Collective excitations in confined Fermi gases

The techniques which have led to the achievement of Bose-Einstein condensat ion in atomic vapours are being used to trap and cool dilute gases of fermi onic alkali atoms, with the ultimate aim of realizing new superfluid system s, We present a short review of progress in evaluating collective excitatio ns of small amplitude in degenerate Fermi gases under harmonic confinement, both in the normal and in the superfluid state. After recalling the role o f collisions and the consequences of the superfluid phase transition in the collective dynamics of homogeneous Fermi fluids, we discuss: (i) one- and two-component normal Fermi gases under confinement in collisional and colli sionless regimes; (ii) the analogue of the Anderson-Bogolubov phonon in a t rapped Fermi superfluid; and (iii) the scissors mode of a confined two-comp onent Fermi gas as a marker of the superfluid phase transition. Some exact results for ground-state properties of a Fermi gas under spherical harmonic confinement are reported in the appendix. (C) 2001 Elsevier Science B.V. A ll rights reserved.