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Physical Review A

Zero sound modes of dilute Fermi gases with arbitrary spin

Sungkit Yip, Tin-Lun Ho

Published Jun 1, 1999• 49 citations
Publisher

Abstract

Motivated by the recent success of optical trapping of alkali-metal bosons, we have studied the zero sound modes of dilute Fermi gases with arbitrary spin-$f$, which are spin-$S$ excitations $(0<~S<~2f)$. The dispersion of the mode (S) depends on a single Landau parameter ${F}^{(S)}$, which is related to the scattering lengths of the system through a simple formula. Measurement of (even a subset of) these modes in finite magnetic fields will enable one to determine all the interaction parameters of the system.

DOI
10.1103/physreva.59.4653

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Motivated by the recent success of optical trapping of alkali-metal bosons, we have studied the zero sound modes of dilute Fermi gases with arbitrary spin-fff, which are spin-SSS excitations (0< S< 2f)(0<~S<~2f)(0< S< 2f). The dispersion of the mode (S) depends on a single Landau parameter F(S){F}^{(S)}F(S), which is related to the scattering lengths of the system through a simple formula. Measurement of (even a subset of) these modes in finite magnetic fields will enable one to determine all the interaction parameters of the system.
Motivated by the recent success of optical trapping of alkali bosons, we have studied the zeroth sound modes of dilute Fermi gases with arbitrary spin-f, which are spin-S excitations (0≤S≤2f0\leq S\leq 2f0≤S≤2f). The dispersion of the mode (S) depends on a single Landau parameter F(S)F^{(S)}F(S), which is related to the scattering lengths of the system through a simple formula. Measurement of (even a subset of) these modes in finite magnetic fields will enable one to determine all the interaction parameters of the system.
Landau showed that a nonideal Fermi gas at zero temperature can sustain collective oscillations of the acoustical type (zeroth sound). The altenuation of zeroth sound in a dilute Fermi gas with repulive intereacitions was considered. The problem was formulted interms of the Green function G which describes the paropation of density fluctuations through the system. The simplest approximation of G led to Landau's dispersion law which wae analyzed in some detail. The contribution of the phonons' zero point oscillations to the ground- state energy was estimated and found to lead to a term which has an essential singuarty at the origin of the coupling constant plane. The energy and width of the phonon are given by the poles in the spectral representation of G, and the location of these poles was determined from the Fredholm solution of an apparoximate integral equation satisfied by G. In this way it is showa that ths width, divided by the displacement of the collective state above the single- particle continunna of the free gas, vanishes linearly in the long wavelength limit. It is also shows that in the limit of extreme dilution the correct damping; can be obtained by merely taking the finite lifetimemore » of single-particles excitations into account and ignoring the dissipative effects of the noninstantaneous interactions betweein the particles in the medium. Finally, it is alao argued that the Fredholm method is the natural tool for discussing many problems in the theory of collective motion. (auth)« less
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal ppp-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.
We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass ${m}^{*}\ensuremath{\gtrsim}2m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a one-dimensional tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with nonzero F0{F}_{0}F0​ and F1{F}_{1}F1​ Landau parameters.