate the static structure factor of an interacting Fermi gas near the BEC-BCS crossover at large momenta.

• Due to short-range two-body interactions, we predict that the structure factor of unlike spin correlations $S_{\uparrow\downarrow}(q)$ falls off as $1/q$ in a universal scaling region with large momentum $\hbar q$ and large scattering length.
• The scaling coefficient is determined by the celebrated Tan's contact parameter, which links the short-range behavior of many-body systems to their universal thermodynamic properties.
• By implementing this new Tan relation together with the random-phase approximation and the virial expansion theory in various limiting cases, we show how to calculate $S_{\uparrow\downarrow}(q)$ at zero and finite temperatures for arbitrary interaction strengths, at momentum transfer higher than the Fermi momentum.