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arXiv:0901.3438 · Physical Review A

Zero sound and first sound in a disk-shaped normal Fermi gas

G. Mazzarella, Luca Salasnich, Flavio Toigo

Published Feb 12, 2009• 12 citations
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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 $\ensuremath{\mu}$ 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.

DOI
10.1103/physreva.79.023615

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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 \ensuremathμ\ensuremath{\mu}\ensuremathμ of the fermionic fluid as a function of the uniform planar density \ensuremathρ\ensuremath{\rho}\ensuremathρ and find that \ensuremathμ\ensuremath{\mu}\ensuremathμ 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 cs0{c}_{s}^{0}cs0​ of the zero sound. We find that also cs0{c}_{s}^{0}cs0​ changes its slope in correspondence of the filling of the harmonic axial modes and that this effect depends on the Fermi-Fermi scattering length aF{a}_{F}aF​. In the collisional regime, we calculate the velocity cs{c}_{s}cs​ of first sound showing that cs{c}_{s}cs​ displays jumps at critical densities fixed by the scattering length aF{a}_{F}aF​. Finally, we discuss the experimental achievability of these zero sound and first sound waves with ultracold alkali-metal atoms.
Abstract We investigate the first sound of a normal dilute and ultracold twocomponent 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. PACS numbers: 03.75.Ss, 67.40.Mj, 68.65.-k 1
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We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy, and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity, and the second sound velocity. We compare our analytical results with other theoretical predictions and experimental data of ultracold atoms and dilute neutron matter.
We consider a Fermi gas at unitarity trapped by a highly elongated harmonic potential and solve the equations of two fluid hydrodynamics at finite temperature. The propagation of sound waves as well as the discretized solutions in the presence of weak axial trapping are considered. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both first sound and second sound solutions are calculated as a function of temperature and the role of the superfluid density is explicitly pointed out. The density fluctuations in the second sound wave are found to be large enough to be measured as a consequence of the finite thermal expansion coefficient of the gas. Emphasis is given to the comparison with recent experimental data.
We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.