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

TL;DR

This paper predicts a universal $1/q$ decay of the static structure factor in strongly correlated Fermi gases at large momenta, linking it to Tan's contact parameter, and offers methods for experimental verification.

Contribution

It introduces a new Tan relation for the static structure factor at large momenta and provides a theoretical framework to calculate it across different interaction regimes.

Findings

Structure factor $S_{ extbackslash u2192 extbackslash u2192 extbackslash u2192$ scales as $1/q$ at large momenta.

The scaling coefficient is directly related to Tan's contact parameter.

The paper offers practical methods to measure contact via static structure factor experiments.

Abstract

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. Our results provide a way to experimentally confirm a new Tan relation and to accurately measure the value of contact parameter.