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 $p$ -wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.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 $p$-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.

arXiv:0906.4403Physical Review AFeb 5, 201073 citations

Zero sound modes of dilute Fermi gases with arbitrary spin

Sungkit Yip, Tin-Lun Ho

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.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.

Physical Review AJun 1, 199949 citations

Damping of Zero Sound in a Fermi Liquid

Boris Luk’yanchuk, D. M. Semiz

Journal of Experimental and Theoretical PhysicsJan 1, 19710 citations

Dispersion of First Sound in a Weakly Interacting Ultracold Fermi Liquid

Thomas Repplinger, Songtao Huang, Yunpeng Ji +2 more

Abstract At low temperature, a normal gas of unpaired spin‐1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length , the sole parameter of the short‐range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, as the uncontrolled error made by the relaxation time approximations increases when the temperature drops below the Fermi temperature. Here, sound waves in the hydrodynamic regime are studied up to second order in the Chapman‐Enskog's expansion. It is found that the frequency of the sound wave is shifted above its linear departure as where and are the speed and wavenumber of the sound wave and the typical collision time scales as . Besides the shear viscosity, the coefficient is described by a single second‐order collision time, which is computed exactly from an analytical solution of the transport equation, resulting in a positive dispersion . The results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second‐order hydrodynamics.Abstract At low temperature, a normal gas of unpaired spin‐1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length , the sole parameter of the short‐range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, as the uncontrolled error made by the relaxation time approximations increases when the temperature drops below the Fermi temperature. Here, sound waves in the hydrodynamic regime are studied up to second order in the Chapman‐Enskog's expansion. It is found that the frequency of the sound wave is shifted above its linear departure as where and are the speed and wavenumber of the sound wave and the typical collision time scales as . Besides the shear viscosity, the coefficient is described by a single second‐order collision time, which is computed exactly from an analytical solution of the transport equation, resulting in a positive dispersion . The results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second‐order hydrodynamics.

arXiv:2409.10099Annalen der PhysikAug 28, 20252 citations

On the hydrodynamic sound in polarized Fermi liquids

Jerzy Czerwonko

Physics Letters AJun 1, 19833 citations

p

-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.

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.