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

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%.

5 pages, 1 figure

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