We report the attainment of simultaneous quantum degeneracy in a mixed gas of bosons (lithium-7) and fermions (lithium-6). The Fermi gas has been cooled to a temperature of 0.25 times the Fermi temperature by thermal collisions with the evaporatively cooled bosons. At this temperature, the spatial size of the gas is strongly affected by the Fermi pressure resulting from the Pauli exclusion principle and gives clear experimental evidence for quantum degeneracy.

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...

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The triplet s-wave scattering length of 6 Li is determined using two-photon photoassociative spectroscopy of the diatomic a 3 ⌺ u ϩ state of 6 Li 2 . The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be ͑Ϫ2160Ϯ250)a 0 , where a 0 is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving 6 Li and 7 Li determined from this and our previous spectroscopic investigations is given.