Expansion of an Interacting Fermi Gas

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.

Figure 1

Ratio $\chi =E_{\mathrm{i}\mathrm{n}\mathrm{t}}/E_{ho}$ as a function of the universal parameter $a{N}^{1/6}/a_{ho}$ calculated with the mean field functional (9) up to the collapse point $a{N}^{1/6}/a_{ho}=-0.61$ (full line); the dashed line is the linear prediction ([10]).

Figure 2

Aspect ratio as a function of time for the expansion of the normal (lower curves) and superfluid phase (upper curves) for $\lambda =0.1$ and two different values of the parameter $\chi$: $\chi =0$ (full line) and $\chi =-0.4$ (dashed line).

Figure 3

Aspect ratio as a function of time for the expansion of the normal (lower curves) and superfluid phase (upper curves) for $\lambda =0.3$ and different values of the parameters $\chi$: $\chi =0$ (full line) and $\chi =-0.4$ (dashed line).