Phase separation in a two-species atomic Bose-Einstein condensate with an interspecies Feshbach resonance

We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.