Eur. Phys. J. D 8, 361-369 (2000)

Density profiles and collective excitations of a trapped two-component Fermi vapour

M. Amoruso¹, I. Meccoli², A. Minguzzi¹ and M. P. Tosi^1,3

¹ Istituto Nazionale di Fisica della Materia and Classe di Scienze, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
² Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Università di Parma, Parco Area delle Scienze 7a, 43100 Parma, Italy
³ Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy

Received: 19 August 1999
Revised: 27 September 1999
Published online: 15 March 2000

Abstract

We discuss the ground state and the small-amplitude excitations of a degenerate vapour of fermionic atoms placed in two hyperfine states inside a spherical harmonic trap. An equations-of-motion approach is set up to discuss the hydrodynamic dissipation processes from the interactions between the two components of the fluid beyond mean-field theory and to emphasize analogies with spin dynamics and spin diffusion in a homogeneous Fermi liquid. The conditions for the establishment of a collisional regime via scattering against cold-atom impurities are analyzed. The equilibrium density profiles are then calculated for a two-component vapour of ⁴⁰K atoms: they are little modified by the interactions for presently relevant values of the system parameters, but spatial separation of the two components will spontaneously arise as the number of atoms in the trap is increased. The eigenmodes of collective oscillation in both the total particle number density and the concentration density are evaluated analytically in the special case of a symmetric two-component vapour in the collisional regime. The dispersion relation of the surface modes for the total particle density reduces in this case to that of a one-component Fermi vapour, whereas the frequencies of all other modes are shifted by the interactions.