Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

TL;DR

This paper investigates the collective excitations of a zero-temperature, spin-polarized, 2D dipolar Fermi gas in a harmonic trap, revealing how bulk and surface mode frequencies depend on interaction strength and particle number.

Contribution

It introduces a hydrodynamic approach to analyze excitation spectra, highlighting the insensitivity of surface modes to interaction strength due to local energy density.

Findings

Bulk mode frequencies increase with interaction strength.

Surface mode frequencies are independent of interactions in large particle limit.

Surface excitations' insensitivity is due to local energy density, not the equation of state.

Abstract

The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi von Weizs\"acker hydrodynamic theory. We focus on repulsive interactions, and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are {\em independent} of the interactions in the large particle limit. We argue quite generally that it is the {\em local} character of the two-dimensional energy density which is responsible for the insensitivity of surface excitations to the dipolar interaction strength, and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.