We study the prospects for observing superfluidity in a spin-polarized atomic gas of 6 Li atoms, using state-of-the-art interatomic potentials. We determine the spinodal line and show that a BCS transition to the superfluid state can indeed occur in the (meta)stable region of the phase diagram if the densities are sufficiently low. We also discuss the stability of the gas due to exchange and dipolar relaxation and conclude that the prospects for observing superfluidity in a magnetically trapped atomic 6 Li gas are particularly promising for magnetic bias fields larger than 10 T. PACS numbers: 03.75.Fi, 32.80.Pj, 42.50.Vk Ultracold atomic gases have received much attention in recent years, because of their novel properties. For instance, these gases are well suited for high-precision measurements of single-atom properties and for the observation of collisional and optical phenomena that reflect the (Bose or Fermi) statistics of the constituent particles. Moreover, a large variety of experimental techniques are available to manipulate the atomic gas samples by means of electromagnetic fields, which offers the exciting possibility to achieve the required conditions for quantum degeneracy and to study macroscopic quantum effects in their purest form.At present, most experimental attempts towards quantum degeneracy have been performed with bosonic gases and have been aimed at the achievement of Bose-Einstein condensation. In particular, most of the earlier experiments used atomic hydrogen [1,2]. These experiments provided crucial ingredients for the recent attempts with alkali vapors, for which the experimental advances towards the degeneracy regime were so rapid that Bose-Einstein condensation has actually been reported now for the isotopes 87 Rb [3] and 7 Li [4].In view of these exciting developments it seems timely to investigate theoretically also the properties of spinpolarized atomic 6 Li, since 6 Li is a stable fermionic isotope of lithium that can be trapped and cooled in much the same way as its bosonic counterpart. Therefore, magnetically trapped 6 Li promises to be an ideal system to study degeneracy effects in a weakly interacting Fermi gas, thus providing valuable complementary information on the workings of quantum mechanics at the macroscopic level. Moreover, using a combination of theoretical analysis and experimental results [5][6][7], accurate knowledge of the interparticle (singlet and triplet) potential curves of lithium have recently been obtained, which lead to the prediction of a large and negative s-wave scattering length a of 24.6 3 10 3 a 0 (a 0 is the Bohr radius) for a spin-polarized 6 Li gas. This is important for two reasons: First, the fact that the scattering length is negative implies that at the low temperatures of interest [L ¿ r V , where L ͑2ph 2 ͞mk B T͒ 1͞2 is the thermal de Broglie wavelength of the atoms and r V is the range of the interaction] the effective interaction between the lithium atoms is attractive, and we expect a BCS-like phase transition to a superfluid state ...

We report on a study of the superfluid state of spin-polarized atomic 6 Li confined in a magnetic trap. Density profiles of this degenerate Fermi gas and the spatial distribution of the BCS order parameter are calculated in the local-density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore, we consider the mechanical stability of an interacting twocomponent Fermi gas, in the case of both attractive and repulsive interatomic interactions. For spin-polarized 6 Li we also calculate the decay rate of the gas and show that within the mechanically stable regime of phase space, the lifetime is long enough to perform experiments on the gas below and above the critical temperature if a bias magnetic field of about 5 T is applied. Moreover, we propose that a measurement of the decay rate of the system might signal the presence of the superfluid state.

We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold 6 Li. The magnetic-field dependence of the s-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at Bϭ0.08 T and Bϭ1.98 T. We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation. ͓S1050-2947͑98͒50703-2͔PACS number͑s͒: 32.80. Pj, 03.75.Fi, 67.40.Ϫw, 42.50.Vk The observation of Bose-Einstein condensation in atomic alkali-metal gases ͓1-3͔ has triggered an enormous interest in degenerate atomic gases. At present, one of the most important goals is to achieve quantum degeneracy in a fermionic gas. In the case of fermionic 6 Li, it has been shown theoretically that a BCS transition to a superfluid state could be realized at a critical temperature on the order of temperatures obtained in the BEC experiments ͓4͔. This relatively high critical temperature is due to the fact that 6 Li has a very large and negative triplet s-wave scattering length a T ϭϪ2160a 0 ͓5͔, where a 0 is the Bohr radius, and that at sufficiently large magnetic fields a mixture of the upper two hyperfine states ͉6͘ and ͉5͘ is essentially electron-spin polarized ͓6͔.The disadvantage of such a large triplet s-wave scattering length is that the exchange and dipolar relaxation rates for the gas are also anomalously large. Nevertheless, to suppress this decay, one can apply a magnetic bias field. In Ref. ͓4͔, we used the distorted-wave Born approximation ͑DWBA͒ to calculate the corresponding decay rate constants for these decay processes and found that, at large magnetic fields B Ͼ10 T, the dipolar rates are dominant, but at smaller magnetic fields, the exchange rates greatly exceed those due to the dipolar interaction. However, the DWBA is only valid at magnetic fields BϾ0.1 T, and we were at that time unable to make predictions at lower, experimentally more convenient fields.The aim of the present paper is to provide useful information on the s-wave scattering length and exchange decay rate constants at lower magnetic fields. In view of the ongoing experiments, we will concentrate on collisions involving the following antisymmetrized hyperfine states: ͉͕65͖͘, ͉͕64͖͘, ͉͕54͖͘, and ͉͕21͖͘. The first three mixtures contain states that are low-field seeking at sufficiently high field, and therefore can be confined in a magnetic trap. In contrast, the combination ͉͕21͖͘ cannot be magnetically trapped, but can be confined in a far-off-resonance optical trap. We do not consider any other combination of high-field-seeking states, since the ͉͕21͖͘ mixture cannot decay through collisions and is therefore most favorable experimentally. In addition, van Abeelen et al. ͓7͔ have already considered the ͉͕62͖͘ combination, which is low-field seeking at very weak magnetic fields B р26ϫ10 Ϫ4 T, but does not have as large an s-wave scatt...

We study the stability of a Bose condensate of atomic 7 Li in a ͑harmonic oscillator͒ magnetic trap at nonzero temperatures. In analogy to the stability criterion for a neutron star, we conjecture that the gas becomes unstable if the free energy as a function of the central density of the cloud has a local extremum which conserves the number of particles. Moreover, we show that the number of condensate particles at the point of instability decreases with increasing temperature, and that for the temperature interval considered, the normal part of the gas is stable against density fluctuations at this point. ͓S1050-2947͑96͒07312-X͔

We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose-Einstein condensate at frequencies which are much larger than those predicted by the mean-field theory. ͓S1050-2947͑97͒00509-X͔