Trapped unitary two-component Fermi gases with up to ten particles

TL;DR

This study investigates small two-component Fermi gases at unitarity using a Gaussian basis set, focusing on energies, contacts, and structural properties, and introduces a new extrapolation scheme to zero-range interactions.

Contribution

It presents a novel extrapolation method for zero-range energies and provides detailed calculations for systems with up to ten particles at unitarity.

Findings

Ground state energies for up to ten particles are determined.

A new scheme effectively removes linear and quadratic dependencies on the two-body range.

Calculated Tan contact and structural properties agree with existing literature.

Abstract

The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground state energy for systems with up to ten particles interacting through finite-range two-body potentials for both even and odd number of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.