Low-lying excitation modes of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

Abstract

By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.

Ground state of an ultracold Fermi gas of tilted dipoles in elongated traps

“…Indeed, the quantum-mechanical expectation values of the system observables, which are required for the calculation of the properties of nonrelativistic quantum systems based on exact diagonalization, can be obtained as their phase-space averages, weighted by the Wigner function. In the case where the dipolar orientation axis lies along one of the trapping axes, an accurate ansatz for the Wigner function takes the simple form [38][39][40][41][42][43][44][45][46][47] r R…”

“…This ansatz is motivated by the Fermi-Dirac distribution of a noninteracting Fermi gas at zero temperature, whose Wigner function has the above form. A theory based on the above ansatz [38,47] was successfully used to determine the deformation of the FS, while its extension [46] enabled a detailed analysis of the ground state and the time-offlight (TOF) expansion dynamics of the system for different collisional regimes. Furthermore, numerical comparisons [59,60] have confirmed that, even in the case of polar molecules with masses of the order of 100 atomic units and an electric dipole moment as large as 1D, the above variational ansatz yields highly accurate results, within a fraction of per mille.…”

“…Theoretical predictions which take the DDI into account, however, have shown that the antisymmetry of the wave function leads to the deformation of the FS into an ellipsoid [38]. The ground-state [39,40] and the dynamic properties of such systems have been systematically investigated theoretically and numerically in the collisionless regime [41][42][43], in the hydrodynamic regime [44,45], as well as in the whole collisional range from one limiting case to the other [46,47]. The FS deformation was also recently theoretically studied in mixtures of dipolar and non-dipolar fermions [48], as well as in the presence of a weak lattice confinement [49].…”

“…The Hartree-Fock mean-field approximation, which includes energy terms up to first-order in the DDI, is sufficiently accurate to qualitatively explain and quantitatively describe results of ongoing experiments. However, up to now, existing theories are limited to a fixed orientation of the dipoles, which has to coincide with one of the trap axes [38,46,47,50]. Such a restriction greatly simplified theoretical considerations, but, on the other hand, limited their scope since the anisotropy of the DDI is best controlled by the dipoles' orientation with respect to the trap axes.…”

Second-order interaction corrections to the Fermi surface and the quasiparticle properties of dipolar fermions in three dimensions

“…In contrast, for a rapidly rotating 2D system of dipolar fermions the Wigner crystal phase is possibly the ground state for low densities, while for higher densities it turns into a Laughlin liquid state [43,44]. Further studies focused on finite-temperature effects [27,[45][46][47][48], dynamical properties in the collisionless and hydrodynamic regimes [49][50][51][52][53][54][55], bilayer configurations [56][57][58][59], and quench dynamics [60]. However, less attention has been paid to the quasiparticle properties in the Fermi liquid phase beyond the mean-field level.…”