Elastic and inelastic collisions of6Liatoms in magnetic and optical traps

Abstract

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...

Universality in phase transitions for ultracold fermionic atoms

“…For the broad Feshbach resonance in the 6 Li system the molecule state belongs to a singlet of the electron spin, resulting in µ M ≈ 0. The microscopic value ofμ = ∂ν Λ /∂B obtains its essential contribution from the magnetic moment of the atoms in the open channel, which is well approximated [58] by the Bohr magneton µ B = 5.788 · 10 −11 MeV/T = 0.2963MeV −1 . For 40 K we takeμ = 1.57µ B [59].…”

Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium

“…This has lead to the development of models that require minimal knowledge of the molecular potentials (see, e.g., [33][34][35][36]) at the expense of accuracy and applicability. A powerful, yet computationally light description of the near-threshold molecular spectrum is the ABM [13,14].…”

Collisional relaxation in a fermionic gas

“…In a realistic case, we can consider 10 8 fermions in an isotropic magnetic trap with ω/2π = 100 Hz (T F = 4 µK, r F = 0.17 mm). The density of the fermionic gas is 5 10 12 cm −3 , giving a mean field energy created by the Fermi cloud on P equal to 10 nK [21,22], which is negligible with respect to E F , as assumed in this paper.…”