Dynamical Instabilities in a two-component Bose condensate in a 1d optical lattice

In this paper we carry out a stability analysis of the Bloch states of a two-component Bose-Einstein condensate confined to a 1d optical lattice. We consider two concrete systems: a mixture of two hyperfine states of Rubidium-87 and a mixture of Sodium-23 and Rubidium-87. The former is seen to exhibit similar phenomena to a single component condensate while the latter also suffers an instability to phase separation at small Bloch wave vectors. It is shown that sufficiently deep optical lattices can remove this latter instability, potentially allowing imiscible cold atoms species to be held in intimate contact and transported within an experimental system.