Sound wave propagation in strongly elongated fermion clouds at finite collisionality

Abstract

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 confined in the normal state 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 solving numerically the Vlasov-Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture, and 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 3/5 relative to threedimensional behaviour.Submitted to: J. Phys. B: At. Mol. Phys.

Zero and First Sound in Normal Fermi Systems

“…studied collective modes in trapped gases extensively and intensively [17,18,19]. Tosi's group studied collective modes by solving the Boltzmann equation numerically [20,21,22,23]. They studied the dipole mode of two component trapped gases as a function of a collision rate in some situations [20,21], and the crossover between zero and first sound modes in the cigar-shaped trap [22,23].…”

Bernstein–Greene–Kruskal and Case–Van Kampen Modes for the Landau–Vlasov Equation

“…The last step is the determination of the normalization constant A, once a specific external potential is chosen. For the harmonic potential (5), it is convenient to introduce the rescaling…”

“…The Landau-Vlasov equation is obtained from the Boltzmann-Vlasov equation [1][2][3][4] neglecting the collision operator. The dynamics of ultracold bosonic systems, e.g., in the crossover from collisionless to collisional regimes needs the Boltzmann-Vlasov equation [5]. Hydrodynamic equations [6,7] are useful tools in the collisional case, for instance, for Bose-Einstein condensates [6] or the superfluid Fermi gas in the BCS-BEC crossover [8].…”

Fermi-liquid theory of ultracold trapped Fermi gases: Implications for pseudogap physics and other strongly correlated phases

“…While it is relatively straightforward to use more sophisticated approaches [13], in order to focus on the central physics, we apply Hartree-Fock theory [11,21]. Here Σ σ = gn σ, where g = 4π 2 a/m, σ = −σ, and a is the two-body s-wave scattering length.…”