Breathing mode of two-dimensional atomic Fermi gases in harmonic traps

TL;DR

This paper investigates the breathing mode frequency of two-dimensional atomic Fermi gases in harmonic traps, revealing deviations from the expected value due to broken symmetry and providing bounds and calculations for the frequency.

Contribution

It introduces a method to calculate the breathing mode frequency considering interaction effects and symmetry breaking in 2D Fermi gases.

Findings

Breathing mode frequency can deviate up to 8% from 2ω₀.

Upper bounds for the breathing mode frequency are established.

Hydrodynamic calculations agree with the bounds.

Abstract

For two-dimensional (2D) atomic Fermi gases in harmonic traps, the SO(2,1) symmetry is broken by the interatomic interaction explicitly via the contact correlation operator. Consequently the frequency of the breathing mode $\omega_B$ of the 2D Fermi gas can be different from $2\omega_0$, with $\omega_0$ the trapping frequency of harmonic potentials. At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for $\omega_B$. We further calculate $\omega_B$ through the Euler equations in the hydrodynamic regime. The obtained value of $\omega_B$ satisfies the upper bounds and shows deviation from $2\omega_0$ which can be as large as about 8%.