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We present a many-body description for two-component ultracold bosonic gaseswhen one of the species is in the weakly interacting regime and the other iseither weakly or strongly interacting. In the one-dimensional limit the lattercase system is a hybrid in which a Tonks-Girardeau gas is immersed in aBose-Einstein condensate, which is an example of a new class of quantum systeminvolving a tunable, superfluid environment. We describe the process of phaseseparation microscopically and semiclassically in both situations and show thatthe quantum correlations are maintained in the separated phase.

Quantum gas mixtures in different correlation regimes