Zero Sound and First Sound in a Disk-Shaped Normal Fermi gas

Abstract

We study the zero sound and the first sound in a dilute and ultracold disk-shaped normal Fermi gas with a strong harmonic confinement along the axial direction and uniform in the two planar directions. Working at zero temperature we calculate the chemical potential $\mu$ of the fermionic fluid as a function of the uniform planar density $\rho$ and find that $\mu$ changes its slope in correspondence to the filling of harmonic axial modes (shell effects). Within the linear response theory, and under the random phase approximation, we calculate the velocity $c_s^0$ of the zero sound. We find that also $c_s^0$ changes its slope in correspondence of the filling of the harmonic axial modes and that this effect depends on the Fermi-Fermi scattering length $a_F$. In the collisional regime, we calculate the velocity $c_s$ of first sound showing that $c_s$ displays jumps at critical densities fixed by the scattering length $a_F$. Finally, we discuss the experimental achievability of these zero sound and first sound waves with ultracold alkali-metal atoms.

9 pages, 5 figures, editorially approved for publication on Phys. Rev. A

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• Itinerant ferromagnetism of two-dimensional repulsive fermions with Rabi coupling
• Nonequilibrium Kinetics of One-Dimensional Bose Gases
• Application of Madelung Hydrodynamics to Plasmonics and Nonlinear Optics in Two-Dimensional Materials
• Two-dimensional quasi-ideal Fermi gas with Rashba spin-orbit coupling
• Three-component Fermi gas with SU(3) symmetry: BCS-BEC crossover in three and two dimensions
• Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity