Density Functional of a Two-Dimensional Gas of Dipolar Atoms: Thomas-Fermi-Dirac Treatment

TL;DR

This paper develops a density functional approach for a two-dimensional gas of dipolar atoms, providing analytical solutions for density and energy, and explores effects of magnetic fields on spin polarization.

Contribution

It introduces a Thomas-Fermi-Dirac density functional for 2D dipolar fermions, including analytical solutions and spin polarization effects under magnetic fields.

Findings

Analytical density and energy expressions for trapped dipolar gases.

Weak-interaction limit relevant for experiments.

Magnetic field strength needed for full spin polarization.

Abstract

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.