Trapping-potential dependence of the unitary Fermi gas at the BCS-BEC crossover

TL;DR

This paper develops an effective field theory framework to analyze how trapping potentials influence the properties and excitation spectrum of the unitary Fermi gas across the BCS-BEC crossover, revealing significant infrared deviations.

Contribution

It introduces a hierarchical EFT approach incorporating the trapping potential effects on the superfluid Fermi gas, including derivative and WKB expansions, to compute energy spectra and structure factors.

Findings

Infrared deviations in phonon dispersion due to trapping potential

Explicit energy spectrum calculations in different regions

Modified dynamic structure factor from density fluctuations

Abstract

Cold-atom experiments which measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical scale in the superfluid EFT which, inter alia, describes the acoustic branch of excitations in the far infrared well below the scale of the superfluid gap. In this EFT there is a clear hierarchy of scales, and corrections to the homogeneous system due to the trapping potential may be organized into three regions with distinct power counting that relies on both the EFT derivative expansion, and the WKB approximation, which is an expansion in gradients of the trapping potential. The energy spectrum of the superfluid system is obtained in each of the regions by explicit computation of the phonon-field fluctuations, and by the modifications to the dynamic structure factor due to the corresponding density fluctuations. The most significant deviations from linear dispersion due to the trapping potential are found in the far infrared region of the superfluid EFT.