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 $\ensuremath{\mu}$ of the fermionic fluid as a function of the uniform planar density $\ensuremath{\rho}$ and find that $\ensuremath{\mu}$ 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.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 $\ensuremath{\mu}$ of the fermionic fluid as a function of the uniform planar density $\ensuremath{\rho}$ and find that $\ensuremath{\mu}$ 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.

arXiv:0901.3438Physical Review AFeb 12, 200912 citations

Sound in a Unitary Fermi Gas

Parth Patel, Biswaroop Mukherjee, Zhenjie Yan +6 more

Bulletin of the American Physical SocietyJun 1, 20180 citations

{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.