Collisional Stability of Double Bose Condensates

Abstract

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 $^{87}R\mathrm{b}$ $|1,\ensuremath{-}1〉$ 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 $(5.45\ifmmode\pm\else\textpm\fi{}0.26\mathrm{nm})$ scattering lengths for two colliding $^{87}R\mathrm{b}$ atoms in their $|1,\ensuremath{-}1〉$ or $|2,2〉$ states.