Expansion of an Interacting Fermi Gas

Abstract

We study the expansion of a dilute ultracold sample of fermions initially trapped in a 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, similarly to what happens with Bose-Einstein condensates. Viceversa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.Since the first experiments on trapped Bose-Einstein condensates the imaging of the expanding cloud, following the sudden switching off of the confining potential, has provided crucial information on the novel features exhibited by atomic gases in conditions of quantum degeneracy. These include, in particular, the bimodal structure of an expanding Bose gas at finite temperature and the anisotropy of the asymptotic profile of the condensate [1,2]. In the Thomas-Fermi limit, where the Gross-Pitaevskii equations coincide with the hydrodynamic theory of superfluids, the anisotropy of the expanded gas reflects the anisotropy of the pressure force which is stronger in the direction of tighter confinement [3]. The predictions of the hydrodynamic equations and of the consequent scaling behaviour exhibited by BoseEinstein condensates during the expansion have been investigated by several authors ( [4], [5], [6]), providing excellent agreement with experiments [7,8] and pointing out the difference with respect to the expansion of a non condensed gas. In the latter case, in the collisionless regime, the density profile approaches an isotropic shape, independent of the initial deformation of the gas.In this letter we study the problem of the expansion of an ultracold sample of fermions initially trapped in an anisotropic harmonic trap. We will show that also in the case of fermions the expansion of the gas provides valuable information about the state of the system and the role of interactions. We will consider a gas of atoms interacting with attractive forces. This is a natural requirement for the realization of Cooper-pairs and hence for the achievement of the superfluid phase [9]. Such interactions are naturally present in some fermionc species like 6 Li and can otherwise be obtained by changing the scattering length profiting of the presence of a Feshbach resonance.The description of the expansion of a cold fermionic gas in the normal and superfluid phase requires different theoretical approaches. For the normal phase we use the formalism of the Landau-Vlasov equations, while in the superfluid phase we study the expansion using the hydrodynamic theory of superfluids.We consider the case of two different fermionic states, hereafter called 1 and 2, initially confined in a harmonic trap. We assume that the two species are pres...

Stability and free expansion of a dipolar Fermi gas

“…Within the semi-classical framework, the state of the system is described by the phase space distribution function f (r, v, t) which, in the collisionless regime, satisfies the Boltzman-Vlasov kinetic equation [13] …”

“…This scaling transformation was first introduced to study the free expansion of a Bose-Einstein condensate [14], and the collective oscillations of a classical Bose gas [15]. Recently, it was also generalized to study the free expansion and the collective excitation of both normal and superfluid Fermi gases [13,16]. Following the standard procedure [13,15,16], the Boltzman-Vlasov equation (2) can be reduced to the coupled equations for the scaling parameters b j , which, in dimensionless form [17], reads…”

“…Recently, it was also generalized to study the free expansion and the collective excitation of both normal and superfluid Fermi gases [13,16]. Following the standard procedure [13,15,16], the Boltzman-Vlasov equation (2) can be reduced to the coupled equations for the scaling parameters b j , which, in dimensionless form [17], reads…”

Density-functional theory for fermions close to the unitary regime

“…This makes it possible to study the system as it evolves from a dilute Fermi gas with weak attractive interactions to a bosonic gas of diatomic molecules. This transition from a superfluid BCS state to Bose Einstein condensation (BEC) has been the subject of many experimental [2,3,4,5,6,7,8,9,10,11,12] and theoretical works [13,14,15,16,17,18,19,20,21,22,23].…”

Generalized Gibbs ensembles for time-dependent processes

“…However, many systems studied in physics do not correspond to this mathematical limit of infinite systems [13] and, in fact, finite systems are now, per se, a subject of a very intense research activity, from metallic clusters [3,4] to Bose condensates [5,6], from nanoscopic systems [7] to atomic nuclei [8,9] and elementary particles [10]. The question thus arises: can the equilibrium of a finite systems be defined.…”