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Journal of Physics Conference Series

Density functional theory investigation of two-dimensional dipolar fermions in a harmonic trap

Hande Ustunel, Saeed H. Abedinpour, B. Tanatar

Published Dec 8, 2014• 6 citations
Publisher

Abstract

We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems.

DOI
10.1088/1742-6596/568/1/012020

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•Mar 15, 2018•7 citations
We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems.
Abstract The spin-polarized 2D dipolar Fermi gas trapped in a harmonic potential provides an opportunity to study the many-fermion systems with strong particle–particle correlation in a controlled fashion. In this paper, we investigate the role of the correlation part of the interaction energy on the ground-state properties and on the collective oscillation frequencies of a 2D dipolar Fermi gas by employing density functional theory (DFT) within local density approximation. We employ a purely density-based, orbital-free approach of DFT to study the ground-state properties. We employ an orbital-free approach, as it is suitable for handling a large number of fermions (10 3 –10 4 atoms/molecules), which are typically the number of atoms/molecules contained in the samples of dipolar Fermi gas created in the laboratories. We derive analytical expressions for the frequencies of the monopole and quadrupole modes of the collective oscillations by employing a method based on the sum-rule approach of linear response theory. We find that the exchange and correlation part of the fermion–fermion interaction contributes significantly to the total energy, and their contributions increase with increasing number of fermions and interaction strength. In particular, the correlation part lowers the total energy of the 2D dipolar fermionic system, thereby stabilizing the system. Similarly, the inclusion of the correlation effect lowers the frequencies of the monopole mode of the collective oscillations appreciably in comparison to the case when this effect is not taken into account. On the other hand, the frequency of the quadrupole mode of the collective oscillations is not appreciably altered by the correlation part of the interaction over a wide range of values of interaction strength and number of fermions.
We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a function of strength of interaction between two fermions by employing variational method with Hylleraas-like explicitly correlated wave function. Furthermore, we perform calculations of ground state energy within Hartree-Fock approximation and the magnitude of correlation energy is estimated by subtracting these results from the corresponding wave function based results. We also carry out calculations of ground state energies within the realm of density functional theory by using recently reported expressions for exchange and correlation energies under local density approximation. By comparing correlated wave function based results with those obtained using density functional theory approach we examine the role of fermion-fermion correlation and assess the accuracy of local density approximation based expression for the correlation energy functional.
We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas--Fermi--von Weizs\"acker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions and provide physical insight into why it can be represented as a local functional. Finally, a simple and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.
Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters; rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.
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.
The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.