Dynamic structure factor of a strongly correlated Fermi superfluid within a density functional theory approach

TL;DR

This paper develops an improved density functional theory approach to accurately analyze the dynamic structure factor of strongly correlated Fermi superfluids across the BCS-BEC crossover, providing insights into collective and single-particle excitations.

Contribution

It introduces an enhanced random phase approximation within density functional theory for better modeling of Fermi superfluids at the crossover.

Findings

Accurate description of collective phonon modes and fermionic excitations.

Identification of the energy gap threshold for single-particle excitations.

Predictions for experimental measurement of the pairing gap using Bragg spectroscopy.

Abstract

We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen-Cooper-Schrieffer superfluids to Bose-Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory - the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov-de Gennes equations, the use of the density functional theory greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s-wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at $2\Delta$. The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap $\Delta$. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with $^{6}$Li or $^{40}$K atoms using Bragg spectroscopy.