Effect of correlation on the properties of 2D spin-polarized dipolar Fermi gas

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 (103–104 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.