Breathing oscillations and quasi-low-dimensional structures of weakly-interacting degenerate Fermi gases in highly-anisotropic traps

TL;DR

This paper studies how quasi-low-dimensional structures influence breathing oscillations in weakly-interacting degenerate Fermi gases confined in highly-anisotropic traps, revealing mode-specific effects and developing a semi-classical theoretical framework.

Contribution

It introduces an extended Thomas-Fermi approximation and analyzes the impact of QLD structures on collective oscillation frequencies in anisotropic Fermi gases.

Findings

QLD structures affect longitudinal modes only

Transverse modes are unaffected in first-order perturbation

Theoretical framework matches time-evolution simulations

Abstract

We theoretically investigate breathing oscillations of weakly-interacting degenerate Fermi gases in highly-anisotropic harmonic oscillator traps. If the traps are not highly anisotropic, the fermions behave as three-dimensional (3D) gases and exhibit the coupled breathing oscillations as studied in a previous paper [T. Maruyama and T. Nishimura, Phys. Rev. A 75 (2007) 033611]; Otherwise the fermions exhibit quasi-low-dimensional (QLD) properties derived from specific structures in their single-particle spectrum, called QLD structures. In the present paper, we focus on effects of the QLD structures on the breathing oscillations of the two-component fermions with symmetric population densities. Here we develop the semi-classical Thomas-Fermi approximation extended to the highly-anisotropic systems and obtain the collective frequencies in the sum-rule-scaling method and perturbation theory. As a result, we reveal that the effects of the QLD structures can not be seen in the transverse modes in the first-order perturbation and appear only in the longitudinal modes with hierarchies reflecting the QLD structures. We also demonstrate time-evolution of the oscillations in the present framework.