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

¹ ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology - Melbourne 3122, Australia
² Department of Physics, Renmin University of China - Beijing 100872, China

^a hhu@swin.edu.au

Received: 18 March 2010
Accepted: 6 July 2010

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 show that the structure factor of unlike spin correlations S_↑↓(q) falls off as 1/q in a universal scaling region with large momentum ℏq 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 structure-factor Tan relation together with the random-phase approximation and the virial expansion theory in various limiting cases, we show how to calculate S_↑↓(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 one of the Tan relations and to accurately measure the value of contact parameter.