Static structure factor of a strongly correlated Fermi gas at large momenta
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
Accepted: 6 July 2010
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.
PACS: 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties / 03.75.Ss – Degenerate Fermi gases / 05.30.Fk – Fermion systems and electron gas
© EPLA, 2010