# Surface Effects in the Unitary Fermi Gas

## TL;DR

This paper develops an extended Thomas-Fermi density functional including gradient terms to accurately describe surface effects in the superfluid unitary Fermi gas, especially with few atoms, and analyzes collective surface oscillations.

## Contribution

It introduces an ETF functional with gradient terms that improves surface density predictions and calculates collective oscillation frequencies considering atom number dependence.

## Key findings

- ETF functional matches Monte Carlo density profiles
- Surface oscillation frequencies depend on atom number
- Gradient terms are essential for small systems

## Abstract

We study the extended Thomas-Fermi (ETF) density functional of the superfluid unitary Fermi gas. This functional includes a gradient term which is essential to describe accurately the surface effects of the system, in particular with a small number of atoms, where the Thomas-Fermi (local density) approximation fails. We find that our ETF functional gives density profiles which are in good agreement with recent Monte Carlo results and also with a more sophisticated superfluid density functional based on Bogoliubov-de Gennes equations. In addition, by using extended hydrodynamics equations of superfluids, we calculate the frequencies of collective surface oscillations of the unitary Fermi gas, showing that quadrupole and octupole modes strongly depend on the number of trapped atoms.