Superfluidity in Sympathetic Cooling with Atomic Bose-Einstein Condensates

The dynamical structure of an atomic Bose-Einstein condensate limits the efficiency of the condensate in cooling slow impurity atoms. To illustrate the point, we show that an impurity atom moving in a homogeneous zero-temperature condensate is not scattered incoherently if its velocity is lower than the condensate sound velocity $c$, limiting cooling to velocities $v\ge c$. This striking effect is an expression of superfluidity and provides a direct means to detect the fundamental property of superfluidity in atomic condensates. Furthermore, we show that the fermionic lithium isotope, ${}^6\mathrm{Li}$, is a reasonable candidate for sympathetic cooling by a ${}^{23}\mathrm{Na}$ condensate.