Shell Effects in the First Sound Velocity of an Ultracold Fermi Gas

We investigate the first sound of a normal dilute and ultracold two-component Fermi gas in a harmonic microtube, i.e. a cylinder with harmonic transverse radial confinement in the length-scale of microns. We show that the velocity of the sound that propagates along the axial direction strongly depends on the dimensionality of the system. In particular, we predict that the first-sound velocity display shell effects: by increasing the density, that is by inducing the crossover from one-dimension to three-dimensions, the first-sound velocity shows jumps in correspondence with the filling of harmonic modes. The experimental achievability of these effects is discussed by considering 40 K atoms.