Scientific Report - BEC

Polarized Fermi gases 201/ω0τP54.543.532.521.510.5T=0.03T FT=000 0.05 0.1 0.15 0.2 0.25 0.3δX/R ↑Figure 2: The quantity 1/ω (s)D τ P determining the dampingof the dipole mode as a function of the amplitude of theoscillation for T =0andT =0.03 T F↑ .approximation. We found that the superfluid core disappears for values of the totalpolarization P =(N ↑ − N ↓ )/(N ↑ − N ↓ ) larger than the critical value P c =0.77, inagreement with the experimental results of the MIT group [2, 3]. Moreover, both thein situ column and density profiles of the two spin components agree very well with theexperimental values (see Fig. 1). It is worth noticing that the proper inclusion of interactioneffects in the normal phase is crucial to correctly describe the superfluid/normalquantum phase transition. The BCS mean-field approach would predict the incorrectvalue P c ≃ 1 for the critical polarization.Collective oscillations and collisional effectsThe functional (2) for the normal phase is particularly well suited to study the highlypolarized limit where the number of particles in the spin-down component is muchsmaller than in the spin-up component (N ↓ ≪ N ↑ ). In this limit the collective oscillationsof a trapped gas can be classified into two cathegories: the in-phase oscillations,where the motion is basically dominated by the majority component, and the out-ofphase(spin) oscillations where the minority component moves in the trap, the majorityone being practically at rest. The spin dipole frequency is given by the simple formula[6]√ (ω (s)D= ω mim ∗ 1+ 3 )5 A (2)