The Unitary Fermi Gas in a Harmonic Trap and its Static Response

TL;DR

This paper uses harmonic trapping to determine the leading gradient corrections in the superfluid local density approximation for the unitary Fermi gas, revealing a new universal constant for static response.

Contribution

It introduces the first measurement of the q^2 coefficient of the static response in the UFG, showing it is half of the mean-field prediction and establishing a new universal constant.

Findings

Leading order correction to SLDA is negative.

Predicted static response coefficient c = 1.5(3).

Result is a universal constant measurable experimentally.

Abstract

We use harmonically trapped systems to find the leading gradient corrections of the supefluid local density approximation (SLDA) - a density functional theory (DFT) describing the unitary Fermi gas (UFG). We find the leading order correction to be negative, and predict the q^2 coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant.