Heating rates in collisionally opaque alkali-metal atom traps: Role of secondary collisions - art. no. 063614

Grazing collisions with background gas are the major cause of trap loss and trap heating in atom traps. To first order, these effects do not depend on the trap density. In collisionally opaque trapped atom clouds, however, sc attered atoms with an energy E larger than the effective trap depth E,lf, w hich are destined to escape from the atom cloud, will have a finite probabi lity for a secondary collision. This results in a contribution to the heati ng rate that depends on the column density [nl] of the trapped atoms, i.e., the product of density and characteristic size of the trap. For alkali-met al atom traps, secondary collisions are quite important due to the strong l ong-range interaction with like atoms. We derive a simple analytical expres sion for the secondary heating rate, showing a dependency proportional to [ nl] epsilon (1/2)(eff). When extrapolating to a vanishing column density, o nly primary collisions with the background gas will contribute to the heati ng rate. This contribution is rather small, due to the weak long-range inte raction of the usual background gas species in an ultrahigh-vacuum system-H e, Ne, or Ar-with the trapped alkali-metal atoms. We conclude that the tran sition between trap-loss collisions and heating collisions is determined by a cutoff energy 200 muK less than or equal to epsilon (eff) less than or e qual to 400 muK, much smaller than the actual trap depth epsilon in most ma gnetic traps. Atoms with an energy epsilon (eff) <E<epsilon escape into the Oort cloud: a mechanism of effective traploss in the microkelvin range of trap temperatures. We present results of secondary heating rates for the al kali-metal atoms Li through Cs as a function of the effective trap depth, t he column density of the trap, and the species in the background gas. The p redictions of our model an in good agreement with the experimental data of Myatt for heating rates in high-density Rb-87-atom magnetic traps at JILA, including the effect of the rf shield and the composition of the background gas. It is shown that collisions with atoms from the Oort cloud also contr ibute to the heating rate. For Rb-85 the calculated heating rate is below t he experimentally observed value at JILA, supporting the idea that inelasti c collisions in the trap are the major source of heating.