Collisional Stability of Double Bose Condensates

This paper presents quantitative calculations of collisional loss rates for pure ${}_{}{}^{23}{}_{}{}^{}N\mathrm{a}$ or ${}_{}{}^{87}{}_{}{}^{}R\mathrm{b}$ atoms in a binary mixture of hyperfine states $|F,M〉$. We find that the recent observation of a dual Bose condensate consisting of ${}_{}{}^{87}{}_{}{}^{}R\mathrm{b}$ $|1,-1〉$ and $|2,2〉$ atoms is unique and will not occur in Na. We attribute this to the unexpectedly small inelastic spin-exchange rate associated with ${}_{}{}^{87}{}_{}{}^{}R\mathrm{b}$ s-wave hyperfine collisions. This fortuitous result arises from nearly equal $(5.45\pm 0.26\mathrm{nm})$ scattering lengths for two colliding ${}_{}{}^{87}{}_{}{}^{}R\mathrm{b}$ atoms in their $|1,-1〉$ or $|2,2〉$ states.