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

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.

12 pages, 4 figures, 1 table

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• d-wave collapse and explosion of a dipolar Bose-Einstein condensate
• Pure Gas of Optically Trapped Molecules Created from Fermionic Atoms
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Observation of a two-dimensional Fermi gas of atoms
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Crossover from 2D to 3D in a weakly interacting Fermi gas
• Coherent collapse of a dipolar Bose-Einstein condensate for different trap geometries
• Berezinskii-Kosterlitz-Thouless transition in trapped quasi-two-dimensional Fermi gas near a Feshbach resonance

Cited by in corpus (15)

• Ground-state densities of repulsive two-component Fermi gases
• Thomas-Fermi von Weizsäcker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas
• Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
• Leading gradient correction to the kinetic energy for two-dimensional fermion gases
• Systematic corrections to the Thomas-Fermi approximation without a gradient expansion
• Airy-averaged gradient corrections for two-dimensional fermion gases
• Density-functional theory for the crystalline phases of a two-dimensional dipolar Fermi gas
• Kohn-Sham theory of rotating dipolar Fermi gas in two dimensions
• Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime
• Ground state of a two component dipolar Fermi gas in a harmonic potential
• Kohn-Sham approach to Fermi gas superfluidity: the bilayer of fermionic polar molecules
• Self-consistent field theory of polarized BEC: dispersion of collective excitation
• Energy functionals of single-particle densities: A unified view
• Testing the nonlocal kinetic energy functional of an inhomogeneous, two-dimensional degenerate Fermi gas within the average density approximation
• Ordered phases in a bilayer system of dipolar fermions