Dipolar decay in two recent Bose-Einstein condensation experiments.

Abstract

After the recent breakthrough to Bose-Einstein condensation ~BEC! in dilute ultracold atomic gases of Li, Na, and Rb @1–3#, it has become a priority to try to understand the finite lifetime of the trapped gas sample, in particular below the transition temperature. Since the mechanism of the decay is not yet completely clarified, it is useful to consider the theoretical predictions for the various possible partial decayrate constants. In this paper we present the decay-rate constants for the dipolar decay of the hyperfine states involved. For the case of Li that result has been given in a previous paper @4#. The dipolar decay-rate constants for Na and Rb will be considered here. In Fig. 1 we show the groundstate hyperfine structure for Na, Rb, and Rb as a function of magnetic field. In the following we refer to each of the hyperfine states in terms of the ~lower-case! single-atom quantum numbers f ,mf , although f is a good quantum number only for B50. Capital quantum numbers F ,MF are reserved for two-atom states involved in collisions. Instead of the doubly polarized f ,mf52,12 state in Na that we studied previously @4#, we will concentrate here on the 1,21 state for which BEC was realized experimentally @3#. As Fig. 1 shows, special significance has to be attributed to the field range up to 316 G in which the 1,21 state can be trapped in a static magnetic trap as a low-field seeking state. Also in the case of Rb we will concentrate on the dipolar decay of the state involved in the recent BEC experiment @1#, the doubly polarized 2,12 state. For completeness we will give the analogous result also for the isotope Rb. The method used has been sketched in Ref. @5#. Decay channels considered are all exothermal two-body decay channels not forbidden by selection rules, i.e., all are available combinations of lowerenergy f 1mf 1, f 2mf 2 combinations with MF5mf 11mf 2 at