Existence and stability of coupled atomic-molecular Bose-Einstein condensates

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We analyze the model of an atomic Bose-Einstein condensate (BEC) parametrically coupled to a molecular BEC via a photoassociation process. We show that an interplay of nonlinear inter- and intra-species interactions leads to the formation of mutually trapped states of a hybrid condensate, which are spatially localized even without a trap. The untrapped atomic-molecular condensates with a large number of atoms in either fraction are shown to be dynamically stable in the framework of a mean field theory.