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

Luca Salasnich, Flavio Toigo

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

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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Sound wave propagation in strongly elongated fermion clouds at finite collisionality

P. Capuzzi, Patrizia Vignolo, F. Federici +1 more

We evaluate the transition from zero-sound to first-sound behaviour with increasing collisionality in the propagation of density waves through an ultracold gaseous mixture of fermionic atoms in the normal state confined inside a cigar-shaped harmonic trap. We study for this purpose the evolution of the one-body distribution functions associated with a density perturbation generated in the central region of the cloud, as obtained by numerical solution of the Vlasov–Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture. The speed of propagation of the density disturbance is found to decrease in both cases as the magnitude of the coupling strength is increased. The results are compared with the values of the speed of zero sound and of first sound, as obtained analytically from the limit of vanishing collisionality and from linearized hydrodynamics. The main effects of the quasi-one-dimensional confinement are the stabilization of zero-sound excitations in the attractive regime before collapse and the lowering of the hydrodynamic sound velocity by a factor relative to three-dimensional behaviour.

arXiv:cond-mat/0511578•Journal of Physics B Atomic Molecular and Optical Physics•May 2, 2006•7 citations
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
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 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.
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.
We theoretically investigate the critical behavior of a second-sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature Tc{T}_{c}Tc​, the frequency or the sound velocity of the second-sound mode crucially depends on the critical exponent $\ensuremath{\beta}$ of the superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like ${(1\ensuremath{-}T/{T}_{c})}^{\ensuremath{\beta}\ensuremath{-}1/2}$ when $\ensuremath{\beta}<1/2$. In a highly elongated trap, the speed of the second sound reduces by a factor of $1/\sqrt{2\ensuremath{\beta}+1}$ from that in a homogeneous three-dimensional superfluid. Our prediction could readily be tested by measurements of second-sound wave propagation in a setup, such as that exploited by Sidorenkov et al. [Nature (London) 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.
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.
This thesis is devoted to the study of the hydrodynamic behavior of the unitary Fermi gas trapped by a highly elongated harmonic potential. Propagation of sound is one of the most exciting features exhibited by interacting many-body systems. It provides crucial information on the dynamic behavior of the system as well as on key thermodynamic quantities. The propagation of sound is particularly interesting in superfluids where two-fluid hydrodynamic theory predicts the occurrence of two different sounds: first sound, where the normal and superfluid component oscillate in phase, and second sound, where the two components oscillate with opposite phase. In the thesis, we investigate the propagation of sound waves of the unitary Fermi gas in a cylindrical geometry by solving the equations of two-fluid hydrodynamics in the `1D' scenario at finite temperature. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both the 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, which is the strategy used in a recent experiment carried out at Innsbruck where second sound was detected in the unitary Fermi gas. We also provide an investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state.
We evaluate the transition from zero-sound to first-sound behaviour with increasing collisionality in the propagation of density waves through an ultracold gaseous mixture of fermionic atoms in the normal state confined inside a cigar-shaped harmonic trap. We study for this purpose the evolution of the one-body distribution functions associated with a density perturbation generated in the central region of the cloud, as obtained by numerical solution of the Vlasov–Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture. The speed of propagation of the density disturbance is found to decrease in both cases as the magnitude of the coupling strength is increased. The results are compared with the values of the speed of zero sound and of first sound, as obtained analytically from the limit of vanishing collisionality and from linearized hydrodynamics. The main effects of the quasi-one-dimensional confinement are the stabilization of zero-sound excitations in the attractive regime before collapse and the lowering of the hydrodynamic sound velocity by a factor relative to three-dimensional behaviour.