Dispersive effects in the unitary Fermi gas

TL;DR

This paper explores how dispersive effects influence the physical properties of the zero-temperature unitary Fermi gas, including density profiles, surface tension, collective modes, and shock wave dynamics, using density functional theory.

Contribution

It introduces analytical formulas for density profiles, surface tension, and collective oscillation frequencies, and analyzes dispersive shock waves in colliding fermionic clouds.

Findings

Analytical density profile and surface tension for semi-infinite domain

Formula for quadrupole mode frequency under harmonic confinement

Observation of dispersive shock waves consistent with experiments

Abstract

We investigate within density functional theory various physical properties of the zero-temperature unitary Fermi gas which critically depend on the presence of a dispersive gradient term in the equation of state. First, we consider the unitary Fermi superfluid gas confined to a semi-infinite domain and calculate analytically its density profile and surface tension. Then we study the quadrupole modes of the superfluid system under harmonic confinement finding a reliable analytical formula for the oscillation frequency, which reduces to the familiar Thomas-Fermi one in the limit of a large number of atoms. Finally, we discuss the formation and propagation of dispersive shock waves in the collision between two resonant fermionic clouds, and compare our findings with recent experimental results.