Collective oscillations of an interacting trapped Fermi gas

Abstract

We calculate the effects of two-body interactions on the low frequency oscillations of a normal Fermi gas confined in a harmonic trap. The mean field contribution to the collective frequencies is evaluated in the collisionless regime using a sum rule approach. We also discuss the transition between the collisionless and hydrodynamic regime with special emphasis to the spin dipole mode in which two atomic clouds occupying different spin states oscillate in opposite phase. The spin dipole mode is predicted to be overdamped in the hydrodynamic regime. The relaxation time is calculated as a function of temperature and the effects of Fermi statistics are explicitly pointed out.Comment: 4 pages, 1 figure include

Thermodynamics of Ultracold Fermi Gases

“…Closely related problems were studied in previous works, namely the axial breathing mode relaxation of a spin-balanced Fermi gas [241,242,243] and the spin dipole mode of an imbalanced Fermi gas [244]. We adapt here these calculations to the speci c case of the axial breathing mode of a spin-imbalanced Fermi gas.…”

“…In the hydrodynamic regime, out-of-phase oscillations are expected to be over-damped, as shown in [241] on the example of the spin dipole mode. However, the gas dynamics approaches a collisionless behavior at large polarization, and we expect the out-of-phase mode to become observable.…”

“…Within this Fermi liquid picture, the gas is merely a mixture of two Fermi seas with di erent atom numbers. Collective oscillations have already been modeled in this context using Boltzmann equation, but for slightly di erent situations, namely for spin-balanced gases [241,242,243] or for the spin dipole mode in spin-imbalanced Fermi gases [244]. In Appendix C we adapt these calculations to the case relevant to our experiment, the axial breathing mode of a two-component Fermi gas with di erent atom numbers.…”

Collective excitations of degenerate Fermi gases in anisotropic parabolic traps

“…In the high-temperature limit the effects of quantum statistics become irrelevant and one obtains the same results as for Bose gases, which were considered earlier, for isotropic traps, and even for some modes in axially symmetric traps by Griffin et al [14]. Using a sum-rule approach Vichi and Stringari [11] analyzed interaction effects on the collective oscillations of Fermi gases trapped in parabolic potentials of rotational or axial symmetry. Amoruso et al [13] also investigated the collective excitations of trapped degenerate Fermi-gases both in the hydrodynamic and the collisionless regime for isotropic and, for some dipolar and quadrupolar modes, also for axially symmetric parabolic traps.…”

“…In view of these successful experimental and theoretical developments for the Bose-systems, it seems to be of considerable interest to apply similar methods also to degenerate Fermi systems [11,12]. On the one hand these systems seem to be very different from their bosonic counterparts.…”