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

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 $\hslash q$ 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.

8 pages, 3 figures; revised according to the Referee's suggestions; publised version

References in corpus (12)

• Theory of ultracold Fermi gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Bragg spectroscopy of a strongly interacting Fermi gas
• Number of closed-channel molecules in the BEC-BCS crossover
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Virial expansion for a strongly correlated Fermi gas
• Theory of RF-spectroscopy of strongly interacting Fermions
• Coherence and clock shifts in ultracold Fermi gases with resonant interactions
• Pseudo-gap pairing in ultracold Fermi atoms
• BCS-BEC crossover in an asymmetric two-component Fermi gas
• Dynamic response of strongly correlated Fermi gases in the quantum virial expansion

Cited by in corpus (13)

• Universal Relations for Identical Bosons from 3-Body Physics
• Universal contact of strongly interacting fermions at finite temperatures
• Contact and sum-rules in a near-uniform Fermi gas at unitarity
• Making statistics work: a quantum engine in the BEC-BCS crossover
• Dynamic spin response of a strongly interacting Fermi gas
• Large-momentum distribution of a polarized Fermi gas and p-wave contacts
• Quantitative comparison between theoretical predictions and experimental results for Bragg spectroscopy of a strongly interacting Fermi superfluid
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover
• Deep inelastic scattering on ultracold gases
• Short range correlations - The important role of few-body dynamics in many-body systems
• Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas
• Many-body theories of density response for a strongly correlated Fermi gas
• Universal Relations for Fermions with Large Scattering Length